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Development of Some Novel
Spatial-Domain and Transform-
Domain Digital Image Filters
A thesis submitted in fulfillment of the
requirements for the degree of Doctor of Philosophy
by
NILAMANI BHOI
Department of Electronics and Communication Engineering
National Institute of Technology Rourkela INDIA
January 2009
hellip dedicated to my loving parents
CERTFICATE
This is to certify that the thesis titled ldquoDDeevveellooppmmeenntt ooff SSoommee
NNoovveell SSppaattiiaall--DDoommaaiinn aanndd TTrraannssffoorrmm--DDoommaaiinn DDiiggiittaall IImmaaggee
FFiilltteerrssrdquo submitted to the National Institute of Technology Rourkela
(INDIA) by Nilamani Bhoi Roll No 50607001 for the award of the
degree of DDooccttoorr ooff PPhhiilloossoopphhyy iinn EElleeccttrroonniiccss aanndd CCoommmmuunniiccaattiioonn
EEnnggiinneeeerriinngg is a bona fide record of research work carried out by him
under my supervision and guidance
The candidate has fulfilled all the requirements
The thesis which is based on candidatersquos own work has not been
submitted elsewhere for a degreediploma
In my opinion the thesis is of standard required of a PhD degree in
Engineering
To the best of my knowledge Mr Bhoi bears a good moral
character and decent behavior
Dr Sukadev Meher
Asst Professor
Department of Electronics ampCommunication Engineering
National Institute of Technology
Rourkela-769008 (INDIA)
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters
i
PREFACE
Digital Image Processing developed during last three decades has become a
very important subject in electronics and computer engineering Image restoration is
one of the many areas it encompasses Image deblurring and image denoising are the
two sub-areas of image restoration
When an image gets corrupted with noise during the processes of acquisition
transmission storage and retrieval it becomes necessary to suppress the noise quite
effectively without distorting the edges and the fine details in the image so that the
filtered image becomes more useful for display andor further processing
Two spatial-domain and three transform-domain digital image filters are
proposed in this doctoral thesis for efficient suppression of additive white Gaussian
noise (AWGN) The filters are tested on low moderate and high noise conditions and
they are compared with existing filters in terms of objective and subjective evaluation
Under low noise conditions though many filters are very good in terms of objective
evaluations the resulting output images of almost all filters give nearly equal visual
quality Hence efforts are made here to develop efficient filters for suppression of
AWGN under moderate and high noise conditions The execution time is taken into
account while developing filters for online and real-time applications such as
television photo-phone etc
Therefore the present research work may be treated as
(i) developmental work and
(ii) applied research work
I would be happy to see other researchers using the results reported in the thesis
for developing better image filters Moreover I will be contended to find these filters
implemented for practical applications in near future
Nilamani Bhoi
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters
ii
ACKNOWLEDGEMENT
I express my indebtedness and gratefulness to my teacher and supervisor
Prof Sukadev Meher for his continuous encouragement and guidance I needed his
support guidance and encouragement throughout the research period I am obliged to
him for his moral support through all the stages during this doctoral research work I
am indebted to him for the valuable time he has spared for me during this work
I am thankful to Prof S K Patra Head Department of Electronics amp
Communication Engineering who provided all the official facilities to me I am also
thankful to other DSC members Prof G Panda and Prof B Majhi for their
continuous support during the doctoral research work
I would like to thank all my colleagues and friends MR Meher R Kulkarni
CS Rawat and Ratnakar Yadav for their company and cooperation during this
period
I take this opportunity to express my regards and obligation to my parents
whose support and encouragement I can never forget in my life
I would like to thank my wife Sima and son Pratik for their patience and
cooperation I canrsquot forget their help who have managed themselves during the tenure
of my Ph D work I duly acknowledge the constant moral support they provided
throughout
Lastly I am thankful to all those who have supported me directly or indirectly
during the doctoral research work
Nilamani Bhoi
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters
iii
BIO-DATA OF THE CANDIDATE
Name of the candidate Nilamani Bhoi
Fatherrsquos Name Premaraj Bhoi
Present Address PhD Scholar
Dept of Electronics and
Communication Engg
National Institute of
Technology Rourkela-769008
Permanent Address AT-Budhikhamar
PO-Kalamati
Dist-Sambalpur-768111
ACADEMIC QUALIFICATION
(i) B E in Electrical Engineering University College of Engg Burla
Sambalur University BURLA Orissa INDIA
(ii) M E in Electronic Systems amp Tele-Communication Engineering
Jadavpur University Kolkata WestBengal INDIA
PUBLICATION
(i) Published 01 paper in International Journals
(ii) Communicated 02 papers to International Journals
(iii) Published 08 papers in National and International Conferences
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filter iv
CONTENTS Page No
Certificate
Preface i
Acknowledgement ii
Bio-data of the Candidate iii
Contents iv
Abstract
vi
List of Abbreviations used x
List of Symbols used
xii
1 INTRODUCTION 1 Preview
11 Fundamentals of Digital Image Processing 3 12 Noise in Digital Images 8
13 Literature Review 12 14 Problem Statement 18
15 Image Metrics 19
16 Chapter-wise Organization of the Thesis 23 17 Conclusion 24
2 Study of Image Denoising Filters 25
Preview
21 Order Statistics Filter 27
22 Wiener and Lee Filter 29
23 Anisotropic Diffusion (AD) and Total Variation (TV)
Filters
32
24 Bilateral Filter 36
25 Non-local Means (NL-Means) Filter 38
26 Wavelet Domain Filters 42
27 Simulation Results 52
28 Conclusion 79
CONTENTS
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters
v
3 Development of Novel Spatial-Domain Image Filters 81
Preview
31 Development of Adaptive Window Wiener Filter 84
32 Development of Circular Spatial Filter 89
33 Simulation Results 95
34 Conclusion 122
4 Development of Transform-Domain Filters 124
Preview
41 Development of Gaussian Shrinkage based DCT-domain Filter
127
42 Development of Total Variation based DWT-domain Filter 133
43 Development of Region Merging based DWT-domain
Filter
137
44 Simulation Results 140
45 Conclusion 167
5 Development of Some Color Image Denoising Filters 168
Preview
51 Multi-Channel Color Image Filtering 171
52 Multi-Channel Mean Filter 177
53 Multi-Channel LAWML Filter 179
54 Development of Multi-Channel Circular Spatial Filter 181
55 Development of Multi-Channel Region Merging based
DWT-domain Filter
183
56 Simulation Results 185
57 Conclusion 209
6 Conclusion 211
Preview
61 Comparative Analysis 213
62 Conclusion 221
63 Scope for Future Work 222
References 223
Contribution by the Candidate 237
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filter vi
Abstract
Some spatial-domain and transform-domain digital image filtering algorithms
have been developed in this thesis to suppress additive white Gaussian noise
(AWGN)
In many occasions noise in digital images is found to be additive in nature
with uniform power in the whole bandwidth and with Gaussian probability
distribution Such a noise is referred to as Additive White Gaussian Noise (AWGN)
It is difficult to suppress AWGN since it corrupts almost all pixels in an image The
arithmetic mean filter commonly known as Mean filter can be employed to suppress
AWGN but it introduces a blurring effect Image denoising is usually required to be
performed before display or further processing like segmentation feature extraction
object recognition texture analysis etc The purpose of denoising is to suppress the
noise quite efficiently while retaining the edges and other detailed features as much as
possible
In literature many efficient digital image filters are found that perform well
under low noise conditions But their performance is not so good under moderate and
high noise conditions Thus it is felt that there is sufficient scope to investigate and
develop quite efficient but simple algorithms to suppress moderate and high power
noise in an image
The filter-performances are usually compared in terms of peak-signal-to-noise
ratio (PSNR) mean squared error (MSE) and mean absolute error (MAE) These are
simply mathematically defined image metrics that take care of noise power level in
the whole image Large values of PSNR and small values of MSE indicate less noise
power in an image irrespective of the degradations undergone So the quality of an
image obtained from a filter can not be judged properly with these objective
evaluation image metrics (PSNR MSE MAE) Recently an image metric known as
universal quality index (UQI) is proposed in the literature that takes care of human
visual system (HVS) A higher value of UQI usually guarantees better subjective
evaluation automatically even if it is an objective evaluation measure So the filter
performance should be compared in terms of UQI values as well Further the image
Abstract
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters
vii
denoising filters also degrade an original (noise-free) image This degradation is
termed as method noise In many applications the images are corrupted with very low
power AWGN Under such circumstances the method noise should also be evaluated
and considered while developing good filters The method noise is described as an
error voltage level in terms of its mean absolute value when the input to the filter is
noise-free In addition the execution time taken by a filter should be low for online
and real-time image processing applications
The present doctoral research work is focused on developing quite efficient
image denoising filters in spatial-domain and transform-domain to suppress AWGN
quite effectively without yielding much distortion and blurring The performances of
the developed filters are compared with the existing filters in terms of peak-signal-to-
noise ratio root-mean-squared error universal quality index method noise and
execution time
The approaches adopted and the novel filters designed are summarized here
(A) Spatial-Domain Filters Two novel spatial-domain image denoising filters
(i) Adaptive Window Wiener Filter (AWWF) and (ii) Circular Spatial Filter (CSF) are
developed
(i) Adaptive Window Wiener Filter (AWWF) The adaptive window Wiener filter
(AWWF) suppresses Gaussian noise under low and moderate noise conditions very
efficiently The work begins by using a mean filter on a noisy image to get the blurred
version of the image Using an edge detection algorithm the edges of the resulted
blurred image are found out Many edge detection algorithms are available in the
literature The Wiener filter of variable size is applied throughout the noisy image to
suppress the noise The window size is made bigger in homogenous and smooth
regions and is made smaller in edge and complex regions
(ii) Circular Spatial Filter (CSF) A novel circular spatial filter (CSF) is proposed
for suppressing additive white Gaussian noise (AWGN) In this method a circular
spatial-domain window whose weights are derived from two independent functions
(i) spatial distance and (ii) gray level distance is employed for filtering The proposed
filter is different from Bilateral filter and performs well under moderate and high
Abstract
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters
viii
noise conditions The filter is also capable of retaining the edges and intricate details
of the image
(B) Transform-Domain Filters Three novel transform-domain filters (i)
Gaussian Shrinkage based DCT-domain Filter (GS-DCT) (ii) Total Variation based
DWT-domain Filter (TV-DWT) (iii) Region Merging based DWT-domain filter(RM-
DWT) are developed to suppress the Gaussian noise effectively
(i) Gaussian Shrinkage based DCT-domain Filter (GS-DWT) The proposed filter
presents a simple image denoising scheme by using an adaptive Gaussian smoothing
based thresholding in the discrete cosine transform (DCT) domain The edge pixel
density on the current sliding window decides the threshold level in the DCT domain
for removing the high frequency components eg noise Since the hard threshold
approach is discontinuous in nature and it tends to yield artifacts (like Gibbs
phenomenon) in the recovered image a method of associating Gaussian weights to
DCT coefficients is proposed This reduces artifacts and yields better PSNR values
(ii) Total Variation based DWT-domain Filter (TV-DWT) In the proposed filter
the total variation (TV) algorithm is applied on a noisy image decomposed in wavelet
domain for suppression of Gaussian noise After the decomposition process four
different energy bands low-low (LL) low-high (LH) high-low (HL) and high-high
(HH) are found The LL subband of a single decomposed noisy image is used to find
the horizontal vertical and diagonal edges Using the pixel position of horizontal
edges the corresponding wavelet coefficients in HL subband is retained thresholding
others to zero Adopting the same procedure the vertical and diagonal details of LH
and HH subbands are retained The method TV is applied to LL subband for one
iteration only Applying inverse wavelet transform on modified wavelet coefficients
we get back the image with little noise This small amount of noise can further be
suppressed using the TV algorithm for one iteration once again in the spatial-domain
(iii) Region Merging based DWT-domain Filter (RM-DWT) The proposed region
merging based DWT-domain (RM-DWT) filter introduces an image denoising
scheme with region merging approach in wavelet-domain In the proposed method
Abstract
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters
ix
the wavelet transform is applied on the noisy image to yield the wavelet coefficients
in different subbands A region including the denoising point in the particular subband
is partitioned in order to get distinct sub-regions The signal-variance in a sub-region
is estimated by using maximum likelihood (ML) estimation It distinguishes a sub-
region with some non-zero ac signal power from a sub-region containing no ac signal
power The sub-regions containing some appreciable ac signal power are merged
together to get a large homogenous region However if the sub-region including
denoising point has no ac signal power this sub-region can be merged with other
likelihood sub-regions with zero ac signal power to get a homogenous region Now in
a large homogenous region in wavelet domain the signal variance is estimated with
better accuracy Using the estimated signal variance the wavelet coefficients of
original (noise-free) decomposed image in wavelet domain are estimated using the
minimum mean squared error (MMSE) estimator
Since the Circular Spatial Filter and Region Merging based DWT-Domain
Filter give very good performance in denoising gray-scale images two multi-channel
filters Multi-channel Circular Spatial Filter (MCSF) and Multi-channel Region
Merging based DWT-Domain Filter (MRM-DWT) are developed for suppression of
AWGN from color images The developed filters MCSF and MRM-DWT are based
on three-channel-processing (RGB- processing) and hence are necessarily 3-Channel
CSF and 3-Channel RM-DWT respectively
The AWWF perform well under moderate noise conditions The developed
circular spatial filter (CSF) suppresses AWGN efficiently under moderate and high
noise conditions The GS-DCT filter suppresses additive noise in DCT-domain and
works well when the noise power is moderate The developed filter TV-DWT takes
less execution time as compared to other filters When the noise power is low the
proposed wavelet-domain filter RM-DWT suppress additive noise effectively
Among all developed filters and existing filters CSF is found to be best for
suppressing AWGN
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filter x
List of Abbreviations used
Abbreviations
1 AWGN Additive White Gaussian Noise
2 SPN Salt and Pepper Noise
3 RVIN Random Valued Impulse Noise
4 SN Speckle Noise
5 DCT Discrete Cosine Transform
6 CWT Continuous Wavelet Transform
7 DWT Discrete Wavelet Transform
8 LL Low-Low
9 LH Low-High
10 HL High-Low
11 HH High-High
12 PEP Percentage of Edge Pixels
13 ML Maximum Likelihood
14 SURE Steinrsquos Unbiased Risk Estimate
15 DS Directional Smoothing
16 MED Median
17 MSE Mean Squared Error
18 MAE Mean Absolute Error
19 RMSE Root Mean Squared Error
20 MMSE Minimum Mean Squared Error
21 PSNR Peak Signal to Noise Ratio
List of Abbreviations used
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters
xi
22 CPSNR Color Peak Signal to Noise Ratio
23 UQI Universal Quality Index
24 HVS
Human Visual System
SOME IMPORTANT FILTERS AVAILABLE IN LITERATURE
25 MF Mean Filter
26 ATM Alpha Trimmed Mean
27 AD Anisotropic Diffusion
28 TV Total Variation
29 NL-Means Non-local Means
30 LAWML Locally Adaptive Window based Maximum Likelihood
31 M-MF Multi-Channel Mean Filter
32 M-LAWML Multi-Channel Locally Adaptive Window based
Maximum Likelihood
DEVELOPED FILTERS
33 AWWF Adaptive Window Wiener Filter
34 CSF Circular Spatial Filter
35 GS-DCT Gaussian Shrinkage based DCT
36 TV-DWT Total Variation based DWT
37 RM-DWT Region Merging based DWT
38 MCSF Multi-Channel Circular Spatial Filter
39 MRM-DWT Multi-Channel Region Merging based DWT
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filter xii
List of Symbols used
Symbols
1 f(xy) Original (noise-free) Digital Image
with discrete spatial coordinates (xy)
2 η Random Variable Noise
3 fAWGN g Noisy Image Corrupted with AWGN
4 fSPN Image corrupted with Salt and Pepper Noise
5 fRVIN Image corrupted with Random-Valued Impulse Noise
6 ˆ ( )f x y Filtered Output Image
7 TE Execution Time
8 MN Method Noise
9 2
nσ Noise Variance
10 dg Gray-level Distance
11 ds Spatial Distance
12 cp Center Pixel its gray-scale value
13 wg Gray-level Kernel
14 wd Distance Kernel
15 L Total Number of Pixels in a Window
16 TU Universal Threshold
17 TSURE Threshold of SureShrink
18 TB Threshold of BayesShrink
19 TOS Threshold of OracleShrink
20 TOT Threshold of OracleThresh
21 ( )hTξ sdot Soft Thresholding Operation
List of Symbols used
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters
xiii
22 ( )hT
ζ sdot Hard Thresholding Operation
23 F Original Decomposed Image in Wavelet-Domain
24 Y Noisy Decomposed Image in Wavelet-Domain
25 F Estimated (Filtered) Image Decomposed in Wavelet-Domain
26 Γ Shrinkage function for NeighShrink
27 N Neighborhood in Wavelet-Domain
28 C Color Space
Chapter 1
Introduction
Chapter-1 Introduction
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 2
Preview
Image processing has got wide varieties of applications in computer vision
multimedia communication television broadcasting etc that demand very good
quality of images The quality of an image degrades due to introduction of additive
white Gaussian noise (AWGN) during acquisition transmission reception and
storage retrieval processes It is very much essential to suppress the noise in an image
and to preserve the edges and fine details as far as possible In the present research
work efforts are made to develop efficient spatial-domain and transform-domain
image filters that suppress noise quite effectively
The following topics are covered in this chapter
Fundamentals of Digital Image Processing
Noise in Digital Images
Literature Review
Problem Statement
Image Metrics
Chapter-wise Organization of the Thesis
Conclusion
1
Chapter-1 Introduction
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 3
11 Fundamentals of Digital Image Processing
Digital Image Processing usually refers to the processing of a 2-dimensional
(2-D) picture signal by a digital hardware The 2-D image signal might be a
photographic image text image graphic image (including synthetic image)
biomedical image (X-ray ultrasound etc) satellite image etc In a broader context it
implies processing of any 2-D signal using a dedicated hardware eg an application
specific integrated circuit (ASIC) or using a general-purpose computer implementing
some algorithms developed for the purpose
An image is a 2-D function (signal) ( )f x y where x and y are the spatial
(plane) coordinates The magnitude of f at any pair of coordinates (xy) is the
intensity or gray level of the image at that point In a digital image xy and the
magnitude of f are all finite and discrete quantities Each element of this matrix (2-D
array) is called a picture element or pixel Image processing refers to some algorithms
for processing a 2-D image signal ie to operate on the pixels directly (spatial-
domain processing) or indirectly (transform-domain processing) Such a processing
may yield another image or some attributes of the input image at the output
It is a hard task to distinguish between the domains of image processing and
any other related areas such as computer vision Though essentially not correct
image processing may be defined as a process where both input and output are
images At the high level of processing and after some preliminary processing it is
very common to perform some analysis judgment or decision making or perform
some mechanical operation (robot motion) These areas are the domains of artificial
intelligence (AI) computer vision robotics etc
Digital image processing has a broad spectrum of applications such as digital
television photo-phone remote sensing image transmission and storage for business
applications medical processing radar sonar and acoustic image processing
Chapter-1 Introduction
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 4
robotics and computer aided manufacturing (CAM) and automated quality control in
industries Fig 11 depicts a typical image processing system [12]
Most of the image-processing functions are implemented in software A
significant amount of basic image processing software is obtained commercially
Major areas of image processing are [126]
(i) Image Representation
(ii) Image Transformation
(iii) Image Enhancement
(iv) Image Restoration
(v) Color Image Processing
(vi) Transform-domain Processing
(vii) Image Compression
(viii) Morphological Image Processing
(ix) Image Representation and Description
(x) Object Recognition
Image processing begins with an image acquisition process Fig 12 illustrates
such a process When illumination energy is incident upon an object it reflects some
part of it depending on its surface-reflectance Thus the image created f(xy) is a 2-D
planar projection of a 3-D object in general and os directly proportional to the
illumination energy i(xy) incident on the object and the reflectance r(xy) of the
object Mathematically it may be expressed as
( ) ( ) ( )f x y K i x y r x y= (11)
where 0 ( )i x ylt lt infin (12)
0 ( ) 1r x ylt lt (13)
and K is a constant for the physical acquisition process
Under perfect ideal conditions the process-constant K is space-invariant and the
whole process of image acquisition is noise-free In fact both the assumptions are
invalid in any practical acquisition system Therefore a practical image contains some
distortion and noise and hence needs to undergo a process of restoration [2]
Chapter-1 Introduction
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 5
Fig 12 An example of image acquisition process
(a) illumination energy source (b) an object
(c) imaging system (d) 2-D planar image
(b)
(a)
(c)
(d)
Imaging
System
Sampler and
Quantizer
Digital Storage
System
Digital
Computer
Online
Buffer
Display
Device
Observe Digitize Store Refresh Process Output
Fig11 A typical digital image processing system
Object
Transmitter
Recorder
Chapter-1 Introduction
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 6
Image processing may be performed in the spatial-domain or in a transform-
domain To perform a meaningful and useful task a suitable transform eg discrete
Fourier transform (DFT) [1] discrete cosine transform (DCT) [1517] discrete
Hartley transform (DHT) [143-145] discrete wavelet transform (DWT) [10-1418-
21] etc may be employed Depending on the application a suitable transform is
used
Image enhancement techniques are used to highlight certain features of
interest in an image Two important examples of image enhancement are (i)
increasing the contrast and (ii) changing the brightness level of an image so that the
image looks better It is a subjective area of image processing On the other hand
image restoration is very much objective The restoration techniques are based on
mathematical and statistical models of image degradation Denoising (filtering) [4-5]
and deblurring [146-147] tasks come under this category
Image processing is characterized by specific solutions hence a technique that
works well in one area may totally be inadequate in another The actual solution to a
specific problem still requires a significant research and development
Image restoration [126148-149] is one of the prime areas of image
processing and its objective is to recover the images from degraded observations The
techniques involved in image restoration are oriented towards modeling the
degradations and then applying an inverse procedure to obtain an approximation of
the original image Hence it may be treated as a deconvolution operation
Depending on applications there are various types of imaging systems X-ray
Gamma ray ultraviolet and ultrasonic imaging systems are used in biomedical
instrumentation In astronomy the ultraviolet infrared and radio imaging systems are
used Sonic imaging is performed for geological exploration Microwave imaging is
employed for radar applications But the most commonly known imaging systems are
visible light imaging Such systems are employed for applications like remote
sensing microscopy measurements consumer electronics entertainment electronics
etc
The images acquired by optical electro-optical or electronic means are likely
to be degraded by the sensing environment The degradation may be in the form of
sensor noise blur due to camera misfocus relative object camera motion random
Chapter-1 Introduction
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 7
atmospheric turbulence and so on [1-2] The noise in an image may be due to a noisy
channel if the image is transmitted through a medium It may also be due to electronic
noise associated with a storage-retrieval system
Noise in an image is a very common problem An image gets corrupted with
different types of noise during the processes of acquisition transmission reception
and storage retrieval Noise may be classified as substitutive noise (impulsive noise
eg salt amp pepper noise random-valued impulse noise etc) and additive noise (eg
additive white Gaussian noise) The impulse noise of low and moderate noise
densities can be removed easily by simple denoising schemes available in the
literature The simple median filter [1360-61] works very nicely for suppressing
impulse noise of low density However now-a-days many denoising schemes [28-40]
are proposed which are efficient in suppressing impulse noise of moderate and high
noise densities In many occasions noise in digital images is found to be additive in
nature with uniform power in the whole bandwidth and with Gaussian probability
distribution Such a noise is referred to as Additive White Gaussian Noise (AWGN)
It is difficult to suppress AWGN since it corrupts almost all pixels in an image The
arithmetic mean filter commonly known as Mean filter [1-6] can be employed to
suppress AWGN but it introduces a blurring effect
Efficient suppression of noise in an image is a very important issue Denoising
finds extensive applications in many fields of image processing Image denoising is
usually required to be performed before display or further processing like texture
analysis [45-51] object recognition [52-55] image segmentation [56-58] etc
Conventional techniques of image denoising using linear and nonlinear techniques
have already been reported and sufficient literature is available in this area [1-6]
Recently various nonlinear and adaptive filters have been suggested for the
purpose The objectives of these schemes are to reduce noise as well as to retain the
edges and fine details of the original image in the restored image as much as possible
However both the objectives conflict each other and the reported schemes are not
able to perform satisfactorily in both aspects Hence still various research workers are
actively engaged in developing better filtering schemes using latest signal processing
Chapter-1 Introduction
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 8
techniques In this doctoral research work efforts have been made in developing
some novel filters to suppress AWGN quite efficiently
12 Noise in Digital Images
In this section various types of noise corrupting an image signal are studied
the sources of noise are discussed and mathematical models for the different types of
noise are presented
121 Sources of Noise
During acquisition transmission storage and retrieval processes an image
signal gets contaminated with noise Acquisition noise is usually additive white
Gaussian noise (AWGN) with very low variance In many engineering applications
the acquisition noise is quite negligible It is mainly due to very high quality sensors
In some applications like remote sensing biomedical instrumentation etc the
acquisition noise may be high enough But in such a system it is basically due to the
fact that the image acquisition system itself comprises of a transmission channel So if
such noise problems are considered as transmission noise then it may be concluded
that acquisition noise is negligible The acquisition noise is considered negligible due
to another fact that the human visual system (HVS) canrsquot recognize a large dynamic
range of image That is why an image is usually quantized at 256 levels Thus each
pixel is represented by 8 bits (1 byte) The present-day technology offers very high
quality sensors that donrsquot have noise level greater than half of the resolution of the
analog-to-digital converter (ADC) ie noise magnitude in time domain ( )8
22
1 Vtn sdotlt
where n(t) is the noise amplitude at any arbitrary instant of time t and V is the
maximum output of the sensor and is also equal to the maximum allowed input
voltage level for the ADC That is for V = 33 volts the noise amplitude should be
less than ~ 65 mV In many practical applications the acquisition noise level is much
below this margin Thus the acquisition noise need not be considered
Hence the researchers are mostly concerned with the noise in a transmission
system Usually the transmission channel is linear but dispersive due to a limited
Chapter-1 Introduction
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 9
bandwidth The image signal may be transmitted either in analog form or in digital
form
When an analog image signal is transmitted through a linear dispersive
channel the image edges (step-like or pulse like signal) get blurred and the image
signal gets contaminated with AWGN since no practical channel is noise free If the
channel is so poor that the noise variance is high enough to make the signal excurse to
very high positive or high negative value then the thresholding operation done at the
front end of the receiver will contribute to saturated max and min values Such noisy
pixels will be seen as white and black spots Therefore this type of noise is known as
salt and pepper noise (SPN) In essence if analog image signal is transmitted then the
signal gets corrupted with AWGN and SPN as well Thus there is an effect of mixed
noise
If the image signal is transmitted in digital form through a linear dispersive
channel then inter-symbol interference (ISI) takes place In addition the presence of
AWGN in a practical channel can not be ignored This makes the situation worse Due
to ISI and AWGN it may so happen that a lsquo1rsquo may be recognized as lsquo0rsquo and vice-
versa Under such circumstances the image pixel values have changed to some
random values at random positions in the image frame Such type of noise is known
as random-valued impulse noise (RVIN)
122 Mathematical Representation of Noise
The AWGN SPN and RVIN are mathematically represented below The
Gaussian noise is given by
( )ttn GAWGN η=)( (14)
( ) ( )AWGN G
f f x y x yηrArr = + (15)
where ( )tGη is a random variable that has a Gaussian probability distribution It is an
additive noise that is characterized by its variance 2σ where σ represents its
standard deviation In (15) the noisy image is represented as a sum of the original
Chapter-1 Introduction
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 10
uncorrupted image and the Gaussian distributed random noise Gη When the variance
of the random noise Gη is very low ( )G
x yη is zero or very close to zero at many
pixel locations Under such circumstances the noisy image AWGN
f is same or very
close to the original image ( )f x y at many pixel locations ( )x y
Let a digital image ( )f x y after being corrupted with SPN of density d be
represented by SPN
f (xy) Then the noisy image SPN
f (xy) is mathematically
represented as
SPN
with probability 1
( ) 0 2
1 2
f(xy) p d
f x y p d
p d
= minus
= = =
(16)
The impulse noise occurs at random locations ( )x y with a probability of d
The SPN and RVIN are substitutive in nature A digital image corrupted with RVIN
of density d RVIN
f (xy) is mathematically represented as
RVIN
with probability 1( )
( ) with probability
f(xy) p df x y
x y p dη
= minus=
=
(17)
Here ( )x yη represents a uniformly distributed random variable ranging
from 0 to 1 that replaces the original pixel value ( )f x y The noise magnitude at any
noisy pixel location (xy) is independent of the original pixel magnitude Therefore
the RVIN is truly substitutive
Another type of noise that may corrupt an image signal is the speckle noise
(SN) In some biomedical applications like ultrasonic imaging and a few engineering
applications like synthesis aperture radar (SAR) imaging such a noise is encountered
Chapter-1 Introduction
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 11
The SN is a signal dependent noise ie if the image pixel magnitude is high then the
noise is also high Therefore it is also known as multiplicative noise and is given by
( ) ( )tSttnSN
)( η= (18)
( ) ( ) ( ) ( ) SN
f x y f x y x y f x yηrArr = + (19)
where ( )tη is a random variable and ( )tS is the magnitude of the signal The noisy
digital image SN
f (xy) is represented mathematically in (19) The noise is
multiplicative since the imaging system transmits a signal to the object and the
reflected signal is recorded In the forward transmission path the signal gets
contaminated with additive noise in the channel Due to varying reflectance of the
surface of the object the reflected signal magnitude varies So also the noise varies
since the noise is also reflected by the surface of the object Noise magnitude is
therefore higher when the signal magnitude is higher Thus the speckle noise is
multiplicative in nature
The speckle noise is encountered only in a few applications like ultrasonic
imaging and SAR whereas all other types of noise ie AWGN SPN and RVIN
occur in almost all the applications The AWGN is the most common among all
Under very low noise variance it may look like RVIN In general some combinations
of AWGN SPN and RVIN may represent a practical noise Such type of noise is
known as mixed noise Some effective schemes are available in the literature [41-44]
for filtration of mixed noise
The proposed filters developed in subsequent chapters are meant for
suppression of AWGN To avoid ambiguity the noisy image is taken as g(xy) in the
subsequent chapters Thus the noisy image is expressed as
( ) ( ) ( )g x y f x y x yη= + (110)
where g(xy) is the same as fAWGN expressed in (15)
Chapter-1 Introduction
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 12
13 Literature Review
Noise introduced in an image is usually classified as substitutive (impulsive
noise eg salt amp pepper noise random-valued impulse noise etc) and additive
(eg additive white Gaussian noise) noise
The impulsive noise of low and moderate noise densities can be removed
easily by simple denoising schemes available in the literature The simple median
filter [3] works very nicely for suppressing impulsive noise of low density However
many efficient filters have been developed for removal of impulsive noise of
moderate and high noise densities Chen et al [28] have developed a nonlinear filter
called tri-state median filter for preserving image details while effectively
suppressing impulsive noise The standard median filter and the center weighted
median (CWM) filter are incorporated into noise detection framework to determine
whether a pixel is corrupted before applying the filtering operation A nonlinear non-
iterative multidimensional filter the peak-and-valley filter [29] is developed for
impulsive noise reduction The filter consists of a couple of conditional rules that
identify the noisy pixels and replace their gray level values in a single step F Russo
has developed an evolutionary neural fuzzy system for noise cancellation in image
data [30] The proposed approach combines the advantages of the fuzzy and neural
paradigms The network structure is designed to exploit the effectiveness of fuzzy
reasoning in removing noise without destroying the useful information in input data
Farbiz et al have proposed a fuzzy logic filter for image enhancement [31] It is able
to remove impulsive noise and smooth Gaussian noise Also it preserves edges and
image details H-L Eng and K-K Ma have proposed a noise adaptive soft-switching
(NASM) filter [32] A soft-switching noise-detection scheme is developed to classify
each pixel to be uncorrupted pixel isolated impulsive noise non-isolated impulsive
noise or image objectrsquos edge pixel lsquoNo filteringrsquo a standard median filter or the
proposed fuzzy weighted median filter is then employed according to respective
characteristic type identified T Chen and HR Wu have developed a scheme for
adaptive impulse detection using CWM filters [33] In addition to the removal of
noise from gray images some color image denoising filters [34-40] are also
developed for efficient removal of impulsive noise from color images
Chapter-1 Introduction
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 13
In many occasions noise in digital images is found to additive white Gaussian
noise (AWGN) with uniform power in the whole bandwidth and with Gaussian
probability distribution Traditionally AWGN is suppressed using linear spatial
domain filters such as Mean filter [1-6] Wiener filter [12962-64] etc Linear
techniques possess mathematical simplicity but have the disadvantage of yielding
blurring effect They also do not perform well in the presence of signal dependant
noise Nonlinear filters [4] are then developed to avoid the aforementioned
disadvantages The well known nonlinear mean filters such as harmonic mean
geometric mean Lp mean contra-harmonic mean proposed by Pitas et al [5] are
found to be good in preserving edges Another good edge preserving filter is Lee filter
[79] proposed by JS Lee In the flat parts of the signal the output of the Lee filter is
almost equal to the local signal mean But in the rapidly varying parts of signal the
output of the Lee filtering is almost equal to the observed signal value Thus the Lee
filtering can smooth noise and preserve edges efficiently Anisotropic diffusion [67-
68] is also a powerful filter where local image variation is measured at every point
and pixel values are averaged from neighborhoods whose size and shape depend on
local variation Diffusion methods average over extended regions by solving partial
differential equations and are therefore inherently iterative More iteration may lead
to instability where in addition to edges noise becomes prominent Rudin et al
proposed total variation (TV) filter which is also iterative in nature Later a simple
and noniterative scheme for edge preserving smoothing is proposed that is known as
Bilateral filter [70] Bilateral filter combines gray levels or colors based on both their
geometric closeness and their photometric similarity and prefers near values to
distant values in both domain and range A filter named non local means (NL-Means)
[88] is proposed which averages similar image pixels defined according to their local
intensity similarity
T Rabie [110] proposed a simple blind denoising filter based on the theory of
robust statistics Robust statistics addresses the problem of estimation when the
idealized assumptions about a system are occasionally violated The contaminating
noise in an image is considered as a violation of the assumption of spatial coherence
of the image intensities and is referred as an outlier system A denoised image is
estimated by fitting a spatially coherent stationary image model to the available noisy
Chapter-1 Introduction
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 14
data using a robust estimator-based regression method within an optimal size adaptive
window Another robust image denoising method based on the bi-weight mid-
regression is proposed by Hou et al [116] is found to be effective in suppressing
AWGN Kernel regression is a nonparametric class of regression method used for
image denoising [119]
F Russo [111] proposed a new method for automatic enhancement of noisy
images The most relevant feature of the proposed approach is a novel procedure for
automatic tuning that takes into account the histograms of the edge gradients
Fuzzy techniques can be applied to develop filters for suppression of additive
noise Ville et al [113] proposed a fuzzy filter for suppression of AWGN The filter
consists of two stages The first stage computes a fuzzy derivative for eight different
directions The second stage uses these fuzzy derivatives to perform fuzzy smoothing
by weighting the contributions of neighboring pixel values The filter can be applied
iteratively to effectively reduce high noise
Kervrann et al [114] developed a novel adaptive and patch-based approach
for image denoising and representation The method is based on a pointwise selection
of small image patches of fixed size in the variable neighborhood of each pixel This
method is general and can be applied under the assumption that there exist repetitive
patterns in a local neighborhood of a point
A novel method using adaptive principal components is proposed by Mureson
and Parks [115] for suppression of AWGN The method uses principal components on
a local image patches to derive a 2-D locally adaptive basis set The local principal
components provide the best local basis set and the largest eigenvector is in the
direction of the local image edge
Dabov et al [121] proposed a novel image denoising strategy based on an
enhancement sparse representation in transform-domain The enhancement of sparsity
is achieved by grouping similar 2-D image fragments (eg blocks) into 3-D data
arrays which is called as ldquogroupsrdquo Collaborative filtering is a special procedure
developed to deal with these 3-D groups The filter is realized with three successive
steps 3-D transformation of a group shrinkage of the transform spectrum and
inverse 3-D transformation
Chapter-1 Introduction
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 15
A spatial adaptive denoising method is developed by M Mignotte [122] which
is based on an averaging process performed on a set of Markov Chain Monte-Carlo
simulations of region partition maps constrained to be spatially piecewise uniform
(ie constant in the grey level value sense) for each estimated constant-value regions
For the estimation of these region partition maps the unsupervised Markovian
framework is adopted in which parameters are automatically estimated in least square
sense
Hirakawa et al [123] proposed an image denoising scheme using total least
squares (TLS) where an ideal image patch is modeled as a linear combination of
vectors cropped from the noisy image The model is fitted to the real image data by
allowing a small perturbation in the TLS sense
Shen et al [125] designed nonseparable Parseval frames from separable
(tensor) products of a piecewise linear spline tight frame These nonseparable
framelets are capable of detecting first and second order singularities in directions that
are integral multiples of 450 Using these framelets two image denoising algorithms
are proposed for suppression of AWGN
A new class of fractional-order anisotropic diffusion equations for image
denoising is proposed in [128] for noise removal These equations are Euler-Lagrange
equations of a cost functional which is an increasing function of the absolute value of
the fractional derivative of the image intensity function so the proposed equations can
be seen as generalization of second-order and fourth-order anisotropic diffusion
equations
Now-a-days wavelet transform is employed as a powerful tool for image
denoising [98-106 129-136] Image denoising using wavelet techniques is effective
because of its ability to capture most of the energy of a signal in a few significant
transform coefficients when natural image is corrupted with Gaussian noise Another
reason of using wavelet transform is due to development of efficient algorithms for
signal decomposition and reconstruction [59] for image processing applications such
as denoising and compression Many wavelet-domain techniques are already available
in the literature Out of various techniques soft-thresholding proposed by Donoho and
Johnstone [98] is most popular The use of universal threshold to denoise images in
wavelet domain is known as VisuShrink [99] In addition subband adaptive systems
Chapter-1 Introduction
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 16
having superior performance such as SureShrink [100101] BayesShrink [102]
NeighShrink [103] SmoothShrink [104] are available in the literature Bala et al
[129] proposed a multivariate thresholding technique for image denoising using
multiwavelets The proposed technique is based on the idea of restoring the spatial
dependence of the pixels of the noisy image that has undergone a multiwavelet
decomposition Coefficients with high correlation are regarded as elements of a vector
and are subject to a common thresholding operation In [130] translation-invariant
contourlet transform is used for image denoising
A number of recent approaches for denosing have taken advantage of joint
statistical relationships by adaptively estimating the variance of a coefficient from a
local neighborhood consisting of coefficients within a sub-band One such method
where statistical relationship of coefficients in a neighborhood is considered is locally
adaptive window maximum likelihood (LAWML) estimation [105] It is important to
construct a statistical model in order to accurately estimate the signal In [106] a
Hidden Markov Model is used in wavelet domain for denoising where the existence
of significant spatial dependencies in the transform coefficients are recognized and
these dependencies are described using data structures P Shui and Y Zhao [117]
proposed an image denoising algorithm using doubly local Wiener filtering with
block-adaptive windows in wavelet domain In [120] M Kazubek demonstrated that
denoising performance of the Wiener filtering can be increased by preprocessing
images with a thresholding operation in wavelet-domain
Tan et al [112] proposed a wavelet domain denoising algorithm by combining
the expectation maximization scheme and the properties of the Gaussian scale mixture
models The algorithm is iterative in nature and the number of iterations depends on
the noise variance For high variance Gaussian noise the method undergoes many
iterations and therefore the method is computational-intensive
J Ma and G Plonka [118] proposed diffusion-based curvelet shrinkage is
proposed for discontinuity-preserving denoising using a combination of a new tight
frame of curvelets with a nonlinear diffusion scheme In order to suppress the pseudo-
Gibbs and curvelet-like artifacts the conventional shrinkage results are further
processed by a projected total variation diffusion where only the insignificant curvelet
Chapter-1 Introduction
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 17
coefficients or high-frequency part of signal are changed by use of a constrained
projection
Portilla et al [124] developed a method for removing noise from digital
images based on a statistical model of the coefficients of an over-complete multiscale
oriented basis Neighborhoods of coefficients at adjacent positions and scales are
modeled as a product of two independent random variables a Gaussian vector and a
hidden positive scalar mulitiplier The latter modulates the local variance of the
coefficients in the neighborhood and is thus able to account for the empirically
observed correlation between the coefficientsrsquo amplitudes Under this model the
Baysian least squares estimate of each coefficient reduces to a weighted average of
the local linear estimates over all possible values of the hidden multiplier variable
Some fractal-wavelet image denoising schemes are explained in [126] Zhong
and Ning [127] proposed a very efficient algorithm for image denoising based on
wavelets and multifractals for singularity detection By modeling the intensity surface
of a noisy image as statistically self-similar multifractal process and taking advantage
of the multiresolution analysis with wavelet transform to exploit the local statistical
self-similarity at different scales the point-wise singularity strength value
characterizing the local singularity at each scale was calculated By thresholding the
singularity strength wavelet coefficients at each scale were classified into two
categories the edge-related and regular wavelet coefficients and the irregular wavelet
coefficients The irregular wavelet coefficients were denoised using an approximate
minimum mean-squared error (MMSE) estimation method while the edge-related and
regular wavelet coefficients were smoothed using the fuzzy weighted mean (FWM)
filter preserving the edges and details when reducing noise
Many color image denoising techniques [137-142] are available in the
literature for suppression of AWGN Lian et al [139] proposed an edge preserving
image denoising via optimal color space projection method SURE-LET multichannel
image denoising is proposed by F Luiser and T Blu [141] where the denoising
algorithm is parameterized as a linear expansion of thresholds (LET) and optimized
using Steinrsquos unbiased risk estimate (SURE) A non-redundant orthonormal wavelet
transform is first applied to the noisy data followed by the (subband-dependent)
vector-valued thresholding of individual multi-channel wavelet coefficients which are
Chapter-1 Introduction
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 18
finally brought back to the image domain by inverse wavelet transform Lian et al
[142] proposed a color image denoising technique in wavelet domain for suppression
of AWGN The proposed method is based on minimum cut algorithm where the inter-
scale and intra-scale correlations of wavelet coefficients are exploited to suppress the
additive noise Some blind techniques using independent component analysis (ICA)
[151152] for image denoising are available in the literature But none of the filters
available in literature is able to achieve perfect restoration Further there is a need to
reduce computational complexity of a filtering algorithm for its use in real-time
applications
Hence it may be concluded that there is enough scope to develop better
filtering schemes with very low computational complexity that may yield high noise
reduction as well as preservation of edges and fine details in an image
14 The Problem Statement
In the present research work efforts are made to develop many efficient
filtering schemes to suppress AWGN For real-time applications like television
photo-phone etc it is essential to reduce the noise power as much as possible and to
retain the fine details and the edges in the image as well Moreover it is very
important to have very low computational complexity so that the filtering operation is
performed in a short time for online and real-time applications
Thus the problem taken for this research work is ldquoDevelopment of Efficient
Image Filters to suppress AWGN for Online and Real-Time Applicationsrdquo Since
linear filters donrsquot perform well nonlinear filtering schemes are adopted for achieving
better performance The processing may be done in spatial-domain or in transform-
domain
Therefore the objective of this doctoral research work is to develop some
novel spatial-domain and transform-domain digital image filters for efficient
suppression of additive white Gaussian noise
Chapter-1 Introduction
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 19
15 Image Metrics
The quality of an image is examined by objective evaluation as well as
subjective evaluation For subjective evaluation the image has to be observed by a
human expert The human visual system (HVS) [109] is so complicated that it is not
yet modeled properly Therefore in addition to objective evaluation the image must
be observed by a human expert to judge its quality
There are various metrics used for objective evaluation of an image Some of
them are mean squared error (MSE) root mean squared error (RMSE) mean absolute
error (MAE) and peak signal to noise ratio (PSNR) [7107]
Let the original noise-free image noisy image and the filtered image be
represented by ( )f x y ( )g x y and ˆ ( )f x y respectively Here x and y represent
the discrete spatial coordinates of the digital images Let the images be of size MtimesN
pixels ie x=123hellipM and y=123hellipN Then MSE and RMSE are defined as
( )1 1
2ˆ ( ) ( )
M N
x y
f x y f x y
M NMSE = =
minus
times
sumsum= (111)
MSERMSE = (112)
The MAE is defined as
( )1 1
ˆ ( ) ( )
M N
x y
f x y f x y
M NMAE = =
minus
times
sumsum= (113)
The PSNR is defined in logarithmic scale in dB It is a ratio of peak signal
power to noise power Since the MSE represents the noise power and the peak signal
power is unity in case of normalized image signal the image metric PSNR is defined
as
)1(log10 10 MSEPSNR = dB (114)
Chapter-1 Introduction
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 20
For the color image processing the color peak signal to noise ratio (CPSNR)
[142] in decibel is used as performance measure The CPSNR is defined as
1
10
110 log
3c
c R G B
CPSNR MSE
minus
isin
= sdot
sum dB (115)
where MSEc is the mean squared error in a particular channel of the color space
Though these image metrics are extensively used for evaluating the quality of
a restored (filtered) image and thereby the capability and efficiency of a filtering
process none of them gives a true indication of noise in an image It is very important
to note that RMSE MAE and PSNR are all related to MSE In addition to these
parameters a new metric universal quality index (UQI) [108] is extensively used in
literature to evaluate the quality of an image now-a-days Further some parameters
eg method noise [88] and execution time [150] are also used in literature to evaluate
the filtering performance of a filter These parameters are discussed below
Universal Quality Index
The universal quality index (UQI) is modeled by considering three different
factors (i) loss of correlation (ii) luminance distortion and (iii) contrast distortion It
is defined by
where
( ) ( )ˆ ˆ
2 2 22
ˆ ˆ
ˆ 22
ˆ
ff f f
f ff f
f fUQI
f f
σ σ σ
σ σ σ σ= sdot sdot
++
1 1
1 1
1( )
1ˆ ˆ( )
M N
x y
M N
x y
f f x yM N
f f x yM N
= =
= =
=times
=times
sumsum
sumsum
( )
( )
22
1 1
22
ˆ
1 1
1( )
1
1 ˆ ˆ( )1
M N
f
x y
M N
fx y
f x y fM N
f x y fM N
σ
σ
= =
= =
= minustimes minus
= minustimes minus
sumsum
sumsum
( )( )ˆ
1 1
1 ˆ ˆ( ) ( )1
M N
f fx y
f x y f f x y fM N
σ= =
= minus minustimes minus
sumsum
(119)
(120)
(121)
(118)
(117)
(116)
Chapter-1 Introduction
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 21
The UQI defined in (116) consists of three components The first component
is the correlation coefficient between the original noise-free image f and the restored
image f that measures the degree of linear correlation between them and its
dynamic range is [-11] The second component with a range of [0 1] measures the
closeness between the average luminance of f and f It reaches the maximum value
of 1 if and only if f equals f The standard deviations of these two images fσ and
fσ are also regarded as estimates of their contrast-levels So the third component in
(116) is necessarily a measure of the similarity between the contrast-levels of the
images It ranges between 0 and 1 and the optimum value of 1 is achieved only when
fσ =f
σ
Hence combining the three parameters (i) correlation (ii) average luminance
similarity and (iii) contrast-level similarity the new image metric universal quality
index (UQI) becomes a very good performance measure
Method Noise
Since linear filters do not perform well nonlinear filters are predominantly
used for suppressing AWGN from an image But an image denoising filter degrades
even an original noise-free input image due to its inherent nonlinear characteristics In
many occasions it unnecessarily yields some noise at the output This is quite
undesirable
The method noise [8889] MN of a filter is defined as noise in the output
image when the input is noise-free It is described as an error voltage level in terms of
its mean absolute value The method noise is defined as
1 =1
M
( )x y
x y==
times
sumsumM N
M N
N
N (122)
where Mˆ( ) ( ) ( )x y f x y f x y= minusN (123)
Chapter-1 Introduction
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 22
( )ˆ ( ) ( )f x y T f x y= (124)
T() is the method (filtering operation)
Execution Time
Execution Time (TE) of a filter is defined as the time taken by a digital
computing platform to execute the filtering algorithm when no other software except
the operating system (OS) runs on it
Though TE depends essentially on the computing systemrsquos clock time-period
yet it is not necessarily dependant on the clock time alone Rather in addition to the
clock-period it depends on the memory-size the input data size and the memory-
access time etc
The execution time taken by a filter should be low for online and real-time
image processing applications Hence a filter with lower TE is better than a filter
having higher TE value when all other performance-measures are identical
Since the execution time is platform dependant some standard hardware
computing platforms SYSTEM-1 SYSTEM-2 and SYSTEM-3 presented in
Table-11 are taken for the simulation work Thus the TE parameter values for the
various existing and proposed filters are evaluated by running these filtering
algorithms on these platforms
Table-11 Details of hardware platforms (along with their operating system) used for simulating
the filters
Hardware platforms Processor Clock (GHz) RAM (GB) Operating System (OS)
SYSTEM-1 Pentium IV Core 2 Duo
Processor
24 2 Windows Vista 64 bit OS
SYSTEM-2 Pentium IV Duo Processor 28 1 Windows XP 32 bit OS
SYSTEM-3 Pentium IV Processor 17 1 Windows XP 32 bit OS
Chapter-1 Introduction
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 23
16 Chapter-wise Organization of the Thesis
The chapter-wise organization of the thesis is outlined
Chapter-1 Introduction
Preview
Fundamentals of Digital Image Processing
Noise in Digital Images
Literature Review
Problem Statement
Image Metrics
Chapter-wise Organization of Thesis
Conclusion
Chapter-2 Study of Image Denoising Filters
Preview
Order Statistics Filter
Wiener and Lee Filter
Anisotropic Diffusion (AD) and Total Variation (TV) Filters
Bilateral Filter
Non-local Means (NL-means) Filter
Wavelet Domain Filters
Simulation Results
Conclusion
Chapter-3 Development of Novel Spatial-Domain Image Filters
Preview
Development of Adaptive Window Wiener Filter
Development of Circular Spatial Filter
Simulation Results
Conclusion
Chapter-4 Development of Transform-Domain Filters
Preview
Development of Gaussian Shrinkage based DCT-domain Filter
Chapter-1 Introduction
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 24
Development of Total Variation based DWT-domain Filter
Development of Region Merging based DWT-domain Filter
Simulation Results
Conclusion
Chapter-5 Development of Some Color Image Denoising Filters
Preview
Multi-Channel Color Image Filtering
Multi-Channel Mean Filter
Multi-Channel LAWML Filter
Development of Multi-Channel Circular Spatial Filter
Development of Multi-Channel Region Merging based DWT-domain Filter
Simulation Results
Conclusion
Chapter-6 Conclusion Preview
Comparative Analysis
Conclusion
Scope for Future Work
17 Conclusion
In this chapter the fundamentals of digital image processing sources of noise
and types of noise in an image the existing filters and their merits and demerits and
the various image metrics are discussed It is obvious that AWGN is the most
important type of noise during acquisition and transmission processes Hence in
common applications like television photo-phone etc the digital images are
supposed to be corrupted with AWGN quite often Therefore it is decided to make
efforts to develop efficient filters to suppress additive noise The various metrics for
describing and quantifying the qualities of an image as well those of a filtering
process are discussed and analyzed here In addition details of various hardware
platforms on which the filtering algorithms are run are mentioned for further
reference in the subsequent chapters
Chapter 2
Study of Image
Denoising Filters
Chapter-2 Study of Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 26
Preview
Image denoising is a common procedure in digital image processing aiming at
the suppression of additive white Gaussian noise (AWGN) that might have corrupted
an image during its acquisition or transmission This procedure is traditionally
performed in the spatial-domain or transform-domain by filtering In spatial-domain
filtering the filtering operation is performed on image pixels directly The main idea
behind the spatial-domain filtering is to convolve a mask with the whole image The
mask is a small sub-image of any arbitrary size (eg 3times3 5times5 7times7 etc) Other
common names for mask are window template and kernel An alternative way to
suppress additive noise is to perform filtering process in the transform-domain In
order to do this the image to be processed must be transformed into the frequency
domain using a 2-D image transform Various image transforms such as Discrete
Cosine Transform (DCT) [21517] Singular Value Decomposition (SVD) Transform
[2] Discrete Wavelet Transform (DWT) [10-1418-21] etc are used
In this chapter various existing spatial-domain and transform-domain image
denoising filters are studied and their filtering performances are compared They are
2
Chapter-2 Study of Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 27
some well-known standard and benchmark filters available in literature Novel filters
designed and developed in this research work are compared against these filters in
subsequent chapters Therefore attempts are made here for detailed and critical
analysis of these existing filters
The organization of the chapter is given below
Order Statistics Filters
Wiener and Lee Filter
Anisotropic Diffusion (AD) and Total Variation (TV) Filters
Bilateral Filter
Non-local Means (NL-Means) Filter
Wavelet Domain Filters
Simulation Results
Conclusion
21 Order Statistics Filters
Usually sliding window technique [126] is employed to perform pixel-by-pixel
operation in a filtering algorithm The local statistics obtained from the neighborhood
of the center pixel give a lot of information about its expected value If the
neighborhood data are ordered (sorted) then ordered statistical information is
obtained If this order statistics vector is applied to a finite impulse response (FIR)
filter then the overall scheme becomes an order statistics (OS) filter [156061]
For example if a 3times3 window is used for spatial sampling then 9 pixel data are
available at a time First of all the 2-D data is converted to a 1-D data ie a vector
Let this vector of 9 data be sorted Then if the mid value (5th
position pixel value in
the sorted vector of length = 9) is taken it becomes median filtering with the filter
weight vector [0 0 0 0 1 0 0 0 0] If all the order statistics are given equal weightage
then it becomes a moving average or mean filter (MF) Strictly speaking the MF is a
simple linear filter and it has nothing to do with the ordered statistics Since the MF
operation gives equal emphasis to each input data it is immaterial whether the input
vector is sorted or not Thus simply to have a generalization of OS filters the MF is
Chapter-2 Study of Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 28
considered a member of this class Otherwise it is quite different from all other
members of this family of filters The median (MED) alpha-trimmed mean (ATM)
min max filters are some members of this interesting family
211 Mean and Median Filters
The moving average or mean filter (MF) is a simple linear filter [1-6] All the
input data are summed together and then the sum is divided with the number of data
It is very simple to implement in hardware and software The computational
complexity is very low It works fine for low power AWGN As the noise power
increases its filtering performance degrades If the noise power is high then a larger
window should be employed for spatial sampling to have better local statistical
information As the window size increases MF produces a reasonably high blurring
effect and thus thin edges and fine details in an image are lost
The median (MED) filter [36061] on the other hand is a nonlinear filter The
median is a very simple operation Once the sorting (ordering) operation is performed
on the input vector the job is done as the mid-value is taken as the output Of course
if the length of the input vector is even then the average of two mid-ordered statistical
data is taken as output Usually such a computation is not required in most of image
processing applications as the window length is normally an odd number Thus the
MED operation can be completed in a very short time That is a MED filter may be
used for online and real-time applications to suppress noise If an image is corrupted
with a very low variance AWGN then this filter can perform a good filtering
operation [42]
212 Alpha Trimmed Mean Filter
The alpha-trimmed mean (ATM) filter [1] is based on order statistics and
varies between a median and mean filter It is so named because rather than
averaging the entire data set a few data points are removed (trimmed) and the
remainders are averaged The points which are removed are most extreme values
both low and high with an equal number of points dropped at each end (symmetric
Chapter-2 Study of Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 29
trimming) In practice the alpha-trimmed mean is computed by sorting the data low
to high and summing the central part of the ordered array The number of data values
which are dropped from the average is controlled by trimming parameter alpha
Let g(st) be a sub-image of noisy image g(xy) Suppose the 2
α lowest and the
2
α highest gray-level values of g(st) are deleted in the neighborhood Sxy Let gr(st)
represent the remaining mn αminus pixels A filter formed by averaging these remaining
pixels is called alpha trimmed mean filter which can be expressed as
( )
1ˆ( ) ( )xy
r
s t S
f x y g s tmn α isin
=minus
sum (21)
The alpha-trimmed mean also known as Rank-Ordered Mean (ROM) filter is
used when an image is corrupted with mixed noise (both Gaussian and salt amp pepper
noise) [42] Choice of parameterα is very critical and it determines the filtering
performance Hence the ATM filter is usually employed as an adaptive filter whose
α may be varied depending on the local signal statistics Therefore it is a
computation-intensive filter as compared to simple mean and median filter Another
problem of ATM is that the detailed behavior of the signal cannot be preserved when
the filter window is large
22 Wiener Filter and Lee Filter
The Wiener filter [962-64] and Lee filter [79-89] are spatial-domain filters
which are developed long back and are used for suppression of additive noise The
details of these two filters are explained below
221 Wiener Filter
Norbert Wiener proposed the concept of Wiener filtering in the year 1942
[16] There are two methods (i) Fourier-transform method (frequency-domain) and
(ii) mean-squared method (spatial-domain) for implementing Wiener filter The
former method is used only for complete restoration (denoising and deblurring)
Chapter-2 Study of Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 30
whereas the later is used for denoising In Fourier transform method of Wiener
filtering normally it requires a priori knowledge of the power spectra of noise and the
original image But in mean-squared method no such a priori knowledge is required
Hence it is easier to use the mean-squared method for image denoising Wiener filter
is based on the least-squared principle ie the filter minimizes the mean-squared
error (MSE) between the actual output and the desired output
Image statistics vary too much from a region to another even within the same
image Thus both global statistics (mean variance etc of the whole image) and
local statistics (mean variance etc of a small region or sub-image) are important
Wiener filtering is based on both the global statistics and local statistics and is given
by
( )2
2 2ˆ ( ) ( )
f
f n
f x y g g x y gσ
σ σ= + minus
+ (22)
where g is the local mean 2
fσ is the local signal variance 2
nσ is the noise variance
and ˆ ( )f x y denotes the restored image
For (2a+1) times (2b+1) window of noisy image g(x y) the local mean g and local
variance 2
gσ are defined by
1( )
a b
s a t b
g g s tL = minus = minus
= sum sum (23)
where L is the total number of pixels in a window ie L = (2a+1) times (2b+1)
and
( )22 1
( )1
a b
g
s a t b
g s t gL
σ= minus = minus
= minusminussum sum (24)
The local signal variance 2
fσ used in (22) is calculated from 2
gσ with a priori
knowledge of noise variance 2
nσ simply by subtracting 2
nσ from 2
gσ with the
assumption that the signal and noise are not correlated with each other
From (22) it may be observed that the filter-output is equal to local mean if
the current pixel value equals local mean Otherwise it outputs a different value the
Chapter-2 Study of Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 31
value being some what different from local mean If the input current value is more
(less) than the local mean then the filter outputs a positive (negative) differential
amount taking the noise variance and the signal variance into consideration Thus the
filter output varies from the local mean depending upon the local variance and hence
tries to catch the true original value as far as possible
In statistical theory Wiener filtering is a great land mark It estimates the
original data with minimum mean-squared error and hence the overall noise power in
the filtered output is minimal Thus it is accepted as a benchmark in 1-D and 2-D
signal processing
222 Lee Filter
The Lee filter [79-82] developed by Jong-Sen Lee is an adaptive filter which
changes its characteristics according to the local statistics in the neighborhood of the
current pixel The Lee filter is able to smooth away noise in flat regions but leaves
the fine details (such as lines and textures) unchanged It uses small window (3times3
5times5 7times7) Within each window the local mean and variances are estimated
The output of Lee filter at the center pixel of location (x y) is expressed as
[ ]ˆ ( ) ( ) ( )f x y k x y g x y g g= minus + (25)
where
22 2
2
2 2
1 ( )
0
n
g n
g
g n
k x y
σσ σ
σ
σ σ
minus gt
= le
(26)
The parameter k(x y) ranges between 0 (for flat regions) and 1 (for regions
with high signal activity)
The distinct characteristic of the filter is that in the areas of low signal activity
(flat regions) the estimated pixel approaches the local mean whereas in the areas of
high signal activity (edge areas) the estimated pixel favors the corrupted image pixel
thus retaining the edge information It is generally claimed that human vision is more
sensitive to noise in a flat area than in an edge area The major drawback of the filter
is that it leaves noise in the vicinity of edges and lines However it is still desirable to
reduce noise in the edge area without sacrificing the edge sharpness Some variants of
Chapter-2 Study of Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 32
Lee filter available in the literature handle multiplicative noise and yield edge
sharpening [83-87]
23 Anisotropic Diffusion (AD) Filter and Total Variation (TV) Filter
Anisotropic Diffusion (AD) and Total Variation (TV) filters are used for
suppressing AWGN from images [6769] The methods are iterative in nature and
they need more iterations as noise variance increases
231 Anisotropic Diffusion (AD) Filter
It has been proven that it is necessary to extract a family of derived images of
multiple scales of resolution in order to be able to identify global objects through
blurring [6566] and that this may be viewed equivalently as the solution of the heat
conduction or diffusion equation given by
2tg C g= nabla (27)
where t
g is the first derivative of the image signal g in time t and 2nabla is the
Laplacian operator with respect to space variables respectively In (27) C is
considered as a constant independent of space location There is no fundamental
reason why this must be so Koenderink [66] considered it so because it simplifies the
analysis greatly Perona and Malik [67] developed a smoothing scheme based on
anisotropic diffusion filtering that overcomes the major drawbacks of conventional
spatial smoothing filters and improves the image quality significantly Perona and
Malik considered the anisotropic diffusion equation as
2
( )[ ( ) ( )]
( )
t
g x y tg div C x y t g x y t
t
C x y t g C g
part= = nabla
part
= nabla + nabla nabla
(28)
where div and nabla define the divergence and gradient operators with respect to space
variables respectively By letting C(x y t) be a constant (28) reduces to (27) the
isotropic diffusion equation
Chapter-2 Study of Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 33
In [68] Perona and Malik considered the image gradient as an estimation of
edges and ( )C U g= nabla in which U() has to be a nonnegative monotonically
decreasing function with U(0) = 1 (in the interval of uniform region) and tends to zero
at infinity There are some possible choices for U() the obvious being a binary
valued function Some other functions [68] could be
2
2( ) exp
sU s
k
= minus
(29)
or
2
1( )
1
U ss
k
=
+
(210)
where k is the threshold level for removing noise Equation (28) can be discretized
using four nearest neighbors (north south east west) and the Laplacian operator [4]
as given by
[ ]1( ) ( ) ( ) ( ) ( ) ( )nn n
N N S S W W E Eg x y g x y C g x y C g x y C g x y C g x yλ+ = + nabla + nabla + nabla + nabla 211)
where 1( )ng x y
+ is the discrete value of g(xy) in the (n+1)th iteration set by n as g is
determined by t in continuous space It follows that
( )( )N N
C U g x y= nabla
( ) ( 1 ) ( )N
g x y g x y g x ynabla = minus minus (212a)
( )( )S SC U g x y= nabla
( ) ( 1 ) ( )Sg x y g x y g x ynabla = + minus (212b)
( )( )W WC U g x y= nabla
( ) ( 1) ( )W g x y g x y g x ynabla = minus minus (212c)
( )( )E E
C U g x y= nabla
( ) ( 1) ( )Eg x y g x y g x ynabla = + minus (212d)
and λ is a single parameter needed for stability [68]
The filtered image is then 1ˆ ( ) ( )nf x y g x y
+=
Chapter-2 Study of Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 34
232 Total Variation (TV) Filter
Rudin et al proposed Total variation (TV) [69] which is a constrained
optimization type of numerical algorithm for removing noise from images The total
variation of the image is minimized subject to constraints involving the statistics of
the noise The constraints are imposed using Lagrange multipliers The solution is
obtained using the gradient-projection method This amounts to solving a time
dependent partial differential equation on a manifold determined by the constraints
As trarrinfin the solution converges to a steady state which is the denoised image
In total variation algorithm the gradients of noisy image g(xy) in four
directions (East West North and South) are calculated The gradients in all four
directions are calculated as follows
( )( ) ( ) ( 1 )N g x y g x y g x ynabla = minus minus (213a)
( )( ) ( 1 ) ( )Sg x y g x y g x ynabla = + minus (213b)
( )( ) ( ) ( 1)W g x y g x y g x ynabla = minus minus (213c)
( )( ) ( 1) ( )E g x y g x y g x ynabla = + minus (213d)
where nabla is the gradient operator
The noisy image undergoes several iterations to suppress AWGN The
resulted output image after (n+1) iterations is expressed as
(214)
( ) ( )( )
( ) ( )( )
( )
1
22
22
( ) ( )
( )
( ) ( ) ( )
( )
( ) ( ) ( )
( ) ( )
n n
n
SN
n n n
S E W
n
EW
n n n
E S N
n n
g x y g x y
g x yt
hg x y m g x y g x y
g x y
g x y m g x y g x y
t g x y g x yλ
+ =
nabla∆
+ nabla nabla + nabla nabla
nabla
+ nabla nabla + nabla nabla
minus ∆ minus
Chapter-2 Study of Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 35
where
( )
( ) min mod( )
sgn sgnmin
2
m a b a b
a ba b
=
+ =
(215)
where
1 0sgn( )
1 0
xx
x
ge=
minus lt (216)
In (214) lsquoλrsquo is a controlling parameter lsquo t∆ rsquo is the discrete time-step and lsquohrsquo is a
constant
A restriction imposed for stability is given by
2
tc
h
∆le (217)
where lsquocrsquo is a constant
The filtered image is then 1ˆ ( ) ( )nf x y g x y
+=
Chapter-2 Study of Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 36
24 Bilateral Filter
The Bilateral filter [70] a nonlinear filter proposed by Tomasi and Manduchi
is used to suppress additive noise from images Bilateral filtering smooths images
while preserving edges by means of a nonlinear combination of nearby image values
The method is noniterative local and simple It combines gray levels or colors based
on both their geometric closeness and their photometric similarity and prefers near
values to distant values
The Bilateral filter kernel w is a product of two sub-kernels (weighing
functions)
(i) photometric (gray-level) kernel wg and
(ii) geometric (distance) kernel wd
The gray-level distance (ie photometric distance) between any arbitrary pixel
of intensity value g(x1 y1) at location (x1 y1) with respect to its center pixel of
intensity value g(x y) at location (x y) is given by
122 2
1 1( ) ( )gd g x y g x y = minus (218)
The photometric or gray-level sub-kernel is expressed by
2
1exp
2
g
g
g
dw
σ
= minus
(219)
where lsquo gσ rsquo is the distribution function for gw
The spatial distance (ie geometric distance) between any arbitrary pixel at a
location (x1 y1) with respect to the center pixel at location (x y) is the Euclidean
distance given by
( ) ( )2 2
1 1sd x x y y= minus + minus (220)
Chapter-2 Study of Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 37
The geometric or distance sub-kernel is defined by
2
1exp
2
sd
d
dw
σ
= minus
(221)
where lsquodσ rsquo is the standard deviation of the distribution function
dw
The kernel for bilateral filter is obtained by multiplying the two sub-kernels
gw and dw
b g dw w w= (222)
The estimated pixel ˆ ( )f x y resulted after sliding the filtering kernel
bw throughout the noisy image is
( ) ( )ˆ ( )
( )
a b
b
s a t b
a b
b
s a t b
w s t g x s y t
f x y
w s t
=minus =minus
=minus =minus
+ +
=sum sum
sum sum (223)
The filter has been used for many applications such as texture removal [71]
dynamic range compression [72] photograph enhancement [7374] It has also been
adapted to other domains such as mesh fairing [7576] volumetric denoising [77] and
exposure corrections of videos [78] The large success of bilateral filter is because of
various reasons such as its simple formulation and implementation The bilateral filter
is also non-iterative ie it achieves satisfying results with only a single pass
Chapter-2 Study of Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 38
25 Non-local Means (NL-Means) Filter
NL-means filter [8889] introduced by Buades et al is based on the natural
redundancy of information in images It is due to the fact that every small window in
a natural image has many similar windows in the same image The property of this
filter is that the similarity of pixels has been more robust to noise by using a region
comparison rather than pixel comparison and also that matching patterns are not
restricted to be local That is the pixels far away from the pixel being filtered are not
penalized
Non-local Means Theory
The NL-Means algorithm assumes that the image contains an extensive
amount of self-similarity Efros and Leung originally developed the concept of self-
similarity for texture synthesis [90] An example of self-similarity is displayed in
Fig 21 It shows three pixels p q1 and q2 and their respective neighborhoods The
neighborhoods of pixels p and q1 are similar but that of p and q2 are dissimilar
Adjacent pixels tend to have similar neighborhoods but non-adjacent pixels will also
have similar neighborhoods when there are similar structures in the image [88] For
example in this figure most of the pixels in the same column as p will have similar
neighborhoods to prsquos neighborhood The self-similarity assumption can be exploited
to denoise an image Pixels with similar neighborhoods can be used to determine the
denoised value of a pixel
Chapter-2 Study of Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 39
Non-local Means Method
Given an image g the filtered value at a point p located at (xy) using the
NL-Means method is calculated as a weighted average of all the pixels in the image
using the following formula
( ) [ ]1 1
1 1
( )
ˆ ( ) ( ) ( ) ( ) ( )x y
f x y NL g x y w x y x y g x yforall
= = sum (224)
[ ] [ ]1 1
1 1 1 1
( )
0 ( ) ( ) 1 ( ) ( ) 1x y
with w x y x y and w x y x yforall
le le =sum (225)
where (x1y1) represents any other image pixel location such as q1 and q2
p
q1
q2
Fig 21 Example of self-similarity in an image
Pixels p and q1 have similar neighborhoods but pixels p and q2
do not have similar neighborhoods Because of this pixel q1 will
have a stronger influence on the denoised value of p than q2
Chapter-2 Study of Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 40
The weights [ ]1 1( )( )w x y x y are based on the similarity between the neighborhoods
of p and any arbitrary pixel q with a user defined radius Rsim The similarity of
[ ]1 1( )( )w x y x y is then calculated as
[ ][ ]1 1
1 1 2
( ) ( )1( ) ( ) exp
p
d x y x yw x y x y
Z h
= minus
(226)
[ ]
1 1
1 1
2( )
( ) ( )expp
x y
d x y x yZ
hforall
= minus
sum (227)
where Zp is the normalizing constant and h is an exponential decay control parameter
The parameter d is a Gaussian weighted Euclidian distance of all the pixels
of each neighborhood
[ ] ( )( ) ( )( )1 1
2
1 1 ( ) ( )
sim
x y x yR
d x y x y G g N g Nσ= minus (228)
N(xy) pixel located at (xy) with its neighborhood
( )1 1x yN any arbitrary pixel located at (x1y1) with its neighborhood
where Gσ is a normalized Gaussian weighting function with zero mean and standard
deviation of σ (usually set to 1) that penalizes pixels far from the center of the
neighborhood window by giving more weight to pixels near the center The center
pixel of the Gaussian weighting window is set to the same value as that of the pixels
at a distance 1 to avoid over-weighting effects
When the pixel to be filtered is compared with itself the self similarity will be very
high which will lead to over-weighting effect To avoid such situation
[ ]( ) ( )w x y x y is calculated as
[ ] ( ) ( )( ) ( ) ( )1 1 1 1( )( ) max w x y x y w x y x y x y x y= forall ne (229)
Chapter-2 Study of Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 41
Non-local Means Parameters
The non-local means algorithm has three parameters The first parameter h is
the weight-decay control parameter which controls where the weights lay on the
decaying exponential curve If h is set too low not enough noise will be removed If
h is set too high the image will become blurred When an image contains white noise
with a standard deviation of σn h should be set between 10 σn and 15 σn [8889]
The second parameter Rsim is the radius of the neighborhoods used to find
the similarity between two pixels If Rsim is too large no similar neighborhoods will
be found but if it is too small too many similar neighborhoods will be found
Common values for Rsim are 3 and 4 to give neighborhoods of size 7times7 and 9times9
respectively [8889]
The third parameter Rwin is the radius of a search window Because of the
inefficiency of taking the weighted average of every pixel for every pixel it will be
reduced to a weighted average of all pixels in a window The window is centered at
the current pixel being computed Common values for Rwin are 7 and 9 to give
windows of size 15times15 and 19times19 respectively [8889]
Non-local means can be applied to other image applications such as non-local
movie denoising [91-93] MRI denoising [9495] image zooming [96] and
segmentation [97]
Chapter-2 Study of Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 42
26 Wavelet-Domain Filters
Wavelet domain filters essentially employs Wavelet Transform (WT) and
hence are named so Fig 22 shows the block schematic of a wavelet-domain filter
Here the filtering operation is performed in the wavelet-domain A brief introduction
to wavelet transform is presented here
261 An Overview of Wavelet Transform
Wavelet transform [18-21] due to its localization property has become an
indispensable signal and image processing tool for a variety of applications including
compression and denoising [98-102] A wavelet is a mathematical function used to
decompose a given function or continuous-time signal into different frequency
components and study each component with a resolution that matches its scale A
wavelet transform is the representation of a function by wavelets The wavelets are
scaled and translated copies (known as daughter wavelets) of a finite length or fast
decaying oscillating waveform (known as mother wavelet) Wavelet transforms are
classified into continuous wavelet transform (CWT) and discrete wavelet transform
(DWT)
The continuous wavelet transform (CWT) [110-13] has received significant
attention for its ability to perform a time-scale analysis of signals On the other hand
the discrete wavelet transform (DWT) is an implementation of the wavelet transform
using a discrete set of wavelet scales and translations obeying some definite rules In
other words this transform decomposes the signals into mutually orthogonal set of
Forward
WT
Filtering Algorithm Inverse
WT
Input
Image
Output
Image
Fig 22 A Wavelet Domain Filter
Chapter-2 Study of Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 43
wavelets The Haar [1] Daubechies[14] Symlets [20] and Coiflets [21] are compactly
supported orthogonal wavelets There are several ways of implementation of DWT
algorithm The oldest and most known one is the Mallat-algorithm or Mallat-tree
decomposition [19] In this algorithm the DWT is computed by successive low-pass
and high-pass filtering of discrete time-domain signal as shown in Fig 23 (a) In this
figure the signal is denoted by the sequence f(n) where n is an integer The low-pass
filter is denoted by G0 while the high-pass filter is denoted by H0 At each level the
high-pass filter produces detailed information d(n) while the low-pass filter
associated with scaling function produces coarse approximations a(n)
The original signal is then obtained by concatenating all the coefficients a(n)
and d(n) starting from the last level of decomposition as shown in Fig 23 (b)
The wavelet decomposition of an image is done as follows In the first level of
decomposition the image is decomposed into four subbands namely HH (high-high)
HL (high-low) LH (low-high) and LL (low-low) subbands The HH subband gives
the diagonal details of the image the HL subband gives the horizontal features while
the LH subband represents the vertical structures The LL subband is low resolution
residual consisting of low frequency components and it is further split at higher levels
of decomposition It is convenient to label the subbands of transform as shown in
Fig 24 In Fig 25 an example of second level of decomposition of Lena image
using Daubechiesrsquo tap-8 (Db-8) wavelet is shown
Chapter-2 Study of Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 44
Fig23 Two-level wavelet Mallat-tree
(a) decomposition
(b) reconstruction
f(n)
d1(n) H0 darr2
G0 darr2
H0 darr2
G0 darr2
a1(n)
d2(n)
a2(n)
(a)
f(n)
d1(n)
H1
darr2 G1
darr2
a1(n)
d2(n)
a2(n)
H1
darr2 G1
darr2
(b)
Chapter-2 Study of Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 45
LL2 HL2
HL1
LH2 HH2
LH1 HH1
Fig24 Subbands of the 2D Wavelet
Transform
Fig25 Two label decomposition of Lena
Image
Chapter-2 Study of Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 46
262 DWT-Domain Filters
Recently a lot of methods have been reported that perform denoising in
DWT-domain [98-106] The transform coefficients within the subbands of a DWT
can be locally modeled as iid (independent identically distributed) random variables
with generalized Gaussian distribution Some of the denoising algorithms perform
thresholding of the wavelet coefficients which have been affected by additive white
Gaussian noise by retaining only large coefficients and setting the rest to zero These
methods are popularly known as shrinkage methods However their performance is
not quite effective as they are not spatially adaptive Some other methods evaluate the
denoised coefficients by an MMSE (Minimum Mean Square Error) estimator in
terms of the noised coefficients and the variances of signal and noise The signal
variance is locally estimated by a ML (Maximum Likelihood) estimator in small
regions for every subband where variance is assumed practically constant These
methods present effective results but their spatial adaptivity is not well suited near
object edges where the variance field is not smoothly varied Further these methods
introduce artifacts in the smooth regions of the output image Some efficient wavelet-
domain filters are discussed in subsequent sub-sections
263 VisuShrink
VisuShrink [99] is thresholding by applying universal threshold [98] proposed
by Dohono and Johnston This threshold is given by
2 logU nT Lσ= (230)
where 2
nσ is the noise variance of AWGN and L is the total number of pixels in an
image
It is proved in [99] that a large fraction of any L number of random data array with
zero mean and variance 2
nσ will be smaller than the universal threshold TU with high
probability the probability approaching 1 as L increases Thus with high probability
a pure noise signal is estimated as being identically zero Therefore for denoising
applications VisuShrink is found to yield a highly smoothed estimate This is because
the universal threshold is derived under the constraint that with high probability the
Chapter-2 Study of Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 47
estimate should be at least as smooth as the signal So the TU tends to be high for large
values of L killing many signal coefficients along with the noise Thus the threshold
does not adapt well to discontinuities in the signal
264 SureShrink
SureShrink [100101] is an adaptive thresholding method where the wavelet
coefficients are treated in level-by-level fashion In each level when there is
information that the wavelet representation of that level is not sparse a threshold that
minimizes Steinrsquos unbiased risk estimate (SURE) is applied SureShrink is used for
suppression of additive noise in wavelet-domain where a threshold TSURE is employed
for denoising The threshold parameter TSURE is expressed as
( )arg min ( hSURE T hT SURE T Y= (231)
SURE(TY) is defined by
( )22 2
1
1( ) 2 min
L
h n n i h i h
i
SURE T Y i Y T Y TL
σ σ=
= minus times le minus
sum (232)
where 2
nσ is the noise variance of AWGN
L is the total number of coefficients in a particular subband
Yi is a wavelet coefficient in the particular subband
[ ]0h UT Tisin TU is Donohorsquos universal threshold
265 BayesShrink
In BayesShrink [102] an adaptive data-driven threshold is used for image
denoising The wavelet coefficients in a sub-band of a natural image can be
represented effectively by a generalized Gaussian distribution (GGD) Thus a
threshold is derived in a Bayesian framework as
2ˆ
ˆn
B
F
Tσ
σ= (233)
Chapter-2 Study of Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 48
where 2ˆnσ is the estimated noise variance of AWGN by robust median estimator and
ˆF
σ is the estimated signal standard deviation in wavelet-domain
The robust median estimator is stated as
( )
1ˆ
06745
ij
n ij
Median YY subband HHσ = isin (234)
This estimator is used when there is no a priori knowledge about the noise variance
The estimated signal standard deviation is calculated as
( )2 2ˆ ˆ ˆmax ( )0F Y nσ σ σ= minus (235)
where 2ˆYσ is the variance of Y Since Y is modeled as zero-mean 2ˆ
Yσ can be found
empirically by
2 2
2 1
1ˆ
n
Y i j
i j
Yn
σ=
= sum (236)
In case 2 2ˆ ˆn Y
σ σge ˆF
σ will become 0 That is B
T becomesinfin Hence for this case
( )maxB ijT Y=
266 OracleShrink and OracleThresh
OracleShrink and OracleThresh [102] are two wavelet thresholding methods
used for image denoising These methods are implemented with the assumption that
the wavelet coefficients of original decomposed image are known The OracleShrink
and OracleThresh employ two different thresholds denoted as TOS and TOT
respectively Mathematically they are represented by
( )2
1
arg min ( )h
h
n
OS T ij ijT
i j
T Y Fξ=
= minussum (237)
Chapter-2 Study of Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 49
( )2
1
arg min ( )h
h
n
OT T ij ijT
i j
T Y Fζ=
= minussum (238)
where with Fij are the wavelet coefficient of original decomposed image
and ( )hTξ i and ( )
hTζ i are soft-thresholding and hard-thresholding functions defined
as
( )( ) sgn( ) max 0T x x x Tξ = minus (239)
and
( ) T
x x x Tζ = gt1 (240)
which keeps the input if it is larger than the threshold T otherwise it is set to zero
267 NeighShrink
Chen et al proposed a wavelet-domain image thresholding scheme by
incorporating neighboring coefficients namely NeighShrink [103] The method
NeighShrink thresholds the wavelet coefficients according to the magnitude of the
squared sum of all the wavelet coefficients ie the local energy within the
neighborhood window The neighborhood window size may be 3times3 5times5 7times7 9times9
etc But the authors have already demonstrated through the results that the 3times3
window is the best among all window sizes []
The shrinkage function for NeighShrink of any arbitrary 3times3 window
centered at (ij) is expressed as
2
21 U
ij
ij
T
S+
Γ = minus
(241)
where UT is the universal threshold and 2
ijS is the squared sum of all wavelet
coefficients in the respective 3times3 window given by
1 12 2
1 1
j i
ij m n
n j m i
S Y+ +
= minus = minus
= sum sum (242)
Chapter-2 Study of Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 50
Here + sign at the end of the formula means to keep the positive values while setting
it to zero when it is negative
The estimated center wavelet coefficient ˆij
F is then calculated from its noisy
counterpart ijY as
ˆij ij ijF Y= Γ (243)
268 SmoothShrink
Mastriani et al proposed SmoothShrink [104] wavelet-domain image
denoising method for images corrupted with speckle noise It employs a convolution
kernel based on a directional smoothing (DS) function applied on the wavelet
coefficients of the noisy decomposed image The size of the window may vary from
3times3 to 33times33 but the studies [104] show that the 3times3 window gives better result as
compared to others Though this approach is meant for speckle noise it is observed
that it works satisfactorily even for additive noise Therefore the method
SmoothShrink is stated here
SmoothShrink Algorithm
Step-1
The average of the wavelet coefficients in four directions (d1 d2 d3 d4) as shown in
Fig 24 is calculated
d1
d2
d3
d4
Fig 26 A 3times3 directional smoothing window showing four directions d1 d2 d3 d4
Chapter-2 Study of Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 51
Step-2
The absolute difference between the center wavelet coefficient and each directional
average is calculated as
1 23 4nn d ijd Y Y n∆ = minus = (244)
where ndY = average of wavelet coefficients in n
th direction
Step-3
The directional average which gives minimum absolute difference is found out
( )arg mindn
nY
d= ∆K (245)
Step-4
The estimated center wavelet coefficient is therefore replaced with the minimum
directional average obtained in Step-3 ie
ˆijF =K (246)
The SmoothShrink algorithm is applied to all subbands of noisy decomposed image
except the LL subband
269 LAWML
Mihcak et al [105] proposed a simple spatially adaptive statistical model for
wavelet coefficients and applied it to image denoising The resulting method for
image denoising is called as locally adaptive window based denoising using maximum
likelihood (LAWML) The size of the window used in the method may be 3times3 5times5
7times7 etc In this method the variance of original decomposed image of a particular
window in a given sub-band is estimated using maximum likelihood (ML) estimator
The ML estimator can be mathematically expressed as
( )2
2 2
0( )
2 2
( )
ˆ ( ) arg max ( )
1max 0 ( )
j N k
n
j N k
k P Y j
Y jL
σσ σ
σ
geisin
isin
=
= minus
prod
sum (247)
Chapter-2 Study of Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 52
where ( )2P σ is the Gaussian distribution with zero mean and variance 2 2
nσ σ+ L is
the number of coefficients in N(k) and 2
nσ is the noise variance of AWGN
The estimated wavelet coefficient of original decomposed image is calculated by
using minimum mean squared error (MMSE) estimator [106]
Thus the estimated wavelet coefficient is calculated by the MMSE estimator given
by
2
2 2
ˆ ( )ˆ ( ) ( )ˆ ( ) n
kF k Y k
k
σ
σ σ= sdot
+ (248)
27 Simulation Results
The existing spatial-domain filters Mean Median Alpha-trimmed-mean
(ATM) Wiener Lee Anisotropic Diffusion (AD) Total Variation (TV) Bilateral
Non-local means and existing wavelet-domain filters VisuShrink SureShrink
BayesShrink OracleShrink NeighShrink SmoothShrink locally adaptive window
maximum likelihood (LAWML) are simulated on MATLAB 70 platform The test
images Lena Pepper Goldhill and Barbara of sizes 512times512 corrupted with AWGN
of standard deviation σn = 5 10 15 20 25 30 35 40 45 and 50 are used for
simulation purpose The peak-signal-to-noise ratio (PSNR) root-mean-squared error
(RMSE) universal quality index (UQI) and method noise and execution time are
taken as performance measures
The PSNR values of the different filters for various images are given in the
tables Table-21 to Table-24 The highest (best) PSNR value for a particular standard
deviation of Gaussian noise is highlighted to show the best performance
The RMSE values of different filters are given in the tables Table-25 to
Table-28 The smallest (best) RMSE value for a particular standard deviation of
Gaussian noise is highlighted for analysis
Chapter-2 Study of Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 53
The UQI of various filters are given in the tables Table-29 to Table-212 The
value of UQI is always less than 1 The highest (best) value of UQI for a particular
standard deviation of Gaussian noise is identified and is highlighted for analysis
The method noise of the various filters is shown in Table-213 The filtering
performance is better if the method noise is very low since it talks of little distortion
when a non-noisy image is passed through a filter Therefore a least value of method
noise for a particular noise standard deviation is highlighted to show the best
performance
The execution time of the different filters is given in Table-214 The filter
having less execution time is usually required for online and real-time applications
The least value of execution time is highlighted
Fig 27 Fig28 and Fig 29 illustrate the resulting performance measures
(PSNR RMSE and UQI) of some high performing filters (Mean ATM BayesShrink
NeighShrink and LAWML) under different noise conditions for various test images
The best performance value for a particular standard deviation of AWGN irrespective
of window size of a filter is taken in the figures These figures based on Table-21 ndash
Table-212 are given for ease of analysis
For subjective evaluation the filtered output images of various filters are
shown in the figures Fig 210 to Fig 217 The images corrupted with AWGN of
standard deviation σn = 15 (moderate-noise) and σn = 40 (high-noise) are applied to
different filters and the resulted output images are shown in these figures
Chapter-2 Study of Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 54
Table-21 Filtering performance of various filters in terms of PSNR (dB) operated on Lena
image under various noise conditions (σn varies from 5 to 50)
Peak-Signal-to-Noise Ratio PSNR (dB) Standard deviation of AWGN
SlNo Denoising Filters 5 10 15 20 25 30 35 40 45 50
Test Image Lena
1 Mean [3times3] 3388 3270 3127 2978 2848 2728 2626 2530 2445 2362
2 Mean [5times5] 2977 2959 2931 2892 2848 2805 2748 2696 2649 2593
3 Mean [7times7] 2766 2760 2750 2737 2721 2701 2677 2649 2623 2589
4 Median [3times3] 3498 3216 2985 2794 2636 2498 2377 2277 2175 2094
5 Median [5times5] 3170 3074 2978 2875 2781 2684 2608 2526 2453 2382
6 Median [7times7] 2960 2917 2865 2813 2758 2699 2644 2601 2545 2496
7 ATM [3times3] 3396 3271 3126 2983 2844 2724 2607 2503 2408 2322
8 ATM [5times5] 2977 2959 2932 2893 2850 2807 2752 2703 2647 2586
9 ATM [7times7] 2788 2759 2752 2741 2728 2713 2689 2666 2641 2613
10 Wiener [3times3] 3788 3401 3137 2915 2738 259 2462 2356 2267 2186
11 Wiener [5times5] 3657 3294 3147 3019 2900 2796 2699 2613 2543 2469
12 Wiener [7times7] 3578 3154 3046 2944 2857 2778 2715 2655 2593 2534
13 AD 3468 3137 3037 2927 2821 2722 2628 2540 2465 2393
14 TV 3549 3322 3170 3025 2901 2785 2677 2585 2492 2412
15 Lee [3times3] 3787 3345 3077 2878 2734 2604 2497 2411 2331 2268
16 Lee [5times5] 3755 3347 3129 2974 2866 2770 2707 2641 2578 2534
17 Lee [7times7] 3712 3304 3091 2952 2857 2784 2728 2677 2630 2595
18 Bilateral [3times3] 3370 3258 3120 2977 2848 2727 2621 2531 2447 2368
19 Bilateral [5times5] 3276 2914 2888 2855 2813 2772 2727 2671 2622 2573
20 Bilateral [7times7] 3109 2662 2655 2643 2630 2613 2589 2573 2547 2519
21 NL-Means 3787 3443 2943 2553 2291 2097 1947 1828 1729 1636
22 VisuShrink 3165 3056 2960 2875 2791 2678 2541 2395 2257 2148
23 SureShrink 2980 2961 2928 2882 2839 2793 2745 2701 2664 2621
24 BayesShrink 3747 3364 3158 3020 2918 2840 2777 2711 2664 2607
25 OracleShrink 3613 3170 2880 2651 2452 2290 2148 2021 1910 1815
26 OracleThresh 3534 2997 2645 2385 2183 2013 1865 1741 1631 1542
27 NeighShrink 3870 3445 3197 3011 2880 2769 2676 2608 2542 2497
28 SmoothShrink 3234 3041 2893 2743 2606 2488 2381 2289 2203 2131
29 LAWML [3times3] 3839 3413 3161 2978 2847 2741 2648 2572 2508 2458
30 LAWML [5times5] 3860 3459 3226 3066 2941 2853 2774 2709 2656 2602
31 LAWML [7times7] 3853 3458 3234 3086 2969 2884 2800 2741 2689 2638
Chapter-2 Study of Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 55
Table-22 Filtering performance various filters in terms of PSNR (dB) operated on Pepper
image under various noise conditions (σn varies from 5 to 50)
Peak-Signal-to-Noise Ratio PSNR (dB) Standard deviation of AWGN
SlNo Denoising Filters 5 10 15 20 25 30 35 40 45 50
Test Image Pepper
1 Mean [3times3] 3190 3116 3015 2899 2788 2682 2586 2495 2415 2345
2 Mean [5times5] 3061 3039 3001 2955 2902 2840 2781 2722 2656 2601
3 Mean [7times7] 2862 2855 2841 2818 2793 2771 2732 2696 2658 2618
4 Median [3times3] 3555 3257 3010 2813 2648 2510 2388 2279 2184 2102
5 Median [5times5] 3423 3276 3130 2996 2872 2764 2665 2568 2493 2419
6 Median [7times7] 3319 3162 3075 2987 2900 2823 2748 2678 2620 2562
7 ATM [3times3] 3233 3174 3058 2932 2810 2694 2582 2483 2398 2312
8 ATM [5times5] 3112 3067 3038 2993 2940 2885 2818 2757 2688 2632
9 ATM [7times7] 2901 2876 2869 2858 2841 2819 2782 2756 2724 2687
10 Wiener [3times3] 3811 3445 3177 2944 2756 2599 2467 2356 2267 2185
11 Wiener [5times5] 3767 3382 3216 3074 2941 2818 2714 2619 2534 2460
12 Wiener [7times7] 3598 3252 3125 3008 2906 2815 2736 2658 2590 2526
13 AD 3348 3068 2979 2881 2782 2685 2597 2511 2436 2361
14 TV 3358 3121 3013 2908 2803 2710 2613 2531 2445 2376
15 Lee [3times3] 3789 3369 3105 2903 2740 2608 2502 2412 2334 2271
16 Lee [5times5] 3777 3391 3177 3028 2902 2805 2727 2656 2594 2547
17 Lee [7times7] 3728 3345 3138 3003 2903 2821 2757 2702 2651 2609
18 Bilateral [3times3] 3176 3107 3006 2897 2785 2683 2584 2497 2420 2348
19 Bilateral [5times5] 3088 2981 2950 2910 2863 2811 2756 2697 2641 2592
20 Bilateral [7times7] 2996 2736 2724 2712 2692 2672 2640 2616 2590 2552
21 NL-Means 3796 3462 2958 2568 2302 2114 1963 1843 1736 1651
22 VisuShrink 2794 2740 2667 2587 2534 2475 2401 2321 2233 2137
23 SureShrink 2671 2667 2658 2642 2625 2596 2564 2529 2496 2454
24 BayesShrink 3743 3369 3145 2990 2898 2824 2745 2669 2598 2505
25 OracleShrink 3648 3200 2895 2666 2474 2307 2163 2040 1930 1835
26 OracleThresh 3532 3017 2694 2450 2236 2044 1889 1762 1654 1564
27 NeighShrink 3829 3437 3194 3017 2868 2755 2652 2578 2509 2451
28 SmoothShrink 2672 2588 2452 2319 2190 2079 1974 1882 1803 1728
29 LAWML [3times3] 3837 3428 3181 3003 2861 2738 2641 2565 2501 2447
30 LAWML [5times5] 3877 3464 3246 3084 2952 2843 2754 2679 2610 2560
31 LAWML [7times7] 3842 3463 3245 3088 2967 2857 2767 2695 2621 2575
Chapter-2 Study of Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 56
Table-23 Filtering performance of various filters in terms of PSNR (dB) operated on Goldhill
image under various noise conditions (σn varies from 5 to 50)
Peak-Signal-to-Noise Ratio PSNR (dB) Standard deviation of AWGN
SlNo Denoising Filters 5 10 15 20 25 30 35 40 45 50
Test Image Goldhill
1 Mean [3times3] 3154 3082 2983 2877 2769 2666 2573 2483 2401 2332
2 Mean [5times5] 2815 2802 2779 2748 2713 2669 2625 2574 2525 2477
3 Mean [7times7] 2648 2644 2634 262 2607 2583 2556 2525 2495 2453
4 Median [3times3] 3376 3044 2878 2722 2590 2467 2361 2265 2177 2102
5 Median [5times5] 3077 2860 2796 2732 2663 2595 2532 2466 2401 2343
6 Median [7times7] 2934 2729 2695 2662 2619 2578 2543 2499 2467 2420
7 ATM [3times3] 3188 3081 2980 2869 2760 2655 2556 2462 2377 2298
8 ATM [5times5] 2912 2803 2782 2757 2721 2685 2648 2605 2557 2515
9 ATM [7times7] 2702 2645 2638 2629 2616 2603 2586 2568 2546 2521
10 Wiener [3times3] 3663 3235 3041 2859 2696 2562 2441 2332 2247 2162
11 Wiener [5times5] 3488 3043 2956 2867 2776 2688 2600 2517 2445 2368
12 Wiener [7times7] 3299 2887 2831 2767 2708 2651 2589 2526 2471 2407
13 AD 3307 2988 2913 2827 2738 2650 2565 2483 2406 2340
14 TV 3311 3130 3019 2913 2809 2716 2627 2541 2462 2378
15 Lee [3times3] 3660 3238 3003 2831 2696 2586 2485 2398 2321 2258
16 Lee [5times5] 3629 3200 2995 2859 2765 2687 2612 2549 2493 2451
17 Lee [7times7] 3598 3156 2948 2822 2732 2662 2605 2559 2515 2469
18 Bilateral [3times3] 3144 3073 2977 2867 2763 2663 2567 2483 2399 2325
19 Bilateral [5times5] 3017 2772 2749 2720 2683 2639 2597 2550 2498 2451
20 Bilateral [7times7] 2913 2575 2564 2550 2532 2512 2485 2462 2427 2400
21 NL-Means 3659 3293 2892 2561 2310 2126 1980 1860 1759 1668
22 VisuShrink 2971 2864 2778 2693 2591 2484 2370 2247 2135 2026
23 SureShrink 2744 2738 2718 2690 2660 2623 2589 2545 2512 2462
24 BayesShrink 3648 3234 3020 2868 2750 2654 2582 2517 2458 2409
25 OracleShrink 3302 2945 2707 2547 2416 2293 2182 2087 2000 1921
26 OracleThresh 3371 2914 2656 2455 2293 2158 2030 1919 1818 1724
27 NeighShrink 3737 3305 3063 2902 2779 2675 2595 2527 2465 2411
28 SmoothShrink 2813 2681 2522 2372 2237 2119 2013 1916 1837 1762
29 LAWML [3times3] 3655 3278 3037 2877 2742 2644 2558 2477 2420 2361
30 LAWML [5times5] 3722 3302 3078 2920 2803 2710 2629 2556 2492 2443
31 LAWML [7times7] 3689 3302 3078 2927 2811 2724 2640 2573 2511 2443
Chapter-2 Study of Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 57
Table-24 Filtering performance of various filters in terms of PSNR (dB) operated on Barbara
image under various noise conditions (σn varies from 5 to 50)
Peak-Signal-to-Noise Ratio PSNR (dB) Standard deviation of AWGN
SlNo Denoising Filters 5 10 15 20 25 30 35 40 45 50
Test Image Barbara
1 Mean [3times3] 2652 2602 2568 2525 2475 2419 2364 2306 2250 2195
2 Mean [5times5] 2381 2376 2368 2357 2343 2325 2304 2284 2256 2231
3 Mean [7times7] 2353 2351 2347 2341 2332 2321 2307 2292 2275 2253
4 Median [3times3] 2766 2585 2509 2431 2352 2276 2202 2133 2062 1998
5 Median [5times5] 2476 2326 2314 2296 2277 2249 2219 2190 2157 2121
6 Median [7times7] 2411 2354 2344 2331 2317 2298 2275 2258 2235 2214
7 ATM [3times3] 3199 3081 2980 2869 2760 2655 2556 2462 2377 2298
8 ATM [5times5] 2906 2803 2782 2757 2721 2685 2648 2605 2557 2515
9 ATM [7times7] 2734 2645 2638 2629 2616 2603 2586 2568 2546 2521
10 Wiener [3times3] 3657 3167 2865 2921 2750 2606 2489 2390 2297 2213
11 Wiener [5times5] 3478 2831 2743 2653 2570 2499 2432 2366 2309 2255
12 Wiener [7times7] 3319 2738 2673 2604 2545 2489 2434 2384 2337 2293
13 AD 2859 2606 2575 2535 2488 2437 2386 2330 2278 2226
14 TV 2749 2647 2599 2548 2494 2442 2388 2333 2281 2231
15 Lee [3times3] 3654 3159 2890 2705 2568 2462 2369 2291 2223 2166
16 Lee [5times5] 3621 3156 2896 2732 2613 2517 2436 2378 2326 2277
17 Lee [7times7] 3609 3130 2880 2722 2610 2528 2464 2406 2358 2319
18 Bilateral [3times3] 2622 2601 2567 2524 2474 2420 2365 2308 2253 2199
19 Bilateral [5times5] 2603 2369 2361 2351 2337 2320 2300 2279 2257 2229
20 Bilateral [7times7] 2558 2317 2314 2308 2301 2293 2280 2267 2252 2231
21 NL-Means 3688 3259 2868 2540 2301 2124 1974 1858 1752 1667
22 VisuShrink 2661 2572 2475 2391 2325 2261 2199 2135 2074 1989
23 SureShrink 2434 2430 2423 2412 2397 2380 2358 2333 2312 2286
24 BayesShrink 3591 3138 2904 2748 2634 2539 2453 2368 2311 2271
25 OracleShrink 3101 2628 2507 2442 2384 2325 2256 2188 2115 2044
26 OracleThresh 3403 2743 2519 2376 2229 2095 1983 1880 1787 1708
27 NeighShrink 3750 3292 3033 2857 2725 2611 2527 2455 2385 2326
28 SmoothShrink 2767 2587 2453 2319 2197 2084 1982 1892 1809 1739
29 LAWML [3times3] 3713 3257 3002 2821 2687 2581 2491 2419 2352 2295
30 LAWML [5times5] 3727 3278 3030 2865 2742 2642 2560 2483 2421 2371
31 LAWML [7times7] 3716 3276 3029 2865 2744 2647 2566 2494 2433 2378
Chapter-2 Study of Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 58
Table-25 Filtering performance of various filters in terms of RMSE operated on a Lena image
under various noise conditions (σn varies from 5 to 50)
Root-Mean-Squared Error (RMSE) Standard deviation of AWGN
SlNo Denoising Filters 5 10 15 20 25 30 35 40 45 50
Test Image Lena
1 Mean [3times3] 515 590 696 827 960 1102 1240 1385 1527 1680
2 Mean [5times5] 828 845 873 913 960 1009 1077 1144 1207 1288
3 Mean [7times7] 1055 1063 1075 1091 1111 1137 1169 1207 1244 1294
4 Median [3times3] 454 627 818 1020 1224 1435 1649 1851 2083 2287
5 Median [5times5] 663 7395 826 930 1035 1157 1264 1389 1512 1642
6 Median [7times7] 844 884 940 999 1063 1139 1213 1275 1359 1438
7 ATM [3times3] 511 589 696 821 9639 1106 1267 1428 1593 1759
8 ATM [5times5] 828 844 869 910 9562 1004 1071 1134 1208 1298
9 ATM [7times7] 1029 1063 1071 1086 1101 1122 1152 1183 1218 1257
10 Wiener [3times3] 325 507 688 887 1088 1290 1496 1690 1874 2057
11 Wiener [5times5] 378 573 678 787 902 1017 1139 1257 1364 1484
12 Wiener [7times7] 414 673 762 859 948 1040 1119 1198 1287 1377
13 AD 470 688 772 874 989 1109 1236 1369 1491 1621
14 TV 428 555 663 782 902 1032 1167 1298 1445 1586
15 Lee [3times3] 325 540 736 925 1094 1269 1438 1588 1741 1871
16 Lee [5times5] 338 540 693 828 938 1050 1129 1218 1310 1377
17 Lee [7times7] 355 566 724 851 948 1032 1101 1167 1234 1285
18 Bilateral [3times3] 526 596 701 826 958 1104 1247 1382 1522 1667
19 Bilateral [5times5] 586 889 915 951 999 1048 1104 1175 1244 1318
20 Bilateral [7times7] 711 1188 1198 1213 1234 1257 1292 1300 1356 1402
21 NL-Means 325 481 859 1349 1823 2279 2708 3108 3483 3876
22 VisuShrink 666 756 844 931 1025 1168 1367 1618 1896 2150
23 SureShrink 825 843 876 923 970 1023 1081 1137 1187 1247
24 BayesShrink 341 530 672 788 886 969 1042 1124 1187 1267
25 OracleShrink 398 663 925 1205 1515 1826 2150 2489 2828 3155
26 OracleThresh 436 809 1213 1637 2065 2512 2978 3435 3899 4320
27 NeighShrink 296 483 642 796 925 1052 1171 1266 1366 1438
28 SmoothShrink 615 769 912 1084 1269 1453 1644 1828 2018 2193
29 LAWML [3times3] 306 501 669 827 961 1086 1209 1319 1420 1505
30 LAWML [5times5] 299 474 621 747 863 955 1046 1127 1198 1275
31 LAWML [7times7] 302 475 615 730 835 921 1015 1086 1153 1223
Chapter-2 Study of Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 59
Table-26 Filtering performance of various filters in terms of RMSE operated on Pepper image
under various noise conditions (σn varies from 5 to 50)
Root-Mean-Squared Error (RMSE) Standard deviation of AWGN
SlNo Denoising Filters 5 10 15 20 25 30 35 40 45 50
Test Image Pepper
1 Mean [3times3] 647 705 792 905 1029 1162 1298 1442 1581 1714
2 Mean [5times5] 751 770 805 849 902 969 1037 1110 1198 1276
3 Mean [7times7] 945 952 968 994 1023 1049 1097 1144 1195 1251
4 Median [3times3] 425 599 795 999 1208 1415 1629 1848 2063 2267
5 Median [5times5] 495 586 693 808 933 1055 1185 1326 14433 1573
6 Median [7times7] 558 668 739 818 902 986 1076 1167 1247 1333
7 ATM [3times3] 616 657 752 869 1002 1145 1303 1461 16116 1779
8 ATM [5times5] 708 744 770 810 861 918 991 1065 1152 1231
9 ATM [7times7] 903 928 935 948 966 991 1035 1065 1106 1155
10 Wiener [3times3] 316 481 655 859 1065 1275 1489 1690 18743 2060
11 Wiener [5times5] 333 517 627 739 861 991 1119 1249 1377 1499
12 Wiener [7times7] 405 601 696 798 897 997 1091 1193 12903 1389
13 AD 540 744 823 923 1035 1157 1280 1415 15428 1680
14 TV 534 701 793 895 1009 1124 1257 1382 15275 1652
15 Lee [3times3] 325 525 714 900 1086 1264 1430 1586 1734 1864
16 Lee [5times5] 329 512 655 780 902 1007 1104 1195 12852 1356
17 Lee [7times7] 348 540 685 803 900 989 1065 1134 12036 1264
18 Bilateral [3times3] 658 711 800 907 1032 1160 1300 1438 15708 1706
19 Bilateral [5times5] 728 823 851 892 943 1002 1065 1142 12189 1287
20 Bilateral [7times7] 810 1091 1106 1122 1149 1175 1220 1254 12903 1349
21 NL-Means 322 471 846 1326 1800 2236 2659 3054 34553 3809
22 VisuShrink 1022 1088 1183 1297 1378 1475 1607 1762 1951 2177
23 SureShrink 1177 1183 1195 1217 1241 1283 1332 1386 1440 1512
24 BayesShrink 342 527 682 815 906 987 1081 1180 1281 1425
25 OracleShrink 382 640 910 1184 1477 1790 2113 2435 2764 3083
26 OracleThresh 437 790 1146 1518 1943 2424 2897 3353 3797 4212
27 NeighShrink 310 487 644 790 938 1069 1203 1310 1419 1517
28 SmoothShrink 1174 1295 1515 1766 2049 2328 2627 2921 3199 3487
29 LAWML [3times3] 307 492 654 803 946 1090 1219 1330 1432 1524
30 LAWML [5times5] 293 472 607 732 852 966 1070 1166 1263 1338
31 LAWML [7times7] 305 473 608 728 837 950 1054 1145 1247 1315
Chapter-2 Study of Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 60
Table-27 Filtering performance of various filters in terms of RMSE operated on Goldhill image
under various noise conditions (σn varies from 5 to 50)
Root-Mean-Squared Error (RMSE) Standard deviation of AWGN
SlNo Denoising Filters 5 10 15 20 25 30 35 40 45 50
Test Image Goldhill
1 Mean [3times3] 675 733 822 929 1052 1184 1318 1462 1607 1740
2 Mean [5times5] 997 1012 1041 1077 1122 1180 1241 1316 1393 1472
3 Mean [7times7] 1209 1214 1229 1248 1267 1303 1344 1393 1442 1513
4 Median [3times3] 523 765 925 1109 1290 1489 1680 1879 2078 2267
5 Median [5times5] 737 946 1017 1096 1188 1285 1382 1489 1606 1716
6 Median [7times7] 870 1101 1145 1188 1249 1310 1364 1433 1489 1570
7 ATM [3times3] 649 734 823 935 1060 1198 1343 1496 1649 1807
8 ATM [5times5] 892 1009 1035 1065 1111 1157 1208 1269 1341 1407
9 ATM [7times7] 1136 1211 1221 1234 1254 1272 1298 1326 1359 1397
10 Wiener [3times3] 375 614 767 946 1142 1333 1532 1739 1917 2114
11 Wiener [5times5] 459 765 846 938 1042 1152 1277 1405 1527 1667
12 Wiener [7times7] 571 918 979 1053 1127 1203 1292 1389 1481 1593
13 AD 566 816 889 981 1088 1206 1328 1461 1596 1723
14 TV 563 693 787 889 1004 1116 1236 1366 1496 1649
15 Lee [3times3] 377 612 803 979 1142 1298 1458 1611 1762 1894
16 Lee [5times5] 390 640 810 946 1055 1155 1259 1354 1443 1514
17 Lee [7times7] 405 673 854 989 1096 1188 1269 1338 1407 1484
18 Bilateral [3times3] 683 739 826 938 1058 1188 1326 1461 1609 1751
19 Bilateral [5times5] 790 1048 1076 1111 1160 1221 1280 1351 1435 1514
20 Bilateral [7times7] 891 1313 1331 1351 1382 1414 1458 1496 1558 1606
21 NL-Means 377 573 892 1336 1782 2203 2601 2993 3363 3735
22 VisuShrink 833 943 1041 1148 1291 1460 1665 1918 2182 2474
23 SureShrink 1082 1090 1115 1152 1192 1244 1294 1361 1414 1498
24 BayesShrink 382 615 788 938 1075 1201 1304 1406 1505 1592
25 OracleShrink 569 859 1129 1358 1579 1819 2068 2307 255 2792
26 OracleThresh 526 890 1198 1510 1819 2125 2463 2799 3144 3503
27 NeighShrink 345 567 749 902 1041 1172 1285 1390 1492 1588
28 SmoothShrink 1000 1164 1398 1661 1941 2223 2512 2808 3076 3353
29 LAWML [3times3] 379 585 772 929 1085 1214 1341 1472 1572 1682
30 LAWML [5times5] 351 569 737 884 1011 1126 1236 1344 1447 1531
31 LAWML [7times7] 364 569 737 877 1002 1108 1220 1318 1415 1531
Chapter-2 Study of Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 61
Table-28 Filtering performance of various filters in terms of RMSE operated on Barbara image
under various noise conditions (σn varies from 5 to 50)
Root-Mean-Squared Error (RMSE) Standard deviation of AWGN
SlNo Denoising Filters 5 10 15 20 25 30 35 40 45 50
Test Image Barbara
1 Mean [3times3] 1203 1275 1326 1393 1475 1574 1677 1792 1912 2037
2 Mean [5times5] 1644 1654 1669 1690 1718 1754 1797 1838 1899 1954
3 Mean [7times7] 1698 1702 1710 1722 1741 1762 1790 1822 1858 1905
4 Median [3times3] 1055 1298 1417 1550 1698 1853 2019 2187 2374 2555
5 Median [5times5] 1474 1751 1774 1813 1851 1912 1981 2047 2126 2216
6 Median [7times7] 1588 1695 1713 1741 1769 1807 1856 1894 1943 1991
7 ATM [3times3] 641 734 823 935 1060 1198 1343 1496 1649 1807
8 ATM [5times5] 898 1009 1035 1065 1111 1157 1208 1269 1341 1407
9 ATM [7times7] 1095 1211 1221 1234 1254 1272 1298 1326 1359 1397
10 Wiener [3times3] 378 527 940 882 1073 1267 1450 1626 1810 1994
11 Wiener [5times5] 465 979 1083 1201 1320 1433 1550 1672 1785 1899
12 Wiener [7times7] 558 1088 1173 1269 1359 1450 1545 1637 1728 1818
13 AD 948 1267 1313 1377 1453 1540 1634 1741 1851 1963
14 TV 1076 1208 1277 1356 1443 1532 1629 1736 1843 1953
15 Lee [3times3] 379 670 912 1132 1326 1496 1665 1823 1971 2106
16 Lee [5times5] 394 673 907 1096 1257 1405 1542 1649 1751 1851
17 Lee [7times7] 399 693 925 1109 1262 1387 1494 1596 1688 1764
18 Bilateral [3times3] 1246 1275 1326 1394 1476 1570 1672 1787 1904 2027
19 Bilateral [5times5] 1273 1665 1680 1700 1728 1762 1802 1848 1894 1958
20 Bilateral [7times7] 1341 1769 1774 1787 1802 1818 1846 1874 1907 1953
21 NL-Means 365 596 938 1369 1802 2208 2626 3001 3391 3740
22 VisuShrink 1191 1319 1475 1625 1754 1888 2027 2182 2341 2582
23 SureShrink 1547 1554 1566 1586 1614 1646 1688 1738 1780 1834
24 BayesShrink 408 687 900 1077 1229 1371 1513 1669 1782 1866
25 OracleShrink 717 1237 1422 1533 1638 1754 1899 2053 2233 2424
26 OracleThresh 507 1084 1402 1654 1959 2285 2600 2927 3258 3568
27 NeighShrink 340 576 776 950 1106 1261 1390 1510 1637 1752
28 SmoothShrink 1054 1297 1513 1766 2032 2314 2603 2887 3177 3443
29 LAWML [3times3] 354 599 804 990 1156 1306 1448 1574 1700 1815
30 LAWML [5times5] 349 585 779 941 1085 1217 1338 1462 1570 1663
31 LAWML [7times7] 353 586 779 941 1082 1210 1329 1443 1549 1650
Chapter-2 Study of Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 62
Table-29 Filtering performance of various filters in terms of UQI operated on a Lena image
under various noise conditions (σn varies from 5 to 50)
Universal Quality Index (UQI) Standard deviation of AWGN
SlNo Denoising Filters 5 10 15 20 25 30 35 40 45 50
Test Image Lena
1 Mean [3times3] 09941 09922 09892 09849 09797 09732 09663 09579 09488 09376
2 Mean [5times5] 09845 09838 09827 09811 09791 09769 09736 09700 09665 09613
3 Mean [7times7] 09743 09739 09733 09725 09714 09701 09683 09659 09636 09601
4 Median [3times3] 09955 09913 09853 09773 09676 09559 09425 09286 09117 08951
5 Median [5times5] 09903 09878 09848 09808 09762 09703 09648 09577 09503 09419
6 Median [7times7] 09841 09824 09801 09775 09745 09709 09669 09636 09585 09539
7 ATM [3times3] 09939 09922 09892 09851 09795 09731 09649 09558 09454 09340
8 ATM [5times5] 09878 09838 09828 09812 09792 09772 09740 09710 09671 09621
9 ATM [7times7] 09812 09739 09734 09728 09720 09710 09694 09678 09659 09637
10 Wiener [3times3] 09977 09943 09896 09827 09742 0964 09517 09386 09249 09098
11 Wiener [5times5] 09958 09926 09897 09861 09818 09768 09709 09646 09581 09503
12 Wiener [7times7] 09907 09897 09868 09833 09797 09755 09715 09671 09617 09557
13 AD 09951 09895 09867 09830 09784 09728 09663 09586 09506 09417
14 TV 09959 09931 09902 09864 09820 09765 09701 09633 09547 09458
15 Lee [3times3] 09977 09936 09881 09813 09740 09650 09554 09456 09346 09239
16 Lee [5times5] 09955 09936 09893 09847 09805 09755 09715 09666 09610 09566
17 Lee [7times7] 09936 09929 09884 09839 09799 09761 09725 09688 09648 09613
18 Bilateral [3times3] 09939 09921 09891 09849 09797 09731 09658 09578 09487 09385
19 Bilateral [5times5] 09916 09828 09816 09802 09781 09757 09728 09686 09646 09598
20 Bilateral [7times7] 09879 09706 09702 09693 09682 09664 09642 09623 09592 09557
21 NL-Means 09977 09947 09840 09616 09318 08971 08601 08230 07861 07451
22 VisuShrink 09902 09874 09843 09809 09769 09704 09607 09473 09321 09178
23 SureShrink 09848 09841 09828 09808 09788 09764 09734 09704 09675 09636
24 BayesShrink 09943 09938 09900 09863 09826 09790 09755 09711 09675 09621
25 OracleShrink 09965 09903 09811 09680 09500 09283 09018 08712 08372 08021
26 OracleThresh 09959 09858 09685 09439 09133 08759 08329 07873 07399 06953
27 NeighShrink 09981 09949 09910 09861 09812 09757 09698 09642 09582 09530
28 SmoothShrink 09729 09658 09521 09336 09118 08867 08687 08284 07984 07661
29 LAWML [3times3] 09979 09945 09902 09850 09797 09740 09676 09613 09547 09484
30 LAWML [5times5] 09980 09950 09915 09877 09835 09797 09755 09712 09670 09622
31 LAWML [7times7] 09980 09951 09916 09882 09845 09811 09773 09731 09693 09649
Chapter-2 Study of Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 63
Table-210 Filtering performance of various filters in terms of UQI operated on Pepper image
under various noise conditions (σn varies from 5 to 50)
Universal Quality Index (UQI) Standard deviation of AWGN
SlNo Denoising Filters 5 10 15 20 25 30 35 40 45 50
Test Image Pepper
1 Mean [3times3] 09927 09912 09889 09856 09814 09762 09702 09631 09557 09476
2 Mean [5times5] 09900 09894 09884 09871 09853 09831 09805 09776 09737 09699
3 Mean [7times7] 09839 09836 09830 09821 09809 09799 09779 09758 09734 09706
4 Median [3times3] 09969 09938 09890 09828 09750 09659 09552 09431 09298 09163
5 Median [5times5] 09957 09940 09916 09885 09848 09805 09756 09696 09641 09578
6 Median [7times7] 09938 09921 09903 09882 09855 09827 09795 09759 09725 09687
7 ATM [3times3] 09929 09924 09901 09868 09824 09772 09706 09631 09553 09460
8 ATM [5times5] 09911 09901 09894 09883 09868 09850 09825 09798 09764 09732
9 ATM [7times7] 09886 09844 09842 09838 09832 09823 09807 09796 09780 09760
10 Wiener [3times3] 09978 09959 09925 09871 09802 09715 09614 09503 09389 09261
11 Wiener [5times5] 09955 09953 09930 09903 09868 09824 09775 09718 09655 09588
12 Wiener [7times7] 09941 09935 09913 09886 09855 09820 09782 09738 09692 09638
13 AD 09949 09901 09879 09848 09809 09761 09707 09641 09571 09488
14 TV 09950 09913 09889 09859 09820 09778 09722 09665 09594 09525
15 Lee [3times3] 09982 09952 09912 09859 09795 09722 09645 09563 09475 09392
16 Lee [5times5] 09960 09954 09925 09893 09857 09820 09784 09742 09701 09665
17 Lee [7times7] 09954 09949 09917 09886 09856 09825 09796 09766 09734 09702
18 Bilateral [3times3] 09925 09912 09888 09855 09813 09762 09700 09632 09559 09476
19 Bilateral [5times5] 09913 09885 09876 09862 09843 09821 09795 09761 09726 09689
20 Bilateral [7times7] 09879 09807 09799 09791 09778 09763 09742 09721 09697 09662
21 NL-Means 09978 09961 09877 09702 09462 09191 08885 08572 08224 07908
22 VisuShrink 09817 09793 09756 09710 09676 09634 09575 09502 09408 09289
23 SureShrink 09751 09749 09743 09732 09720 09700 09675 09645 09613 09568
24 BayesShrink 09980 09952 09919 09883 09855 09826 09789 09745 09696 09617
25 OracleShrink 09975 09928 09855 09753 09617 09437 09222 08974 08697 08400
26 OracleThresh 09967 09893 09775 09610 09372 09049 08683 08294 07885 07484
27 NeighShrink 09983 09959 09928 09891 09845 09798 09743 09692 09636 09579
28 SmoothShrink 09734 09693 09583 09439 09257 09054 08817 08561 08305 08022
29 LAWML [3times3] 09984 09958 09925 09887 09843 09791 09736 09683 09630 09575
30 LAWML [5times5] 09987 09885 09876 09862 09843 09821 09795 09761 09713 09675
31 LAWML [7times7] 09988 09961 09935 09907 09876 09838 09800 09761 09726 09689
Chapter-2 Study of Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 64
Table-211 Filtering performance of various filters in terms of UQI operated on Goldhill image
under various noise conditions (σn varies from 5 to 50)
Universal Quality Index (UQI) Standard deviation of AWGN
SlNo Denoising Filters 5 10 15 20 25 30 35 40 45 50
Test Image Goldhill
1 Mean [3times3] 09939 09928 09909 09884 09850 09809 09762 09705 0964 09575
2 Mean [5times5] 09866 09861 09853 09841 09827 09807 09784 09754 09722 09687
3 Mean [7times7] 09801 09799 09793 09785 09777 09762 09744 09722 09699 09665
4 Median [3times3] 09945 09922 09886 09838 09781 09710 09631 09542 09444 09345
5 Median [5times5] 09916 09880 09861 09839 09812 09780 09746 09705 09658 09610
6 Median [7times7] 09878 09838 09824 09810 09790 09769 09749 09723 09702 09669
7 ATM [3times3] 09946 09928 09909 09883 09850 09809 09760 09703 09639 09569
8 ATM [5times5] 09923 09862 09855 09847 09833 09819 09802 09782 09757 09732
9 ATM [7times7] 09883 09800 09797 09792 09786 09780 09771 09761 09749 09734
10 Wiener [3times3] 09971 09950 09921 09880 09824 09760 09682 09589 09497 09385
11 Wiener [5times5] 09942 09921 09903 09880 09852 09816 09773 09724 09670 09602
12 Wiener [7times7] 09917 09886 09870 09848 09824 09798 09764 09725 09684 09628
13 AD 09957 09910 09893 09869 09838 09801 09755 09702 09641 09578
14 TV 09958 09936 09917 09894 09865 09833 09795 09750 09700 09636
15 Lee [3times3] 09981 09950 09914 09872 09824 09773 09711 09645 09572 09501
16 Lee [5times5] 09956 09946 09912 09879 09848 09817 09780 09743 09704 09670
17 Lee [7times7] 09947 09940 09902 09868 09836 09805 09775 09747 09716 09680
18 Bilateral [3times3] 09938 09927 09908 09881 09848 09807 09757 09703 09636 09565
19 Bilateral [5times5] 09916 09853 09844 09832 09815 09793 09770 09740 09703 09662
20 Bilateral [7times7] 09810 08936 09764 09754 09742 09725 09704 09683 09649 09620
21 NL-Means 09967 09956 09891 09767 09590 09381 09147 08896 08631 08339
22 VisuShrink 09908 09882 09856 09826 09784 09730 09659 09562 09454 09328
23 SureShrink 09843 09840 09831 09819 09804 09785 09765 09736 09712 09673
24 BayesShrink 09981 09950 09917 09881 09842 09801 09761 09719 09673 09627
25 OracleShrink 09957 09901 09828 09750 09660 09546 09412 09266 09105 08926
26 OracleThresh 09964 09895 09810 09699 09563 09404 09206 08981 08732 08443
27 NeighShrink 09984 09957 09925 09891 09854 09813 09773 09731 09684 09638
28 SmoothShrink 09878 09816 09736 09627 09494 09340 09162 08959 08760 08541
29 LAWML [3times3] 09982 09955 09921 09884 09841 09798 09751 09696 09648 09592
30 LAWML [5times5] 09984 09956 09927 09895 09861 09826 09787 09744 09699 09656
31 LAWML [7times7] 09986 09957 09928 09896 09863 09831 09791 09754 09711 09658
Chapter-2 Study of Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 65
Table-212 Filtering performance of various filters in terms of UQI operated on Barbara image
under various noise conditions (σn varies from 5 to 50)
Universal Quality Index (UQI) Standard deviation of AWGN
SlNo Denoising Filters 5 10 15 20 25 30 35 40 45 50
Test Image Barbara
1 Mean [3times3] 09753 09739 09718 09688 09649 09601 09545 09478 09403 09318
2 Mean [5times5] 09560 09554 09545 09532 09515 09491 09462 09433 0939 09346
3 Mean [7times7] 09525 09521 09516 09507 09494 0948 09458 09433 09407 09371
4 Median [3times3] 09818 09733 09683 09622 09549 09466 09371 09268 09145 09024
5 Median [5times5] 09807 09508 09495 09475 09450 09416 09374 09335 09286 09227
6 Median [7times7] 09766 09536 09524 09508 09491 09469 09440 09420 09390 09360
7 ATM [3times3] 09786 09740 09717 09686 09647 09600 09538 09474 09401 09314
8 ATM [5times5] 09769 09555 09548 09538 09524 09504 09481 09458 09430 09398
9 ATM [7times7] 09716 09523 09522 09516 09512 09501 09490 09476 09432 09411
10 Wiener [3times3] 09933 09904 09861 09803 09734 09651 09552 09447 09331 09201
11 Wiener [5times5] 09919 09847 09812 09767 09718 09665 09607 09538 09470 09395
12 Wiener [7times7] 09898 09808 09776 09737 09696 09652 09603 09550 09495 09434
13 AD 09857 09741 09722 09694 09659 09614 09564 09503 09436 09358
14 TV 09816 09766 09738 09707 09668 09626 09576 09520 09461 09396
15 Lee [3times3] 09978 09930 09870 09800 09724 09646 09559 09470 09377 09284
16 Lee [5times5] 09949 09929 09871 09810 09748 09682 09613 09554 09490 09425
17 Lee [7times7] 09932 09925 09865 09805 09744 09688 09634 09576 09519 09469
18 Bilateral [3times3] 09751 09738 09716 09686 09646 09597 09542 09475 09400 09316
19 Bilateral [5times5] 09734 09543 09534 09520 09501 09478 09447 09414 09378 09329
20 Bilateral [7times7] 09688 09483 09477 09466 09453 09436 09414 09386 09357 09312
21 NL-Means 09957 09943 098 65
09716 09516 09285 09010 08737 08423 08127
22 VisuShrink 09777 09726 09661 09596 09540 09479 09417 09342 09261 09138
23 SureShrink 09613 09609 09602 09590 09573 09552 09526 09493 09463 09424
24 BayesShrink 09974 09927 09874 09817 09759 09696 09624 09534 09461 09401
25 OracleShrink 09919 09756 09674 09618 09560 09492 09400 09294 09158 09005
26 OracleThresh 09960 09817 09690 09569 09398 09188 08961 08702 08422 08136
27 NeighShrink 09982 09949 09907 09859 09808 09747 09691 09631 09560 09491
28 SmoothShrink 09813 09726 09630 09501 09344 09159 08949 08721 08477 08233
29 LAWML [3times3] 09974 09944 09900 09846 09789 09728 09663 09598 09524 09433
30 LAWML [5times5] 09976 09946 09904 09860 09813 09763 09710 09650 09589 09517
31 LAWML [7times7] 09981 09947 09905 09861 09814 09765 09713 09656 09598 09521
Chapter-2 Study of Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 66
Table-213 Method Noise MN of various filters operated on different test images
Sl No
Denoising Images
Filters
Lena Pepper Goldholl Barbara
1 Mean [3times3] 262 290 410 668
2 Mean [5times5] 443 408 642 946
3 Mean [7times7] 573 520 793 1035
4 Median [3times3] 132 153 252 438
5 Median [5times5] 270 239 443 693
6 Median [7times7] 395 311 499 744
7 ATM [3times3] 262 290 410 668
8 ATM [5times5] 443 408 642 946
9 ATM [7times7] 573 520 793 1035
10 Wiener [3times3] 186 204 318 387
11 Wiener [5times5] 367 351 540 637
12 Wiener [7times7] 464 387 576 668
13 AD 204 237 295 497
14 TV 211 234 334 573
15 Lee [3times3] 00118 109 00336 00583
16 Lee [5times5] 00530 114 01109 02057
17 Lee [7times7] 01315 201 01853 110
18 Bilateral [3times3] 288 308 423 680
19 Bilateral [5times5] 497 433 663 966
20 Bilateral [7times7] 601 545 826 1104
21 NL-Means 117 137 186 211
22 VisuShrink 318 423 471 637
23 SureShrink 517 673 770 1007
24 BayesShrink 00232 00273 00194 00190
25 OracleShrink 00285 00267 00242 00238
26 OracleThresh 00285 00267 00242 00238
27 NeighShrink 408times10-10
466times10-10
334times10-10
497times10-10
28 SmoothShrink 660 752 645 790
29 LAWML [3times3] 408times10-10
466times10-10
334times10-10
497times10-10
30 LAWML [5times5] 408times10-10
466times10-10
334times10-10
497times10-10
31 LAWML [7times7] 408times10-10
466times10-10
334times10-10
497times10-10
Chapter-2 Study of Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 67
Table-214 Execution time (seconds) TE taken by various filters for Lena image
Execution time (seconds) in three different hardware platforms Sl No Denoisg Filters
SYSTEM-1 SYSTEM-2 SYSTEM-3
1 Mean [3times3] 318 701 1713
2 Mean [5times5] 323 712 1749
3 Mean [7times7] 327 720 1776
4 Median [3times3] 402 742 2445
5 Median [5times5] 409 747 2469
6 Median [7times7] 415 812 2490
7 ATM [3times3] 732 1677 3018
8 ATM [5times5] 809 1723 3056
9 ATM [7times7] 813 1784 3084
10 Wiener [3times3] 787 1559 2806
11 Wiener [5times5] 807 1598 2876
12 Wiener [7times7] 843 1670 3006
13 AD ------ ------- ------
14 TV ------ ------- ------
15 Lee [3times3] 874 1426 3509
16 Lee [5times5] 887 1446 3545
17 Lee [7times7] 968 1579 3779
18 Bilateral [3times3] 536 1100 3265
19 Bilateral [5times5] 583 1353 3520
20 Bilateral [7times7] 588 1359 3639
21 NL-Means 44667 99620 221838
22 VisuShrink 0540 119 392
23 SureShrink 060 134 442
24 BayesShrink 188 415 1369
25 OracleShrink 2 440 1452
26 OracleThresh 197 435 1435
27 NeighShrink 414 912 3009
28 SmoothShrink 108 239 788
29 LAWML [3times3] 367 809 2669
30 LAWML [5times5] 370 815 2689
31 LAWML [7times7] 374 823 2715
Chapter-2 Study of Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 68
Fig 27 Performance comparison of various filters in terms of PSNR (dB) under
different noise levels of AWGN on the images
(a) Lena
(b) Pepper (c) Goldhill
(d) Barbara
σn
PS
NR
(d
B)
PSNR values for Lena Image
PS
NR
(d
B)
PSNR values for Pepper Image P
SN
R (
dB
)
PSNR values for Goldhill Image PSNR values for Barbara Image
PS
NR
(d
B)
(a) (b)
(c) (d)
σn
σn σn
Chapter-2 Study of Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 69
Fig 28 Performance comparison of various filters in terms of RMSE under different noise levels of AWGN on the images
(a) Lena
(b) Pepper
(c) Goldhill
(d) Barbara
RM
SE
RMSE values for Lena Image
RM
SE
RMSE values for Pepper Image
(a) (b)
RM
SE
RMSE values for Goldhill Image
RM
SE
(c) (d)
RMSE values for Barbara Image
σn σn
σn σn
Chapter-2 Study of Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 70
Fig 29 Performance comparison of various filters in terms of UQI under
different noise levels of AWGN on the images
(a) Lena (b) Pepper
(c) Goldhill (d) Barbara
UQ
I UQI values for Lena Image
UQ
I
UQI values for Pepper Image U
QI
UQI values for Goldhill Image
UQ
I
UQI values for Barbara Image
(a) (b)
(c) (d)
σn σn
σn σn
Chapter-2 Study of Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 71
(b)
(f)
(j)
(n)
(a)
(e)
(i)
(m)
(q)
(r)
(c)
(d)
(g)
(h)
(k)
(l)
(o)
(p)
(s)
Fig 210 Performance of Various Filters for Lena Image with AWGN σn = 15
(a) Original image (b) Noisy image
(c) ndash (s) Results of various filtering schemes
(c) Mean (d) Median (e) ATM (f) Wiener (g) AD (h) TV (i) Lee (j) Bilateral
(k) NL-Means (l) VisuShrink (m) SureShrink (n) BayesShrink (o) OracleShrink
(p) OracleThresh (q) NeighShrink (r) SmoothShrink (s) LAWML
Chapter-2 Study of Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 72
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
(j)
(k)
(l)
(m)
(n)
(o)
(p)
(q)
(r)
(s)
Fig 211 Performance of Various Filters for Lena Image (Smooth Region) with
AWGN σn = 15
(a) Original image (b) Noisy image
(c) ndash (s) Results of various filtering schemes
(c) Mean (d) Median (e) ATM (f) Wiener (g) AD (h) TV (i) Lee (j) Bilateral
(k) NL-Means (l) VisuShrink (m) SureShrink (n) BayesShrink (o) OracleShrink
(p) OracleThresh (q) NeighShrink (r) SmoothShrink (s) LAWML
Chapter-2 Study of Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 73
(a) (b) (c) (d) (e) (f) (g)
(h) (i) (j) (k) (l)
(m)
(l) (m) (n)
(o) (p) (q) (r) (s)
Fig 212 Performance of Various Filters for Lena Image (Complex Region) with AWGN σn = 15
(a) Original image (b) Noisy image
(c) ndash (s) Results of various filtering schemes
(c) Mean (d) Median (e) ATM (f) Wiener (g) AD (h) TV (i) Lee (j) Bilateral
(k) NL-Means (l) VisuShrink (m) SureShrink (n) BayesShrink (o) OracleShrink
(p) OracleThresh (q) NeighShrink (r) SmoothShrink (s) LAWML
Chapter-2 Study of Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 74
(a) (b) (c) (d)
(e) (f) (g) (h)
(i) (j) (k)
(l)
(m) (n) (o) (p)
(q) (r) (s)
Fig 213 Performance of Various Filters for Pepper Image with AWGN σn = 15 (a) Original image (b) Noisy image
(c) ndash (s) Results of various filtering schemes
(c) Mean (d) Median (e) ATM (f) Wiener (g) AD (h) TV (i) Lee (j) Bilateral
(k) NL-Means (l) VisuShrink (m) SureShrink (n) BayesShrink (o) OracleShrink
(p) OracleThresh (q) NeighShrink (r) SmoothShrink (s) LAWML
Chapter-2 Study of Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 75
(a) (b) (c) (d)
(e) (f) (g) (h)
(i) (j) (k)
(l)
(m)
(n)
(o)
(p)
(q)
(r)
(s)
Fig 214 Performance of Various Filters for Lena Image with AWGN σn = 40
(a) Original image (b) Noisy image
(c) ndash (s) Results of various filtering schemes
(c) Mean (d) Median (e) ATM (f) Wiener (g) AD (h) TV (i) Lee (j) Bilateral
(k) NL-Means (l) VisuShrink (m) SureShrink (n) BayesShrink (o) OracleShrink
(p) OracleThresh (q) NeighShrink (r) SmoothShrink (s) LAWML
Chapter-2 Study of Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 76
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
(j)
(k)
(l)
(m)
(n)
(o)
(p)
(q)
(r)
(s)
Fig 215 Performance of Various Filters for Lena Image (Smooth Region) with
AWGN σn = 40
(a) Original image (b) Noisy image
(c) ndash (s) Results of various filtering schemes
(c) Mean (d) Median (e) ATM (f) Wiener (g) AD (h) TV (i) Lee (j) Bilateral
(k) NL-Means (l) VisuShrink (m) SureShrink (n) BayesShrink (o) OracleShrink
(p) OracleThresh (q) NeighShrink (r) SmoothShrink (s) LAWML
Chapter-2 Study of Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 77
(a)
(b) (c)
(d)
(f) (g)
(h)
(i)
(e)
(j) (k) (l) (m) (n)
(o) (p) (q) (r) (s)
Fig 216 Performance of Various Filters for Lena Image (Complex Region) with AWGN σn = 40
(a) Original image (b) Noisy image
(c) ndash (s) Results of various filtering schemes
(c) Mean (d) Median (e) ATM (f) Wiener (g) AD (h) TV (i) Lee (j) Bilateral
(k) NL-Means (l) VisuShrink (m) SureShrink (n) BayesShrink (o) OracleShrink
(p) OracleThresh (q) NeighShrink (r) SmoothShrink (s) LAWML
Chapter-2 Study of Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 78
(d)
(a) (b) (c) (d)
(e) (f) (g) (h)
(i) (j) (k)
(l)
(m)
(n)
(o)
(p)
(q)
(r)
(s)
Fig 217 Performance of Various Filters for Pepper Image with AWGN σn = 40
(a) Original image (b) Noisy image
(c) ndash (s) Results of various filtering schemes
(c) Mean (d) Median (e) ATM (f) Wiener (g) AD (h) TV (i) Lee (j) Bilateral
(k) NL-Means (l) VisuShrink (m) SureShrink (n) BayesShrink (o) OracleShrink
(p) OracleThresh (q) NeighShrink (r) SmoothShrink (s) LAWML
Chapter-2 Study of Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 79
28 Conclusion
The performance of various spatial-domain filters Mean Median ATM
Wiener AD TV Lee Bilateral NL-Means and various wavelet-domain filters
VisuShrink SureShrink BayesShrink OracleShrink OracleThresh NeighShrink
SmoothShrink LAWML are studied under low moderate and high noise conditions
From Table-21 to Table-24 it is observed that the filters ATM NeighShrink
and LAWML perform better in terms of PSNR The wavelet-domain filter
NeighShrink performs better under low noise conditions Under moderate noise
conditions LAWML generally gives better performance The spatial-domain filter
ATM works well under high noise conditions
The RMSE values of different filters are shown in tables Table-25 to
Table-28 From the tables it is observed that the filters ATM NeighShrink and
LAWML give better performance as compared to others
From tables Table-29 to Table-212 it is observed that LAWML gives better
UQI values under low and moderate noise conditions When noise level is high the
spatial-domain filter ATM yields better performance in terms of UQI values
Table-213 shows the method noise of different spatial-domain and wavelet-
domain filters From the table it is seen that the method noise of LAWML is
minimum (quite negligible) Hence the LAWML filter is best among all the filters
compared here for yielding minimal noise when the input is undistorted
The execution time of different filters is shown in the Table-214 The wavelet-
domain filter VisuShrink takes least execution time as compared to other spatial-
domain and wavelet-domain filters However among the spatial-domain filters the
simplest mean filter takes quite less execution time as compared to other spatial-
domain filters
Chapter-2 Study of Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 80
For proper judgment of performance of filters the subjective evaluation
should be taken into consideration The filtering performances of various filters on a
smooth region and a complex region of Lena image are shown in the figures
Fig 211 Fig 212 Fig 215 and Fig 216 From these figures it is observed that the
wavelet-domain filters yield artifacts in the smooth regions However the wavelet-
domain filters are effective in preserving the edges and other detailed information up
to some extent Further when the various wavelet-domain filters are compared then it
is observed that NeighShrink and LAWML filters yield very high visual quality
Hence they are expected to be good competitors for the novel filters proposed in this
research work
Chapter 3
Development of
Novel Spatial-Domain
Image Filters
Chapter-3 Development of Novel Spatial-Domain Image Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 82
Preview
Mean and Wiener filters suppress additive white Gaussian noise (AWGN)
from an image very effectively under low and moderate noise conditions But these
filters distort and blur the edges unnecessarily Lee filter and non-local means (NL-
Means) filter work well under very low noise condition The method noise [88] for
these filters is low as compared to other spatial-domain filters The computational
complexity of simple mean filter is low whereas that of NL-Means filter is very high
Mean Wiener Lee and NL-means filters are incapable of suppressing the Gaussian
noise quite efficiently under high noise conditions
Therefore some efficient spatial-domain filters should be designed with the
following ideal characteristics
i) Suppressing Gaussian noise very well under low moderate and high noise
conditions without distorting the edges and intricate details of an image
ii) Having low method noise and
iii) Having less computational complexity
3
Chapter-3 Development of Novel Spatial-Domain Image Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 83
In this chapter two novel spatial-domain image denoising schemes are
proposed The Adaptive Window Wiener filter (AWWF) [P1] developed here is a
very good scheme to suppress Gaussian noise under moderate noise conditions On
the other hand the second proposed filter the Circular Spatial filter (CSF) [P2] is
found to be quite efficient in suppressing the additive noise under moderate and high
noise conditions It also retains the edges and textures of an image very well
The following topics are covered in this chapter
Development of Adaptive Window Wiener Filter
Development of Circular Spatial Filter
Simulation Results
Conclusion
Chapter-3 Development of Novel Spatial-Domain Image Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 84
31 Development of Adaptive Window Wiener Filter
An Adaptive Window Wiener Filter (AWWF) [P1] is developed for suppressing
Gaussian noise under low (the noise standard deviation σnle10) and moderate noise
(10ltσnle 30) conditions very efficiently But it does not perform well under high
noise (30ltσnle5 0) conditions This filter is a modified version of Wiener filter [962]
where the size of the window varies with the level of complexity of a particular region
in an image and the noise power as well A smooth or flat region (also called as
homogenous region) is said to be less complex as compared to an edge region The
region containing edges and textures are treated as highly complex regions The
window size is increased for a smoother region and also for an image with high noise
power
Since the edges in an image are specially taken care of in this algorithm the
proposed filter is found to be good in edge preservation The work begins by using a
mean filter on a noisy image to get the blurred version of the image Using the edge
extraction operator the edges of the resulted blurred image is found out The Wiener
filter of variable size is applied throughout the noisy image to suppress the noise The
window size is made larger in smooth regions and is kept smaller in the regions where
edges are located This scheme is adopted not to blur a complex or edge region too
much
The organization of this section is outlined below
The AWWF Theory
The AWWF Algorithm
Window Selection
Chapter-3 Development of Novel Spatial-Domain Image Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 85
311 The AWWF Theory
It is a fact that a noise-free sample can be estimated with better accuracy from
a large number of noisy samples Similarly in order to estimate a true pixel in a
particular region from a noisy 2-D image a large number of pixels in the
neighborhood surrounding the noisy pixel are required In other words a larger-sized
window surrounding the pixel to be filtered can be considered for better estimation
In a homogenous region the correlation amongst the pixels is high Hence a larger-
sized window can be taken if the pixel to be filtered belongs to a homogenous
region On the other hand a pixel that belongs to a non-homogenous region or the
region containing edges has got less number of correlated pixels in its neighborhood
In such a case smaller-sized window has to be taken for denoising a pixel belonging
to a non-homogenous region However a little bit of noise will still remain in the non-
homogenous or edge region even after filtration But human eye is not so sensitive to
noise in any edge region Hence a variable sized window may be a right choice for
efficient image denoising
In the proposed adaptive window Wiener filter the window is made adaptive
ie the size of the window varies from region to region In a flat or homogenous
region the size of the window taken is large enough The size of window is small in
the regions containing edges The problem here is to distinguish the edge and smooth
regions The edges and smooth regions are easily distinguished if the edge extraction
operators are used Many edge extraction operators such as Sobel Canny Roberts
Prewitt etc are proposed in the literature [22-27] But finding the true edges in a
noisy environment is not so easy The edge extraction operator works well on noise
free images So it is important to make the noisy image a little bit blurred before edge
extraction In the proposed filter the mean filter of window size 5times5 is used when the
noise level is low and moderate to get the blurred version of the noisy image whereas
a 7times7 window is taken for high-noise AWGN The Sobel operator is then used on the
resulted blurred image to find the edges
A small amount of noise still remains in different regions even after passing
the noisy image through the mean filter The Sobel operator is less sensitive to
Chapter-3 Development of Novel Spatial-Domain Image Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 86
isolated high intensity point variations since the local averaging over sets of three
pixels tends to reduce this In effect it is a ldquosmall barrdquo detector rather than a point
detector Secondly it gives an estimate of edge direction as well as edge magnitude at
a point which is more informative Also the Sobel operator is still relatively easy to
implement in hardware form most obviously by a pipeline approach
312 The AWWF Algorithm
The proposed algorithm is given below
Step-1
The noisy image is passed through a mean filter as shown in Fig 31 to get a blurred
version of the image
Step-2
Edge operator (Sobel operator) is applied on the blurred image obtained in Step-1 to
get the edge image The pixels belong to smooth region and edge region are identified
as lsquoprsquo and lsquoqrsquo respectively This operation is shown in Fig 32
Step-3
Adaptive window Wiener filter is applied on the noisy image The size of the window
is varied with the following concepts
A-i) If the center pixel is an edge pixel then the size of the window is small
A-ii) If the center pixel belongs to smooth region the size of the window is large
B-i) If the noise power is low (σnle10 ) then the size of the window is small
B-ii) If the noise power is moderate (10ltσnle30 ) then the size of the window is
medium
B-iii) If the noise power is high (30ltσnle50) then the size of the window is large
This adaptive filtering concept is depicted in Fig 33
Step-4
All the filtered pixels are united together to obtain the denoised (filtered) image as
shown in Fig 34
The exact window sizes taken for various conditions are presented in the next
sub-section
Chapter-3 Development of Novel Spatial-Domain Image Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 87
p1cup q1cup helliphellip = Filtered Image
Mean Filter Noisy Image Blurred Image
Fig 31 Blurred Image resulted from mean filter
Sobel operator
Fig 32 Edge Image using lsquoSobelrsquo operator
Blurred Image
Edge Image
p
q
lsquoprsquo belongs to smooth region
lsquoqrsquo belongs to edge region
Fig 34 Filtered image showing filtered pixels
Fig 33 Filtering operation of AWWF for the pixels lsquoprsquo (belonging to smooth region) and lsquoqrsquo (belonging to edge region)
The pixels lsquop1rsquo and lsquoq1rsquo are the filtered pixels for the corresponding pixels lsquoprsquo and lsquoqrsquo respectively
q
p
Wiener
Filtering
p1 OR q1
Chapter-3 Development of Novel Spatial-Domain Image Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 88
313 Window Selection
The selection of window is based on the level of noise present in the noisy
image If the noise level is unknown a robust median estimator [102] may be applied
to predict the level of noise
When the noise level is low (σnle10)
i) a 3times3 window is selected for filtering the noisy pixels belonging to
homogenous regions
ii) the pixel is unaltered if the noisy pixels belong to edges
When the noise level is moderate (10ltσnle 30)
i) a 5times5 window is chosen for filtration of noisy pixels of flat regions
ii) the window size is 3times3 if the noisy pixels to be filtered are identified as edge
pixels
When the noise level is high (30ltσnle50)
i) a 7times7 window is used for filtration of noisy pixels of flat regions
ii) if the noisy pixels to be filtered are identified as edge pixels the window size
used is 5times5
The proposed filter AWWF is implemented on MATLAB 70 platform and its
simulation results are presented in Section 33
Chapter-3 Development of Novel Spatial-Domain Image Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 89
32 Development of Circular Spatial Filter
A novel circular spatial filter (CSF) is proposed [P2] for suppressing additive
white Gaussian noise (AWGN) In this method a circular spatial-domain window
whose weights are derived from two independent functions (i) spatial distance and
(ii) gray level distance is employed for filtering The proposed filter is different from
Bilateral filter [70] and performs well under moderate and high noise conditions The
filter is also capable of retaining the edges and intricate details of the image
The organization of this section is outlined below
The circular spatial filtering method
The parameter and window selection
Simulation Results
Conclusion
321 The circular spatial filtering method
In circular spatial filter (CSF) the name circular refers to the shape of the
filtering kernel or window being circular In this method the filtering kernel consists
of distance kernel and gray level kernel The circular shaped kernel is moved
invariably throughout the image to remove the noise The proposed filter has got some
resemblance with Bilateral filter where the filtering kernel is a combination of
domain-filtering kernel and range-filtering kernel The weighting function used in
gray level kernel of circular spatial filter is similar to the weighting function used in
range-filtering kernel But the weighting function used in distance kernel of CSF and
domain-filtering kernel of Bilateral filter are different The weighting function used in
domain-filtering kernel is exponential whereas it is a simple nonlinear function in case
of distance kernel of the proposed method
Chapter-3 Development of Novel Spatial-Domain Image Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 90
3211 Distance kernel
In an image the spatial distance between any arbitrary pixel in a particular
window at location (x1y1) and the center pixel at location (xy) is calculated as
( ) ( )2 2
1 1sd x x y y= minus + minus (31)
Now the distance kernel is defined by
max
1 sd
dw
d= minus (32)
where dmax is the maximum radial distance from center
The correlation between pixels goes on decreasing as the distance increases
Hence when wd becomes very small the correlation can be taken as zero When the
small values of distance kernel are replaced by zero we get a circular shaped filtering
kernel The circular shaped kernel is denoted asdcw
3212 Gray level kernel
The gray level distance between any arbitrary pixel g(x1y1) of a particular
window at location (x1y1) and the center pixel g(xy) at location (xy) is calculated as
( )1
2 2 2
1 1| ( ) |gd g x y g x y = minus (33)
The gray level distance dg can be used to find the gray level kernel which is defined
by
2
2exp
2
g
g
g
dw
σ
minus=
(34)
where lsquoσgrsquo is the standard deviation of the distribution function wg
Chapter-3 Development of Novel Spatial-Domain Image Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 91
The filtering kernel of CSF can be prepared from dcw and
gw as
dc gw w w= sdot (35)
The filtering kernel w is slided throughout the image corrupted with noise to get the
estimated output The estimated pixel can be expressed as
( )( ) ( )
ˆ
( )
a b
s a t b
a b
s a t b
w s t g x s y t
f x y
w s t
= minus = minus
= minus = minus
+ +
=
sum sum
sum sum (36)
In the filtering window the center coefficient is given the highest weight The
weight goes on decreasing as distance increases from center and it is zero when
correlation is insignificant A pictorial representation of circular spatial filtering mask
is shown in Figure 31 (a) A more general filtering mask ie a square mask is also
depicted in Figure 31 (b) to illustrate the difference It is evident from Figure 31 (a)
that there are necessarily some zeros in the circular spatial filter mask whereas it is
not so in the case of a general square window shown in Figure 31 (b)
Fig 35 (a) A typical Circular Spatial Filtering mask of size 7 times 7
(b) A square filtering mask of size 7 times 7
(a) (b)
Chapter-3 Development of Novel Spatial-Domain Image Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 92
322 The parameter and window selection
The circular spatial filter has one parameter lsquoσgrsquo which controls the weights in
the gray level kernel For efficient filtering operation the value σg should be
optimum The choice of σg is based on experimentation Two experiments are
performed to find the optimal value of σg
Experiment 1
An experiment is conducted to find the peak-signal-to-noise ratio (PSNR) for
various values of σg under different noise conditions In this experiment Lena and
Goldhill images are selected and their noisy versions are generated by adding
Gaussian noise of standard deviation σn = 30 40 and 50 The PSNR values obtained
are plotted against the values of σg which are shown in Fig 36 From the figure it is
observed that the PSNR values settle at σg = 1 and do not change much even if σg is
increased significantly
Experiment 2
The noisy versions of Lena and Goldhill are used to perform this experiment
Here the universal quality index (UQI) values for different values of σg under the
Gaussian noise of standard deviation σn = 30 40 and 50 are calculated The UQI
values are plotted for different values of σg and are shown in Fig 37 As σg increases
and approaches 1 the UQI value increases and approaches steady state value The
value of UQI remains constant with further increase of σg
From these two experiments it is learnt that the optimum value of σg should
be taken as 1
The selection of window in CSF is equally important as the selection of
parameter The noise levels of AWGN are taken into consideration for selection of
window If there is no a-priori knowledge of the noise level the robust median
estimator is used to find it For low moderate and high noise conditions 3times3 5times5 and
7times7 windows are selected respectively for effective suppression of Gaussian noise
The size of the window is kept constant and is never varied even though the image
statistics change from point to point for a particular noise level
Chapter-3 Development of Novel Spatial-Domain Image Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 93
Fig 36 PSNR vs σg under AWGN of σn = 30 40 and 50
(a) Lena image
(b) Goldhill image
0 1 2 3 4 515
20
25
30
σ = 30
σ = 40
σ = 50n
n
n
gσ
PS
NR
(d
B)
(a)
0 1 2 3 4 516
18
20
22
24
26
28
σ = 30
σ = 40
σ = 50
n
n
n
PS
NR
(d
B)
gσ
(b)
Chapter-3 Development of Novel Spatial-Domain Image Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 94
0 1 2 3 4 507
075
08
085
09
095
1
σ = 30
σ = 40
σ = 50
n
n
n
UQ
I
gσ
(a)
gσ
UQ
I
0 1 2 3 4 508
085
09
095
1
σ = 30
σ = 40
σ = 50
n
n
n
(b)
Fig 37 UQI vs σg under AWGN of σn = 30 40 and 50
(a) Lena image
(b) Goldhill image
Chapter-3 Development of Novel Spatial-Domain Image Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 95
33 Simulation Results
Extensive computer simulation is carried out on MATLAB 70 platform to
access the performance of the proposed filters Adaptive Window Wiener Filter
(AWWF) and Circular Spatial Filter (CSF) and the standard existing filters Mean
filter Median filter Alpha Trimmed Mean (ATM) filter Wiener filter Anisotropic
Diffusion (AD) filter Total Variation (TV) filter Lee filter Bilateral filter Non-local
Means (NL-Means) filter and The test images Lena Pepper Goldhill and Barbara of
sizes 512times512 corrupted with AWGN of standard deviation σn = 5 10 15 20 25
30 35 40 45 and 50 are used for testing the filtering performance The peak-signal-
to-noise ratio (PSNR) root-mean-square error (RMSE) universal quality index
(UQI) method noise and execution time are taken as performance measures
The PSNR values of different filters are given in the tables Table-31 to
Table-34 When the noise level is high the proposed filter CSF exhibits very high
performance For moderate noise conditions its performance is close to that of
AWWF The largest PSNR value for a particular standard deviation of Gaussian noise
is highlighted to show the best performance in these tables
The RMSE values of different filters are given in the tables Table-35 to
Table-38 The smallest (best) RMSE value for a particular standard deviation of
Gaussian noise is highlighted for analysis purpose
The UQI values of various filters are given in the tables Table-39 to Table
312 The largest (best) value of UQI for a particular standard deviation of Gaussian
noise is identified and is highlighted for analysis purpose
The method noise of various filters for different images is given in the
Table 313 It is observed that the Lee filter is the best performer whereas the
NL-Means filter is the second best in terms of method noise The proposed filter CSF
Chapter-3 Development of Novel Spatial-Domain Image Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 96
also gives very low method noise and its performance is comparable with that of the
NL-Means filter
The spatial-domain filters are simulated on three different computing systems
depicted in Table-11 in Section 15 The execution time taken for different filtering
schemes is shown in Table-314 As the AD and TV filters are iterative in nature their
simulation times are not included in the table The execution time of CSF is close to
the simplest mean filter Thus it is quite useful for real-time applications
The performance of proposed filters and some high performing filters in terms
of PSNR RMSE and UQI are illustrated in figures Fig 38 to Fig 310 for easy
analysis
For subjective evaluation the output images of different spatial-domain filters
are shown in the figures Fig 311 to Fig 318 The test images Lena and Pepper are
used for subjective evaluation A smooth region and a complex region of Lena image
are also demonstrated through various figures for critical analysis
Conclusions are drawn in the next section
Chapter-3 Development of Novel Spatial-Domain Image Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 97
Table-31 Filtering performance of various filters in terms of PSNR (dB) operated on Lena image under various noise conditions (σn varies from 5 to 50)
Peak-Signal-to-Noise Ratio PSNR (dB) Standard deviation of AWGN
SlNo Denoising Filters 5 10 15 20 25 30 35 40 45 50
Test Image Lena
1 Mean [3times3] 3388 3270 3127 2978 2848 2728 2626 2530 2445 2362
2 Mean [5times5] 2977 2959 2931 2892 2848 2805 2748 2696 2649 2593
3 Mean [7times7] 2766 2760 2750 2737 2721 2701 2677 2649 2623 2589
4 Median [3times3] 3498 3216 2985 2794 2636 2498 2377 2277 2175 2094
5 Median [5times5] 3170 3074 2978 2875 2781 2684 2608 2526 2453 2382
6 Median [7times7] 2960 2917 2865 2813 2758 2699 2644 2601 2545 2496
7 ATM [3times3] 3396 3271 3126 2983 2844 2724 2607 2503 2408 2322
8 ATM [5times5] 2977 2959 2932 2893 2850 2807 2752 2703 2647 2586
9 ATM [7times7] 2788 2759 2752 2741 2728 2713 2689 2666 2641 2613
10 Wiener [3times3] 3788 3401 3137 2915 2738 259 2462 2356 2267 2186
11 Wiener [5times5] 3657 3294 3147 3019 2900 2796 2699 2613 2543 2469
12 Wiener [7times7] 3578 3154 3046 2944 2857 2778 2715 2655 2593 2534
13 AD 3468 3137 3037 2927 2821 2722 2628 2540 2465 2393
14 TV 3549 3322 3170 3025 2901 2785 2677 2585 2492 2412
15 Lee [3times3] 3787 3345 3077 2878 2734 2604 2497 2411 2331 2268
16 Lee [5times5] 3755 3347 3129 2974 2866 2770 2707 2641 2578 2534
17 Lee [7times7] 3712 3304 3091 2952 2857 2784 2728 2677 2630 2595
18 Bilateral [3times3] 3370 3258 3120 2977 2848 2727 2621 2531 2447 2368
19 Bilateral [5times5] 3276 2914 2888 2855 2813 2772 2727 2671 2622 2573
20 Bilateral [7times7] 3109 2662 2655 2643 2630 2613 2589 2573 2547 2519
21 NL-Means 3787 3443 2943 2553 2291 2097 1947 1828 1729 1636
22 AWWF 3488 3336 3178 3056 2929 2813 2741 2688 2601 2585
23 CSF [3times3] 3719 3287 2971 2735 2551 2397 2269 2155 2060 1970
24 CSF [5times5] 3371 3280 3158 3031 2911 2796 2688 2598 2507 2432
25 CSF [7times7] 3015 2987 2962 2932 2896 2847 2801 2749 2699 2646
Chapter-3 Development of Novel Spatial-Domain Image Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 98
Table-32 Filtering performance various filters in terms of PSNR (dB) operated on Pepper image under various noise conditions (σn varies from 5 to 50)
Peak-Signal-to-Noise Ratio PSNR (dB) Standard deviation of AWGN
SlNo Denoising Filters 5 10 15 20 25 30 35 40 45 50
Test Image Pepper
1 Mean [3times3] 3190 3116 3015 2899 2788 2682 2586 2495 2415 2345
2 Mean [5times5] 3061 3039 3001 2955 2902 2840 2781 2722 2656 2601
3 Mean [7times7] 2862 2855 2841 2818 2793 2771 2732 2696 2658 2618
4 Median [3times3] 3555 3257 3010 2813 2648 2510 2388 2279 2184 2102
5 Median [5times5] 3423 3276 3130 2996 2872 2764 2665 2568 2493 2419
6 Median [7times7] 3319 3162 3075 2987 2900 2823 2748 2678 2620 2562
7 ATM [3times3] 3233 3174 3058 2932 2810 2694 2582 2483 2398 2312
8 ATM [5times5] 3112 3067 3038 2993 2940 2885 2818 2757 2688 2632
9 ATM [7times7] 2901 2876 2869 2858 2841 2819 2782 2756 2724 2687
10 Wiener [3times3] 3811 3445 3177 2944 2756 2599 2467 2356 2267 2185
11 Wiener [5times5] 3767 3382 3216 3074 2941 2818 2714 2619 2534 2460
12 Wiener [7times7] 3598 3252 3125 3008 2906 2815 2736 2658 2590 2526
13 AD 3348 3068 2979 2881 2782 2685 2597 2511 2436 2361
14 TV 3358 3121 3013 2908 2803 2710 2613 2531 2445 2376
15 Lee [3times3] 3789 3369 3105 2903 2740 2608 2502 2412 2334 2271
16 Lee [5times5] 3777 3391 3177 3028 2902 2805 2727 2656 2594 2547
17 Lee [7times7] 3728 3345 3138 3003 2903 2821 2757 2702 2651 2609
18 Bilateral [3times3] 3176 3107 3006 2897 2785 2683 2584 2497 2420 2348
19 Bilateral [5times5] 3088 2981 2950 2910 2863 2811 2756 2697 2641 2592
20 Bilateral [7times7] 2996 2736 2724 2712 2692 2672 2640 2616 2590 2552
21 NL-Means 3796 3462 2958 2568 2302 2114 1963 1843 1736 1651
22 AWWF 3516 3396 3258 3101 3011 2891 2821 2743 2710 2638
23 CSF [3times3] 3680 3275 2968 2739 2552 2400 2271 2159 2063 1973
24 CSF [5times5] 3499 3381 3235 3084 2949 2819 2705 2607 2514 2434
25 CSF [7times7] 3217 3126 3091 3044 2991 2925 2861 2792 2730 2696
Chapter-3 Development of Novel Spatial-Domain Image Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 99
Table-33 Filtering performance of various filters in terms of PSNR (dB) operated on Goldhill image under various noise conditions (σn varies from 5 to 50)
Peak-Signal-to-Noise Ratio PSNR (dB) Standard deviation of AWGN
SlNo Denoising Filters 5 10 15 20 25 30 35 40 45 50
Test Image Goldhill
1 Mean [3times3] 3154 3082 2983 2877 2769 2666 2573 2483 2401 2332
2 Mean [5times5] 2815 2802 2779 2748 2713 2669 2625 2574 2525 2477
3 Mean [7times7] 2648 2644 2634 262 2607 2583 2556 2525 2495 2453
4 Median [3times3] 3376 3044 2878 2722 2590 2467 2361 2265 2177 2102
5 Median [5times5] 3077 2860 2796 2732 2663 2595 2532 2466 2401 2343
6 Median [7times7] 2934 2729 2695 2662 2619 2578 2543 2499 2467 2420
7 ATM [3times3] 3188 3081 2980 2869 2760 2655 2556 2462 2377 2298
8 ATM [5times5] 2912 2803 2782 2757 2721 2685 2648 2605 2557 2515
9 ATM [7times7] 2702 2645 2638 2629 2616 2603 2586 2568 2546 2521
10 Wiener [3times3] 3663 3235 3041 2859 2696 2562 2441 2332 2247 2162
11 Wiener [5times5] 3488 3043 2956 2867 2776 2688 2600 2517 2445 2368
12 Wiener [7times7] 3299 2887 2831 2767 2708 2651 2589 2526 2471 2407
13 AD 3307 2988 2913 2827 2738 2650 2565 2483 2406 2340
14 TV 3311 3130 3019 2913 2809 2716 2627 2541 2462 2378
15 Lee [3times3] 3660 3238 3003 2831 2696 2586 2485 2398 2321 2258
16 Lee [5times5] 3629 3200 2995 2859 2765 2687 2612 2549 2493 2451
17 Lee [7times7] 3598 3156 2948 2822 2732 2662 2605 2559 2515 2469
18 Bilateral [3times3] 3144 3073 2977 2867 2763 2663 2567 2483 2399 2325
19 Bilateral [5times5] 3017 2772 2749 2720 2683 2639 2597 2550 2498 2451
20 Bilateral [7times7] 2913 2575 2564 2550 2532 2512 2485 2462 2427 2400
21 NL-Means 3659 3293 2892 2561 2310 2126 1980 1860 1759 1668
22 AWWF 3434 3234 3087 2918 2815 2720 2638 2539 2510 2446
23 CSF [3times3] 3615 3250 2960 2738 2559 2411 2282 2171 2079 1992
24 CSF [5times5] 3189 3127 3041 2940 2838 2741 2641 2552 2464 2389
25 CSF [7times7] 2914 2854 2836 2809 2776 2730 2692 2644 2590 2534
Chapter-3 Development of Novel Spatial-Domain Image Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 100
Table-34 Filtering performance of various filters in terms of PSNR (dB) operated on Barbara image under various noise conditions (σn varies from 5 to 50)
Peak-Signal-to-Noise Ratio PSNR (dB) Standard deviation of AWGN
SlNo Denoising Filters 5 10 15 20 25 30 35 40 45 50
Test Image Barbara
1 Mean [3times3] 2652 2602 2568 2525 2475 2419 2364 2306 2250 2195
2 Mean [5times5] 2381 2376 2368 2357 2343 2325 2304 2284 2256 2231
3 Mean [7times7] 2353 2351 2347 2341 2332 2321 2307 2292 2275 2253
4 Median [3times3] 2766 2585 2509 2431 2352 2276 2202 2133 2062 1998
5 Median [5times5] 2476 2326 2314 2296 2277 2249 2219 2190 2157 2121
6 Median [7times7] 2411 2354 2344 2331 2317 2298 2275 2258 2235 2214
7 ATM [3times3] 3199 3081 2980 2869 2760 2655 2556 2462 2377 2298
8 ATM [5times5] 2906 2803 2782 2757 2721 2685 2648 2605 2557 2515
9 ATM [7times7] 2734 2645 2638 2629 2616 2603 2586 2568 2546 2521
10 Wiener [3times3] 3657 3167 2865 2821 2750 2606 2489 2390 2297 2213
11 Wiener [5times5] 3478 2831 2743 2653 2570 2499 2432 2366 2309 2255
12 Wiener [7times7] 3319 2738 2673 2604 2545 2489 2434 2384 2337 2293
13 AD 2859 2606 2575 2535 2488 2437 2386 2330 2278 2226
14 TV 2749 2647 2599 2548 2494 2442 2388 2333 2281 2231
15 Lee [3times3] 3654 3159 2890 2705 2568 2462 2369 2291 2223 2166
16 Lee [5times5] 3621 3156 2896 2732 2613 2517 2436 2378 2326 2277
17 Lee [7times7] 3609 3130 2880 2722 2610 2528 2464 2406 2358 2319
18 Bilateral [3times3] 2622 2601 2567 2524 2474 2420 2365 2308 2253 2199
19 Bilateral [5times5] 2603 2369 2361 2351 2337 2320 2300 2279 2257 2229
20 Bilateral [7times7] 2558 2317 2314 2308 2301 2293 2280 2267 2252 2231
21 NL-Means 3688 3259 2868 2540 2301 2124 1974 1858 1752 1667
22 AWWF 3319 3169 3028 2954 2798 2671 2585 2475 2360 2273
23 CSF [3times3] 3188 3013 2922 2851 2698 2666 2551 2445 2249 2169
24 CSF [5times5] 2865 2820 2792 2756 2714 2671 2618 2557 2504 2455
25 CSF [7times7] 2796 2744 2739 2729 2716 2701 2683 2662 2633 2607
Chapter-3 Development of Novel Spatial-Domain Image Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 101
Table-35 Filtering performance of various filters in terms of RMSE operated on a Lena image under various noise conditions (σn varies from 5 to 50)
Root-Mean-Squared Error (RMSE) Standard deviation of AWGN
SlNo Denoising Filters 5 10 15 20 25 30 35 40 45 50
Test Image Lena
1 Mean [3times3] 515 590 696 827 960 1102 1240 1385 1527 1680
2 Mean [5times5] 828 845 873 913 960 1009 1077 1144 1207 1288
3 Mean [7times7] 1055 1063 1075 1091 1111 1137 1169 1207 1244 1294
4 Median [3times3] 454 627 818 1020 1224 1435 1649 1851 2083 2287
5 Median [5times5] 663 7395 826 930 1035 1157 1264 1389 1512 1642
6 Median [7times7] 844 884 940 999 1063 1139 1213 1275 1359 1438
7 ATM [3times3] 511 589 696 821 963 1106 1267 1428 1593 1759
8 ATM [5times5] 828 844 869 910 956 1004 1071 1134 1208 1298
9 ATM [7times7] 1029 1063 1071 1086 1101 1122 1152 1183 1218 1257
10 Wiener [3times3] 325 507 688 887 1088 1290 1496 1690 1874 2057
11 Wiener [5times5] 378 573 678 787 902 1017 1139 1257 1364 1484
12 Wiener [7times7] 414 673 762 859 948 1040 1119 1198 1287 1377
13 AD 470 688 772 874 989 1109 1236 1369 1491 1621
14 TV 428 555 663 782 902 1032 1167 1298 1445 1586
15 Lee [3times3] 325 540 736 925 1094 1269 1438 1588 1741 1871
16 Lee [5times5] 338 540 693 828 938 1050 1129 1218 1310 1377
17 Lee [7times7] 355 566 724 851 948 1032 1101 1167 1234 1285
18 Bilateral [3times3] 526 596 701 826 958 1104 1247 1382 1522 1667
19 Bilateral [5times5] 586 889 915 951 999 1048 1104 1175 1244 1318
20 Bilateral [7times7] 711 1188 1198 1213 1234 1257 1292 1300 1356 1402
21 NL-Means 325 481 859 1349 1823 2279 2708 3108 3483 3876
22 AWWF 459 545 655 754 874 999 1086 1152 1275 1295
23 CSF [3times3] 352 578 831 1094 1351 1614 1869 2131 2379 2639
24 CSF [5times5] 526 583 670 777 892 1017 1152 1280 1420 1550
25 CSF [7times7] 792 818 841 869 907 961 1012 1076 1139 1211
Chapter-3 Development of Novel Spatial-Domain Image Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 102
Table-36 Filtering performance of various filters in terms of RMSE operated on Pepper image under various noise conditions (σn varies from 5 to 50)
Root-Mean-Squared Error (RMSE) Standard deviation of AWGN
SlNo Denoising Filters 5 10 15 20 25 30 35 40 45 50
Test Image Pepper
1 Mean [3times3] 647 705 792 905 1029 1162 1298 1442 1581 1714
2 Mean [5times5] 751 770 805 849 902 969 1037 1110 1198 1276
3 Mean [7times7] 945 952 968 994 1023 1049 1097 1144 1195 1251
4 Median [3times3] 425 599 795 999 1208 1415 1629 1848 2063 2267
5 Median [5times5] 495 586 693 808 933 1055 1185 1326 14433 1573
6 Median [7times7] 558 668 739 818 902 986 1076 1167 1247 1333
7 ATM [3times3] 616 657 752 869 1002 1145 1303 1461 16116 1779
8 ATM [5times5] 708 744 770 810 861 918 991 1065 1152 1231
9 ATM [7times7] 903 928 935 948 966 991 1035 1065 1106 1155
10 Wiener [3times3] 316 481 655 859 1065 1275 1489 1690 18743 2060
11 Wiener [5times5] 333 517 627 739 861 991 1119 1249 1377 1499
12 Wiener [7times7] 405 601 696 798 897 997 1091 1193 12903 1389
13 AD 540 744 823 923 1035 1157 1280 1415 15428 1680
14 TV 534 701 793 895 1009 1124 1257 1382 15275 1652
15 Lee [3times3] 325 525 714 900 1086 1264 1430 1586 1734 1864
16 Lee [5times5] 329 512 655 780 902 1007 1104 1195 12852 1356
17 Lee [7times7] 348 540 685 803 900 989 1065 1134 12036 1264
18 Bilateral [3times3] 658 711 800 907 1032 1160 1300 1438 15708 1706
19 Bilateral [5times5] 728 823 851 892 943 1002 1065 1142 12189 1287
20 Bilateral [7times7] 810 1091 1106 1122 1149 1175 1220 1254 12903 1349
21 NL-Means 322 471 846 1326 1800 2236 2659 3054 34553 3809
22 AWWF 445 510 596 716 795 912 989 1083 1124 1221
23 CSF [3times3] 368 586 836 1088 1349 1606 1864 2121 2371 2629
24 CSF [5times5] 453 517 614 731 854 991 1132 1267 1410 1545
25 CSF [7times7] 628 696 724 765 813 877 9460 1022 1099 1142
Chapter-3 Development of Novel Spatial-Domain Image Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 103
Table-37 Filtering performance of various filters in terms of RMSE operated on Goldhill image
under various noise conditions (σn varies from 5 to 50)
Root-Mean-Squared Error (RMSE) Standard deviation of AWGN
SlNo Denoising Filters 5 10 15 20 25 30 35 40 45 50
Test Image Goldhill
1 Mean [3times3] 675 733 822 929 1052 1184 1318 1462 1607 1740
2 Mean [5times5] 997 1012 1041 1077 1122 1180 1241 1316 1393 1472
3 Mean [7times7] 1209 1214 1229 1248 1267 1303 1344 1393 1442 1513
4 Median [3times3] 523 765 925 1109 1290 1489 1680 1879 2078 2267
5 Median [5times5] 737 946 1017 1096 1188 1285 1382 1489 1606 1716
6 Median [7times7] 870 1101 1145 1188 1249 1310 1364 1433 1489 1570
7 ATM [3times3] 649 734 823 935 1060 1198 1343 1496 1649 1807
8 ATM [5times5] 892 1009 1035 1065 1111 1157 1208 1269 1341 1407
9 ATM [7times7] 1136 1211 1221 1234 1254 1272 1298 1326 1359 1397
10 Wiener [3times3] 375 614 767 946 1142 1333 1532 1739 1917 2114
11 Wiener [5times5] 459 765 846 938 1042 1152 1277 1405 1527 1667
12 Wiener [7times7] 571 918 979 1053 1127 1203 1292 1389 1481 1593
13 AD 566 816 889 981 1088 1206 1328 1461 1596 1723
14 TV 563 693 787 889 1004 1116 1236 1366 1496 1649
15 Lee [3times3] 377 612 803 979 1142 1298 1458 1611 1762 1894
16 Lee [5times5] 390 640 810 946 1055 1155 1259 1354 1443 1514
17 Lee [7times7] 405 673 854 989 1096 1188 1269 1338 1407 1484
18 Bilateral [3times3] 683 739 826 938 1058 1188 1326 1461 1609 1751
19 Bilateral [5times5] 790 1048 1076 1111 1160 1221 1280 1351 1435 1514
20 Bilateral [7times7] 891 1313 1331 1351 1382 1414 1458 1496 1558 1606
21 NL-Means 377 573 892 1336 1782 2203 2601 2993 3363 3735
22 AWWF 489 614 729 884 997 1111 1221 1369 1415 1524
23 CSF [3times3] 397 604 844 1088 1338 1588 1841 2093 2328 2573
24 CSF [5times5] 648 696 767 861 971 1086 1218 1349 1494 1629
25 CSF [7times7] 890 953 971 1004 1042 1099 1147 1213 1290 1377
Chapter-3 Development of Novel Spatial-Domain Image Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 104
Table-38 Filtering performance of various filters in terms of RMSE operated on Barbara image
under various noise conditions (σn varies from 5 to 50)
Root-Mean-Squared Error (RMSE) Standard deviation of AWGN
SlNo Denoising Filters 5 10 15 20 25 30 35 40 45 50
Test Image Barbara
1 Mean [3times3] 1203 1275 1326 1393 1475 1574 1677 1792 1912 2037
2 Mean [5times5] 1644 1654 1669 1690 1718 1754 1797 1838 1899 1954
3 Mean [7times7] 1698 1702 1710 1722 1741 1762 1790 1822 1858 1905
4 Median [3times3] 1055 1298 1417 1550 1698 1853 2019 2187 2374 2555
5 Median [5times5] 1474 1751 1774 1813 1851 1912 1981 2047 2126 2216
6 Median [7times7] 1588 1695 1713 1741 1769 1807 1856 1894 1943 1991
7 ATM [3times3] 641 734 823 935 1060 1198 1343 1496 1649 1807
8 ATM [5times5] 898 1009 1035 1065 1111 1157 1208 1269 1341 1407
9 ATM [7times7] 1095 1211 1221 1234 1254 1272 1298 1326 1359 1397
10 Wiener [3times3] 378 527 940 882 1073 1267 1450 1626 1810 1994
11 Wiener [5times5] 465 979 1083 1201 1320 1433 1550 1672 1785 1899
12 Wiener [7times7] 558 1088 1173 1269 1359 1450 1545 1637 1728 1818
13 AD 948 1267 1313 1377 1453 1540 1634 1741 1851 1963
14 TV 1076 1208 1277 1356 1443 1532 1629 1736 1843 1953
15 Lee [3times3] 379 670 912 1132 1326 1496 1665 1823 1971 2106
16 Lee [5times5] 394 673 907 1096 1257 1405 1542 1649 1751 1851
17 Lee [7times7] 399 693 925 1109 1262 1387 1494 1596 1688 1764
18 Bilateral [3times3] 1246 1275 1326 1394 1476 1570 1672 1787 1904 2027
19 Bilateral [5times5] 1273 1665 1680 1700 1728 1762 1802 1848 1894 1958
20 Bilateral [7times7] 1341 1769 1774 1787 1802 1818 1846 1874 1907 1953
21 NL-Means 365 596 938 1369 1802 2208 2626 3001 3391 3740
22 AWWF 558 663 780 849 1017 1175 1298 1473 1683 1861
23 CSF [3times3] 649 793 879 956 1139 1183 1351 1527 1912 2098
24 CSF [5times5] 941 991 1022 1065 1119 1175 1249 1341 1425 1509
25 CSF [7times7] 1019 1081 1088 1101 1116 1137 1160 1188 1229 1267
Chapter-3 Development of Novel Spatial-Domain Image Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 105
Table-39 Filtering performance of various filters in terms of UQI operated on a Lena image
under various noise conditions (σn varies from 5 to 50)
Universal Quality Index (UQI) Standard deviation of AWGN
SlNo Denoising Filters 5 10 15 20 25 30 35 40 45 50
Test Image Lena
1 Mean [3times3] 09941 09922 09892 09849 09797 09732 09663 09579 09488 09376
2 Mean [5times5] 09845 09838 09827 09811 09791 09769 09736 09700 09665 09613
3 Mean [7times7] 09743 09739 09733 09725 09714 09701 09683 09659 09636 09601
4 Median [3times3] 09955 09913 09853 09773 09676 09559 09425 09286 09117 08951
5 Median [5times5] 09903 09878 09848 09808 09762 09703 09648 09577 09503 09419
6 Median [7times7] 09841 09824 09801 09775 09745 09709 09669 09636 09585 09539
7 ATM [3times3] 09939 09922 09892 09851 09795 09731 09649 09558 09454 09340
8 ATM [5times5] 09878 09838 09828 09812 09792 09772 09740 09710 09671 09621
9 ATM [7times7] 09812 09739 09734 09728 09720 09710 09694 09678 09659 09637
10 Wiener [3times3] 09977 09943 09896 09827 09742 0964 09517 09386 09249 09098
11 Wiener [5times5] 09958 09926 09897 09861 09818 09768 09709 09646 09581 09503
12 Wiener [7times7] 09907 09897 09868 09833 09797 09755 09715 09671 09617 09557
13 AD 09951 09895 09867 09830 09784 09728 09663 09586 09506 09417
14 TV 09959 09931 09902 09864 09820 09765 09701 09633 09547 09458
15 Lee [3times3] 09977 09936 09881 09813 09740 09650 09554 09456 09346 09239
16 Lee [5times5] 09955 09936 09893 09847 09805 09755 09715 09666 09610 09566
17 Lee [7times7] 09936 09929 09884 09839 09799 09761 09725 09688 09648 09613
18 Bilateral [3times3] 09939 09921 09891 09849 09797 09731 09658 09578 09487 09385
19 Bilateral [5times5] 09916 09828 09816 09802 09781 09757 09728 09686 09646 09598
20 Bilateral [7times7] 09879 09706 09702 09693 09682 09664 09642 09623 09592 09557
21 NL-Means 09977 09947 09840 09616 09318 08971 08601 08230 07861 07451
22 AWWF 09953 09934 09898 09865 09820 09765 09721 09690 09620 09568
23 CSF [3times3] 09973 09949 09849 09742 09611 09452 09272 09067 08854 08614
24 CSF [5times5] 09938 09924 09900 09866 09822 09771 09710 09640 09555 09469
25 CSF [7times7] 09912 09848 09839 09828 09813 09789 09765 09735 09700 09659
Chapter-3 Development of Novel Spatial-Domain Image Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 106
Table-310 Filtering performance of various filters in terms of UQI operated on Pepper image
under various noise conditions (σn varies from 5 to 50)
Universal Quality Index (UQI) Standard deviation of AWGN
SlNo Denoising Filters 5 10 15 20 25 30 35 40 45 50
Test Image Pepper
1 Mean [3times3] 09927 09912 09889 09856 09814 09762 09702 09631 09557 09476
2 Mean [5times5] 09900 09894 09884 09871 09853 09831 09805 09776 09737 09699
3 Mean [7times7] 09839 09836 09830 09821 09809 09799 09779 09758 09734 09706
4 Median [3times3] 09969 09938 09890 09828 09750 09659 09552 09431 09298 09163
5 Median [5times5] 09957 09940 09916 09885 09848 09805 09756 09696 09641 09578
6 Median [7times7] 09938 09921 09903 09882 09855 09827 09795 09759 09725 09687
7 ATM [3times3] 09929 09924 09901 09868 09824 09772 09706 09631 09553 09460
8 ATM [5times5] 09911 09901 09894 09883 09868 09850 09825 09798 09764 09732
9 ATM [7times7] 09886 09844 09842 09838 09832 09823 09807 09796 09780 09760
10 Wiener [3times3] 09978 09959 09925 09871 09802 09715 09614 09503 09389 09261
11 Wiener [5times5] 09955 09953 09930 09903 09868 09824 09775 09718 09655 09588
12 Wiener [7times7] 09941 09935 09913 09886 09855 09820 09782 09738 09692 09638
13 AD 09949 09901 09879 09848 09809 09761 09707 09641 09571 09488
14 TV 09950 09913 09889 09859 09820 09778 09722 09665 09594 09525
15 Lee [3times3] 09982 09952 09912 09859 09795 09722 09645 09563 09475 09392
16 Lee [5times5] 09960 09954 09925 09893 09857 09820 09784 09742 09701 09665
17 Lee [7times7] 09954 09949 09917 09886 09856 09825 09796 09766 09734 09702
18 Bilateral [3times3] 09925 09912 09888 09855 09813 09762 09700 09632 09559 09476
19 Bilateral [5times5] 09913 09885 09876 09862 09843 09821 09795 09761 09726 09689
20 Bilateral [7times7] 09879 09807 09799 09791 09778 09763 09742 09721 09697 09662
21 NL-Means 09978 09961 09877 09702 09462 09191 08885 08572 08224 07908
22 AWWF 09974 09960 09941 09912 09888 09852 09791 09745 09700 09656
23 CSF [3times3] 09976 09962 09879 09796 09689 09561 09412 09246 09068 08862
24 CSF [5times5] 09964 09952 09949 09915 09871 09828 09778 09716 09652 09571
25 CSF [7times7] 09925 09913 09906 09895 09889 09861 09838 09810 09785 09766
Chapter-3 Development of Novel Spatial-Domain Image Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 107
Table-311 Filtering performance of various filters in terms of UQI operated on Goldhill image
under various noise conditions (σn varies from 5 to 50)
Universal Quality Index (UQI) Standard deviation of AWGN
SlNo Denoising Filters 5 10 15 20 25 30 35 40 45 50
Test Image Goldhill
1 Mean [3times3] 09939 09928 09909 09884 09850 09809 09762 09705 0964 09575
2 Mean [5times5] 09866 09861 09853 09841 09827 09807 09784 09754 09722 09687
3 Mean [7times7] 09801 09799 09793 09785 09777 09762 09744 09722 09699 09665
4 Median [3times3] 09945 09922 09886 09838 09781 09710 09631 09542 09444 09345
5 Median [5times5] 09916 09880 09861 09839 09812 09780 09746 09705 09658 09610
6 Median [7times7] 09878 09838 09824 09810 09790 09769 09749 09723 09702 09669
7 ATM [3times3] 09946 09928 09909 09883 09850 09809 09760 09703 09639 09569
8 ATM [5times5] 09923 09862 09855 09847 09833 09819 09802 09782 09757 09732
9 ATM [7times7] 09883 09800 09797 09792 09786 09780 09771 09761 09749 09734
10 Wiener [3times3] 09971 09950 09921 09880 09824 09760 09682 09589 09497 09385
11 Wiener [5times5] 09942 09921 09903 09880 09852 09816 09773 09724 09670 09602
12 Wiener [7times7] 09917 09886 09870 09848 09824 09798 09764 09725 09684 09628
13 AD 09957 09910 09893 09869 09838 09801 09755 09702 09641 09578
14 TV 09958 09936 09917 09894 09865 09833 09795 09750 09700 09636
15 Lee [3times3] 09981 09950 09914 09872 09824 09773 09711 09645 09572 09501
16 Lee [5times5] 09956 09946 09912 09879 09848 09817 09780 09743 09704 09670
17 Lee [7times7] 09947 09940 09902 09868 09836 09805 09775 09747 09716 09680
18 Bilateral [3times3] 09938 09927 09908 09881 09848 09807 09757 09703 09636 09565
19 Bilateral [5times5] 09916 09853 09844 09832 09815 09793 09770 09740 09703 09662
20 Bilateral [7times7] 09810 08936 09764 09754 09742 09725 09704 09683 09649 09620
21 NL-Means 09967 09956 09891 09767 09590 09381 09147 08896 08631 08339
22 AWWF 09961 09950 09938 09895 09872 09840 09786 09750 09733 09713
23 CSF [3times3] 09979 09961 09940 09843 09762 09666 09550 09418 09282 09126
24 CSF [5times5] 09944 09935 09920 09899 09873 09847 09797 09749 09693 09630
25 CSF [7times7] 09886 09877 09871 09862 09850 09832 09815 09792 09762 09751
Chapter-3 Development of Novel Spatial-Domain Image Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 108
Table-312 Filtering performance of various filters in terms of UQI operated on Barbara image
under various noise conditions (σn varies from 5 to 50)
Universal Quality Index (UQI) Standard deviation of AWGN
SlNo Denoising Filters 5 10 15 20 25 30 35 40 45 50
Test Image Barbara
1 Mean [3times3] 09753 09739 09718 09688 09649 09601 09545 09478 09403 09318
2 Mean [5times5] 09560 09554 09545 09532 09515 09491 09462 09433 0939 09346
3 Mean [7times7] 09525 09521 09516 09507 09494 0948 09458 09433 09407 09371
4 Median [3times3] 09818 09733 09683 09622 09549 09466 09371 09268 09145 09024
5 Median [5times5] 09807 09508 09495 09475 09450 09416 09374 09335 09286 09227
6 Median [7times7] 09766 09536 09524 09508 09491 09469 09440 09420 09390 09360
7 ATM [3times3] 09786 09740 09717 09686 09647 09600 09538 09474 09401 09314
8 ATM [5times5] 09769 09555 09548 09538 09524 09504 09481 09458 09430 09398
9 ATM [7times7] 09716 09523 09522 09516 09512 09501 09490 09476 09432 09411
10 Wiener [3times3] 09933 09904 09861 09803 09734 09651 09552 09447 09331 09201
11 Wiener [5times5] 09919 09847 09812 09767 09718 09665 09607 09538 09470 09395
12 Wiener [7times7] 09898 09808 09776 09737 09696 09652 09603 09550 09495 09434
13 AD 09857 09741 09722 09694 09659 09614 09564 09503 09436 09358
14 TV 09816 09766 09738 09707 09668 09626 09576 09520 09461 09396
15 Lee [3times3] 09978 09930 09870 09800 09724 09646 09559 09470 09377 09284
16 Lee [5times5] 09949 09929 09871 09810 09748 09682 09613 09554 09490 09425
17 Lee [7times7] 09932 09925 09865 09805 09744 09688 09634 09576 09519 09469
18 Bilateral [3times3] 09751 09738 09716 09686 09646 09597 09542 09475 09400 09316
19 Bilateral [5times5] 09734 09543 09534 09520 09501 09478 09447 09414 09378 09329
20 Bilateral [7times7] 09688 09483 09477 09466 09453 09436 09414 09386 09357 09312
21 NL-Means 09957 09943 09865 09716 09516 09285 09010 08737 08423 08127
22 AWWF 09943 09918 09893 09836 09748 09690 09614 09568 09492 09453
23 CSF [3times3] 09964 09945 09895 09773 09721 09666 09536 09485 09313 09261
24 CSF [5times5] 09913 09896 09866 09838 09793 09779 09692 09576 09517 09458
25 CSF [7times7] 09834 09818 09799 09783 09779 09752 09717 09659 09600 09534
Chapter-3 Development of Novel Spatial-Domain Image Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 109
Table-313 Method Noise MN of various filters operated on different test images
Sl No
Denoising Images
Filters
Lena Pepper Goldholl Barbara
1 Mean [3times3] 262 290 410 668
2 Mean [5times5] 443 408 642 946
3 Mean [7times7] 573 520 793 1035
4 Median [3times3] 132 153 252 438
5 Median [5times5] 270 239 443 693
6 Median [7times7] 395 311 499 744
7 ATM [3times3] 262 290 410 668
8 ATM [5times5] 443 408 642 946
9 ATM [7times7] 573 520 793 1035
10 Wiener [3times3] 186 204 318 387
11 Wiener [5times5] 367 351 540 637
12 Wiener [7times7] 464 387 576 668
13 AD 204 237 295 497
14 TV 211 234 334 573
15 Lee [3times3] 00118 109 00336 00583
16 Lee [5times5] 00530 114 01109 02057
17 Lee [7times7] 01315 201 01853 110
18 Bilateral [3times3] 288 308 423 680
19 Bilateral [5times5] 497 433 663 966
20 Bilateral [7times7] 601 545 826 1104
21 NL-Means 117 137 186 211
22 AWWF 183 206 321 387
23 CSF [3times3] 122 142 183 318
24 CSF [5times5] 272 257 402 675
25 CSF [7times7] 4437 390 619 907
Chapter-3 Development of Novel Spatial-Domain Image Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 110
Table-314 Execution time (seconds) TE taken by various filters for Lena image
Execution time (seconds) in three different hardware
platforms Sl No Denoisg Filters
SYSTEM-1 SYSTEM-2 SYSTEM-3
1 Mean [3times3] 318 701 1713
2 Mean [5times5] 323 712 1749
3 Mean [7times7] 327 720 1776
4 Median [3times3] 402 742 2445
5 Median [5times5] 409 747 2469
6 Median [7times7] 415 812 2490
7 ATM [3times3] 732 1677 3018
8 ATM [5times5] 809 1723 3056
9 ATM [7times7] 813 1784 3084
10 Wiener [3times3] 787 1559 2806
11 Wiener [5times5] 807 1598 2876
12 Wiener [7times7] 843 1670 3006
13 AD ------ ------- ------
14 TV ------ ------- ------
15 Lee [3times3] 874 1426 3509
16 Lee [5times5] 887 1446 3545
17 Lee [7times7] 968 1579 3779
18 Bilateral [3times3] 536 1100 3265
19 Bilateral [5times5] 583 1353 3520
20 Bilateral [7times7] 588 1359 3639
21 NL-Means 44667 99620 221838
22 AWWF 1181 2417 4546
23 CSF [3times3] 338 706 1866
24 CSF [5times5] 343 717 1898
25 CSF [7times7] 352 729 1930
Chapter-3 Development of Novel Spatial-Domain Image Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 111
Fig 38 Performance comparison of various filters in terms of PSNR (dB) under
different noise levels of AWGN on the images
(a) Lena
(b) Pepper
(c) Goldhill
(d) Barbara
PS
NR
(d
B)
PSNR values for Lena Image PSNR values for Pepper Image
PS
NR
(d
B)
(a) (b)
σn σn
PSNR values for Goldhill Image
PS
NR
(d
B)
PSNR values for Barbara Image P
SN
R (
dB
)
(c) (d)
σn σn
Chapter-3 Development of Novel Spatial-Domain Image Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 112
Fig 39 Performance comparison of various filters in terms of RMSE under
different noise levels of AWGN on the images
(a) Lena (b) Pepper
(c) Goldhill (d) Barbara
RM
SE
RMSE values for Lena Image
RM
SE
RMSE values for Pepper Image
(a) (b)
σn σn
RMSE values for Goldhill Image
RM
SE
RMSE values for Barbara Image
RM
SE
(c) (d)
σn σn
Chapter-3 Development of Novel Spatial-Domain Image Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 113
Fig 310 Performance comparison of various filters in terms of UQI under different noise levels of AWGN on the images
(a) Lena
(b) Pepper
(c) Goldhill
(d) Barbara
UQI values for Lena Image
UQ
I
UQI values for Pepper Image
UQ
I
(a) (b)
σn σn
UQ
I
UQ
I
UQI values for Barbara Image UQI values for Goldhill Image
(c) (d)
σn σn
Chapter-3 Development of Novel Spatial-Domain Image Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 114
(a) (b) (c) (d)
(e) (f) (g) (h)
(i) (j) (k) (l)
(m)
Fig 311 Performance of Various Filters for Lena Image with AWGN σn = 15
(a) Original image (b) Noisy image
(c) ndash (m) Results of various filtering schemes
(c) Mean (d) Median (e) ATM (f) Wiener (g) AD (h) TV (i) Lee (j) Bilateral
(k) NL-Means (l) AWWF (m) CSF
Chapter-3 Development of Novel Spatial-Domain Image Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 115
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
(j)
(k)
(l)
(m)
Fig 312 Performance of Various Filters for Lena Image (Smooth Region)
with AWGN σn = 15
(a) Original image (b) Noisy image
(c) ndash (m) Results of various filtering schemes
(c) Mean (d) Median (e) ATM (f) Wiener (g) AD (h) TV (i) Lee
(j) Bilateral (k) NL-Means (l) AWWF (m) CSF
Chapter-3 Development of Novel Spatial-Domain Image Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 116
(a) (b) (c) (d) (e)
(f) (g) (h) (i) (j)
(k) (l) (m)
Fig 313 Performance of Various Filters for Lena Image (Complex Region) with
AWGN σn = 15
(a) Original image (b) Noisy image
(c) ndash (m) Results of various filtering schemes
(c) Mean (d) Median (e) ATM (f) Wiener (g) AD (h) TV (i) Lee (j) Bilateral
(k) NL-Means (l) AWWF (m) CSF
Chapter-3 Development of Novel Spatial-Domain Image Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 117
(a) (b) (c) (d)
(e) (f) (g) (h)
(i) (j) (k) (l)
(m)
Fig 314 Performance of Various Filters for Pepper Image with AWGN σn = 15
(a) Original image (b) Noisy image
(c) ndash (s) Results of various filtering schemes
(c) Mean (d) Median (e) ATM (f) Wiener (g) AD (h) TV (i) Lee (j) Bilateral
(k) NL-Means (l) AWWF (m) CSF
Chapter-3 Development of Novel Spatial-Domain Image Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 118
(a) (b) (c) (d)
(e) (f) (g) (h)
(i) (j) (k) (l)
(m)
Fig 315 Performance of Various Filters for Lena Image with AWGN σn = 40
(a) Original image (b) Noisy image
(c) ndash (s) Results of various filtering schemes
(c) Mean (d) Median (e) ATM (f) Wiener (g) AD (h) TV (i) Lee (j) Bilateral
(k) NL-Means (l) AWWF (m) CSF
Chapter-3 Development of Novel Spatial-Domain Image Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 119
(a) (b) (c)
(d) (e) (f)
(g) (h) (i)
(j) (k) (l)
(m)
Fig 316 Performance of Various Filters for Lena Image (Smooth Region) with
AWGN σn = 40
(a) Original image (b) Noisy image
(c) ndash (m) Results of various filtering schemes
(c) Mean (d) Median (e) ATM (f) Wiener (g) AD (h) TV (i) Lee
(j) Bilateral (k) NL-Means (l) AWWF (m) CSF
Chapter-3 Development of Novel Spatial-Domain Image Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 120
(a) (b) (c) (d) (e)
(f) (g) (h) (i) (j)
(k)
(l) (m)
Fig 317 Performance of Various Filters for Lena Image (Complex Region) with AWGN σn = 40
(a) Original image (b) Noisy image
(c) ndash (m) Results of various filtering schemes
(c) Mean (d) Median (e) ATM (f) Wiener (g) AD (h) TV (i) Lee
(j) Bilateral (k) NL-Means (l) AWWF (m) CSF
Chapter-3 Development of Novel Spatial-Domain Image Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 121
Fig 318 Performance of Various Filters for Pepper Image with AWGN σn = 40
(a) Original image (b) Noisy image
(c) ndash (m) Results of various filtering schemes
(c) Mean (d) Median (e) ATM (f) Wiener (g) AD (h) TV (i) Lee (j) Bilateral
(k) NL-Means (l) AWWF (m) CSF
(d)
(a) (b) (c) (d)
(e) (f) (g) (h)
(i) (j) (k) (l)
(l)
(m)
Chapter-3 Development of Novel Spatial-Domain Image Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 122
34 Conclusion
It is observed that the proposed filters AWWF and CSF are very efficient in
suppressing AWGN from images
It is seen that AWWF outperforms the other existing spatial-domain filters in
suppressing additive noise under moderate noise (10lt σnle30) conditions The PSNR
and UQI values are relatively high as compared to other filters under moderate noise
conditions The NL-means filter shows better performance under low noise (σnle10)
condition
Hence it may be concluded that the AWWF is best spatial-domain filter in
suppressing additive noise under moderate noise conditions It preserves the edges
and fine details very well as observed in Fig 313 compared to other filters The
filter does not perform well under high noise conditions as observed in Fig 317 and
tables Table 31- Table 312
On the other hand the proposed circular spatial filter (CSF) is an excellent
filter for suppressing high power additive noise Its performance is observed to be
much better as compared to other spatial-domain filters under high noise conditions
This is quite evident from the observation tables for PSNR RMSE and UQI
Moreover the visual quality of its output under high noise conditions is very good as
observed in Fig 315 The filter CSF is also seen to preserve fine details and edges and
is seen not to yield unnecessarily high blurring effect in smooth regions under high
noise conditions This is evident from Fig 316
Thus it is observed that the proposed filter AWWF is very good in
suppressing moderate power AWGN whereas the CSF is found to be a very efficient
filter under nigh noise conditions
Comparing the method noise of various spatial-domain filters it is found from
Table 313 that the existing Lee filter is best among all Nevertheless the proposed
filter CSF with a window of 3times3 is also observed to be a good competitor for the test
image Pepper
Chapter-3 Development of Novel Spatial-Domain Image Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 123
The execution time TE taken by a filter is an important measure to find its
computational complexity It is observed from Table 314 that the proposed filter
CSF is second only to the simplest mean filter Hence its computational complexity is
found to be very low whereas the other proposed filter AWWF is observed to possess
moderate computational complexity
The proposed filter CSF may be used in many real-time applications due to its
following advantages [P2]
i) The circular spatial filter has got relatively low computational
complexity as compared to other efficient spatial-domain filters and it
is very close to the simplest mean filter
ii) It suppresses AWGN very effectively from homogenous and
monotonically increasing and decreasing regions as compared to
others
iii) The filter retains the detailed information very well as compared to
other spatial-domain filters
iv) As the method noise is quite less which is very close to NL-Means
filter the filter causes little distortion to the original image
Thus the proposed filtering schemes are observed to be very good
spatial-domain image denoising filters
Chapter 4
Development of
Transform-Domain
Filters
Chapter-4 Development of Transform-Domain Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 125
Preview
Image transforms play an important role in digital image processing Various
image transforms such as Discrete Cosine Transform (DCT) [1517] Singular Value
Decomposition (SVD) Transform [2] Discrete Wavelet Transform (DWT) [18-21]
etc are employed for various applications like image denoising image compression
object recognition etc
The two-dimensional DCT is a very efficient transform for achieving a sparse
representation of image blocks For natural images its decorrelating performance is
close to the optimum Karhunen-Loegraveve (KL) transform [2] Thus the DCT has been
successfully used as the key element in many denoising applications However in the
presence of singularities or edges such near-optimality fails Because of the lack of
sparsity edges can not be restored effectively and ringing artifacts arising from Gibbs
phenomenon become visible
The Discrete Wavelet Transform (DWT) is another powerful tool for image
denoising Image denoising using wavelet techniques is effective because of its ability
to capture most of the energy of a signal in a few significant transform coefficients
4
Chapter-4 Development of Transform-Domain Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 126
when image is corrupted with Gaussian noise One method that has received
considerable attention in recent years is wavelet thresholding or shrinkage an idea of
killing coefficients of low magnitude relative to some threshold The various
thresholding or shrinkage techniques proposed in the literature are VisuShrink [9899]
SureShrink [100101] BayesShrink [102] NeighShrink [103] SmoothShrink [104]
OracleShrink [102] OracleThresh [102 ] etc The windowing techniques such as
locally adaptive window maximum likelihood (LAWML) estimation [105] are also
available in the literature where the statistical relationship of coefficients in a
neighborhood is considered The wavelet domain methods are suitable in retaining the
detailed structures but they introduce mat-like structures in the smooth regions of the
filtered image
In this chapter three transform-domain image denoising filters (i) Gaussian
Shrinkage based DCT-domain (GS-DCT) Filter [P3] (ii) Total Variation based DWT-
domain (TV-DWT) Filter [P4] (iii) Region Merging based DWT-domain (RM-DWT)
Filter [P5] are developed The performances of the developed filters are compared
with existing transform-domain filter in terms of objective and subjective evaluations
to demonstrate the effectiveness of the developed filters
The organization of this chapter is outlined below
Development of Gaussian Shrinkage based DCT-domain Filter
Development of Total Variation based DWT-domain Filter
Development of Region Merging based DWT-domain Filter
Simulation Results
Conclusion
Chapter-4 Development of Transform-Domain Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 127
41 Development of Gaussian Shrinkage based DCT-domain
Filter
The proposed filter Gaussian Shrinkage based DCT-domain (GS-DCT) filter
[P3] presents a simple image denoising scheme by using an adaptive Gaussian
smoothing based thresholding in the discrete cosine transform (DCT) domain The
edge pixel density on the current sliding window decides the threshold level in the
DCT domain for removing the high frequency components eg noise Since the hard
threshold approach is discontinuous in nature and it tends to yield artifacts (like Gibbs
phenomenon) in the recovered image a method of associating Gaussian weights to
DCT coefficients is proposed
The section is organized as follows
bull The Proposed Scheme
bull Mask Selection
bull Parameters Selection
411 The Proposed Scheme
In the proposed method soft thresholding technique is applied in DCT domain
for suppression of additive white Gaussian noise (AWGN) The soft thresholding
decision is based on the image complexity in the windowed data Here the percentage
of edge pixel (PEP) is considered to determine the image complexity The block
diagram of the proposed method is shown in Figure 41 Seven threshold values are
predefined which are selected adaptively depending on the percentage of edge pixels
in the current window The PEP can be defined as follows
100Number of edge pixels
PEPTotal number of pixels in the current window
= times (41)
Thresholding is nothing but considering certain number of DCT coefficients and
making others zero In other words the DCT coefficient matrix is multiplied point-by-
Chapter-4 Development of Transform-Domain Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 128
point by another matrix of same size of suitable values at desired row and column to
get the modified DCT coefficient matrix This matrix is termed as mask The values
of mask are obtained from a Gaussian function defined in equation (42)
2
2
( ) exp2
exp
2
exp2
kxf x A
xA
k
xA
c
σ
σ
= minus
minus =
minus =
(42)
where x = spatial-distance
σ = standard deviation of the Gaussian function
k = a constant
c =σ2k = controlling parameter
Thus a mask contains varying weights for the DCT coefficients These
weights are tapered from low frequency to high frequency components so that noise
gets less scope to reproduce itself Choosing a mask is very important The shaded
portions represented in the Fig41 in the mask represent the non-zero Gaussian values
and rests are zeros
Chapter-4 Development of Transform-Domain Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 129
Fig 41 Block Diagram of the Proposed Filter
INPUT NOISY
IMAGE
7times7
window
DCT
Edge Detection
Percentage of
Edge Pixels Adaptive Threshold
Selection
7times7 DCT Coefficient matrix
FILTERED IMAGE
Masking matrices
IDCT
Point by point matrix
multiplication Mask-1 Mask-2 Mask-3 Mask-4 Mask-5 Mask-6 Mask-7
Chapter-4 Development of Transform-Domain Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 130
412 Mask Selection
The selection of an appropriate mask depends on the PEP value If in a
window the percentage of edge pixels (PEP) is low then the image segment most
probably contains a flat or almost a flat or monotonic region that may be encoded in
DCT domain with less number of coefficients On the other hand if the PEP is high
then the selected image segment must be encoded with more number of DCT
coefficients in order to preserve the edges and fine details of the image Based on this
heuristic a mask selection criterion is proposed here
1 5
2 5 8
3 8 12
4 12 18
5 18 24
6 24 30
7 30
Mask if PEP
Mask if PEP
Mask if PEP
Mask Mask if PEP
Mask if PEP
Mask if PEP
Mask if PEP
le lt le lt le
= lt le lt le
lt le
lt
(43)
The mask provides the Gaussian weights to the DCT coefficients of the image
block The DC coefficient which is located at the upper left corner holds most of the
image energy and represents the average value This DC coefficient should be
retained as it is and hence it should be provided with unity weight Other DCT
coefficients are necessarily given weights less than unity The weights are varied in
accordance with (42)
Chapter-4 Development of Transform-Domain Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 131
413 Parameters Selection
The appropriate value of the parameter lsquoArsquo and the parameter lsquocrsquo has to be
chosen for efficient suppression of Gaussian noise
The selection of parameter lsquoArsquo
In (42) for x = 0 f (0) = A
The DC coefficient of DCT block should be provided with a weight of 1 ie f(0) = 1
Hence A = 1
So the parameter A in (42) is set to 1
The selection of parameter lsquocrsquo
The filtering performance of the proposed method in terms of peak-signal-to-
noise ratio (PSNR) is tested on the noisy images Lena Pepper and Goldhill for
different values of lsquocrsquo The noisy version of the test images are generated by
corrupting the images with Gaussian noise of standard deviation σn = 20 and 30 The
values of c are varied from 001 to 01 It is observed that the PSNR increases upto
c = 004 Between the values of c = 004 and 007 the PSNR almost remains constant
Then the PSNR detoriates slightly beyond 007 The PSNR values obtained are
plotted against the values of c which are shown in Fig 42
It is observed that high values of PSNR are obtained while the parameter lsquocrsquo
lies within 004 to 007 for various images under different noise conditions Therefore
an optimal value of 005 is chosen for the parameter lsquocrsquo in (42) for efficient
suppression of additive noise
The developed filter GS-DCT is tested and its simulation results are presented
in Section 44
Chapter-4 Development of Transform-Domain Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 132
002 004 006 008 0127
28
29
30
31
Lena
Pepper
Goldhill
Pea
k S
ign
al
to N
ois
e R
ati
o (
dB
)
parameter c
(a)
Fig 42 PSNR vs different values of c for noisy images Lena
Pepper and Goldhill under AWGN of
(a) σn = 20
(b) σn = 30
002 004 006 008 0125
26
27
28
29
Lena
Pepper
Goldhill
Pea
k S
ign
al
to N
ois
e R
ati
o (
dB
)
(b)
parameter c
Chapter-4 Development of Transform-Domain Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 133
42 Development of Total Variation based DWT-domain Filter
The proposed filter introduces a Total Variation (TV) based wavelet domain
scheme for image denoising The TV algorithm [69] is employed in spatial-domain
and is found to be effective in suppressing Gaussian noise from a homogenous region
(small variation in image pixel values) of an image corrupted with a low power noise
(standard deviation σnle10) However the method undergoes several iterations for
suppressing the noise when the level of noise is high Hence to estimate the number
of iteration for suppressing noise is a major disadvantage in TV based denoising
Another disadvantage of TV based denoising is to find the tuning parameter lsquoλrsquo The
value of lsquoλrsquo increases with increase of noise
In wavelet domain methods [98-106] the noisy image is decomposed to
around five levels for efficient denoising This leads to increase in computational
complexity extra hardware and extra cost
To take the advantages of TV algorithm for observing image variations in
different directions as well as to take the advantages of wavelet-domain processing for
analyzing an image at different levels of resolution it is proposed to develop a filter
based on TV-algorithm in DWT-domain Here the noisy image is decomposed to
single level and TV algorithm undergoes only single iteration The tuning parameter
lsquoλrsquo in TV algorithm used in the proposed filter varies from 02 to 08
The section is organized as follows
The Proposed Method
The Proposed Algorithm
The Choice of Tuning Parameter
Chapter-4 Development of Transform-Domain Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 134
421 The Proposed Method
In the proposed method the total variation algorithm is applied on a noisy
image decomposed in wavelet domain for suppression of additive white Gaussian
noise (AWGN) After the decomposition process four different subbands low-low
(LL) low-high (LH) high-low (HL) and high-high (HH) are obtained The LL
subband is a coarse (low resolution) version of the image and the HL LH and HH
subbands contain details with vertical horizontal and diagonal orientations
respectively The total number of coefficients in the four subbands is equal to the total
number of pixels in the image The Daubechiesrsquo tap-8 wavelet (Db8) [14] is used in
the proposed method for the purpose of decomposition The edge detection algorithm
is applied on the LL subband of a single decomposed noisy image to find horizontal
vertical and diagonal edges Many edge detection algorithms such as Sobel Canny
Roberts Prewitt etc are proposed in the literature [22-27] In the proposed algorithm
the Sobel operator is used for finding the edges (horizontal vertical and diagonal) of
the LL subband Using the pixel positions of the resulting horizontal edges the
corresponding wavelet coefficients in HL subband are retained thresholding others to
zero Adopting the same procedure the vertical and diagonal details of LH and HH
subands are retained The method TV is applied to LL subband for one iteration only
Applying inverse wavelet transform on modified wavelet coefficients the denoised
image is obtained This output contains some noise The residual noise is quite low as
compared to the input noise level This noise can further be suppressed using the TV
algorithm with single iteration in the spatial-domain
The advantage of Sobel operator
The Sobel operator has the advantage of providing both a differencing and a
smoothing effect [1] Because derivatives enhance noise the smoothing effect is
particularly an attractive feature of Sobel operator The operator also gives an
estimate of edge direction as well as edge magnitude at a point which is more
informative It is relatively easy to implement the operator in hardware most
obviously by a pipeline approach
Chapter-4 Development of Transform-Domain Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 135
422 The Proposed Algorithm
The proposed algorithm is given below
Step ndash 1
The noisy image is decomposed to one level using Daubechiesrsquo tap-8 (Db8) wavelet
This gives rise to four subbands (LL HL LH and HH)
Step ndash 2
The Sobel operator is used to find the horizontal vertical and diagonal edges of the
LL subband obtained in Step-1
Step ndash 3
Using the pixel positions of the resulting horizontal vertical and diagonal edges the
corresponding wavelet coefficients of HL LH and HH subbands are retained
thresholding others to zero This gives rise to the modified wavelet coefficients of the
subbands HL LH and HH ieHL LH andHH respectively
Step ndash 4
Total variation (TV) algorithm with single iteration is applied on the LL subband (low
resolution version of the image) to suppress the Gaussian noise Here the modified
wavelet coefficients corresponding to LL subband ieLL is obtained
Step ndash 5
The inverse wavelet transform is applied on the modified wavelet coefficients
(LL HL LH and HH ) to get the image with a small residual noise f
Step ndash 6
The TV filter with single iteration is applied on the image f obtained in Step-5 to get
the filtered image f
Chapter-4 Development of Transform-Domain Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 136
423 The Choice of Tuning Parameter
The tuning parameter λ of the TV algorithm used in the proposed method is
important for efficient denoising The choice of λ is completely based on
experimentation An experiment is conducted on the various noisy test images at
different noise levels for various values of λ to obtain optimal PSNR The experiment
does not converge to a single value of λ The value is different for different images as
well as for different noise levels However the value of PSNR does not differ much
for slight variations of λ From the experiment it is found that the value of λ is varied
from 02 to 08 The observation details are given in the Table-41
Table-41 Optimal value of λ for TV algorithm used in the proposed filter at different
noise levels of AWGN for obtaining optimal PSNR
Noise level of AWGN
Sl No
Value of λ at different steps
of proposed algorithm
Low
(σnle10)
Moderate
(10lt σnle30)
High
(30lt σnle50)
1 Optimal value of λ in DWT-
domain (for Step-4) 02 04 05
2 Optimal value of λ in
spatial-domain (for Step-6) 03 055 08
The proposed TV-DWT image filtering scheme is implemented on
MATLAB 70 platform and its simulation results are presented in Section 44
Chapter-4 Development of Transform-Domain Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 137
43 Development of Region Merging based DWT-domain Filter
The proposed region merging based DWT-domain (RM-DWT) filter
introduces an image denoising scheme with region merging approach in wavelet-
domain In the proposed method the wavelet transform is applied on the noisy image
to yield the wavelet coefficients in different subbands A region including the
denoising point in the particular subband is partitioned in order to get distinct sub-
regions The signal-variance in a sub-region is estimated by using maximum
likelihood (ML) estimation [105] It distinguishes a sub-region with some reasonably
high ac signal power from a sub-region containing negligible ac signal power The
sub-regions containing some appreciable ac signal power are merged together to get a
large homogenous region However if the sub-region including denoising point has
negligible ac signal power then this sub-region can be merged with other likelihood
sub-regions with negligible ac signal power to get a homogenous region Now in a
large homogenous region in wavelet domain the signal variance is estimated with
better accuracy Using the estimated signal variance the wavelet coefficients of
original (noise-free) decomposed image in wavelet domain are estimated using the
minimum mean squared error (MMSE) estimator [105]
The section is organized as follows
The Proposed Scheme
The Proposed Algorithm
Chapter-4 Development of Transform-Domain Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 138
431 The Proposed Scheme
In order to find the filtered image it is necessary to estimate the wavelet
coefficients of the original (noise-free) image decomposed in wavelet domain The
minimum mean squared error (MMSE) estimator plays an efficient role in estimating
coefficients of original (noise-free) decomposed image from the wavelet coefficients
of noisy decomposed image The minimum mean squared error estimator is defined
as
2
2 2
ˆˆ
ˆk
k k
k n
w yσ
σ σ=
+ (44)
where ˆk
w and k
y are the estimated and known wavelet coefficients in a kth
region of a
particular subband
In (44) 2ˆkσ and 2
nσ are the estimated signal variance and noise variance respectively
It is then important to estimate the signal variance in a region However this
can be estimated from maximum likelihood (ML) principle which is defined as
( )
( )
2
2 2
0(k)
2 2
(k)
arg max P Y(j) |
1max 0 Y j
k
j
n
jM
σσ σ
σ
geisin
isin
=
= minus
prod
sum
N
N
(45)
where Y(j) is the wavelet coefficients in a sub-region N(k) and M is the total number
of coefficients in the particular sub-region
In the proposed scheme the noisy image undergoes five levels of
decomposition in wavelet domain to yield wavelet coefficients in different subbands
The Daubechiesrsquo tap-8 (Db8) [14] wavelet is used for the purpose of decomposition
After a decomposition process four different subbands low-low (LL) low-high
(LH) high-low (HL) and high-high (HH) are found In a particular subband a square
shaped 9times9 region is divided into distinct 3times3 sub-regions So in a large region nine
distinct sub-regions are obtained In each distinct sub-region the signal variance is
estimated using ML estimator Depending upon the ac power level the sub-regions
Chapter-4 Development of Transform-Domain Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 139
are merged to form a larger sub-region for better estimation of signal component
Then the MMSE algorithm is applied to this large sub-region to estimate the wavelet
coefficients of original image
The RM-DWT algorithm is presented below
432 The Proposed Algorithm
The proposed algorithm RM-DWT is presented in the form of a flow-chart
shown in Fig 43
Input
DWT
Get a sub-image by
windowing (Sliding window of size 9times9)
Split into 3times3 sub-regions
Find signal variance using
ML Estimation
Merge similar regions
Estimate wavelet coefficients of original image using MMSE
(applied on large homogenous region)
IDWT
ˆ ( )f x y
Y
Y
( ) ( ) ( )g x y f x y x yη= +
Noisy Image
Output
Fig 43 Flow Chart of the RM-DWT algorithm
Chapter-4 Development of Transform-Domain Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 140
The proposed filter RM-DWT is implemented on MATLAB 70 platform and
its simulation results are presented in Section 44
44 Simulation Results
The proposed transform-domain filters Gaussian Shrinkage based DCT-
domain (GS-DCT) filter Total Variation based DWT-domain (TV-DWT) filter and
Region Merging based DWT-domain (RM-DWT) filter are simulated in MATLAB
70 platform The test images Lena Pepper Goldhill and Barbara of sizes 512times512
corrupted with AWGN of standard deviation σn = 5 10 15 20 25 30 35 40 45 and
50 are used for simulation purpose The performances of the proposed transform-
domain filters are compared with those of existing wavelet-domain filters VisuShrink
SureShrink BayesShrink OracleShrink OracleThresh NeighShrink SmoothShrink
and Locally adaptive window maximum likelihood (LAWML) The peak-signal-to-
noise ratio (PSNR) root-mean-squared error (RMSE) universal quality index (UQI)
method noise (MN ) and execution-time (TE) are taken as performance measures
The PSNR values of the different transform-domain filters for various images
are given in the tables Table-42 to Table-45 The largest PSNR value for a
particular standard deviation of Gaussian noise is highlighted to show the best
performance The PSNR values under different noise conditions are graphically
represented in Fig 44 Only high performing filters are included in the figure
The RMSE values of different filters are given in the tables Table-46 to
Table-49 The smallest RMSE value for a particular standard deviation of Gaussian
noise is highlighted The RMSE values vs Standard deviation of AWGN for various
images are shown in Fig 45 The proposed filters are compared with only some high
performing filters
The UQI of various filters are given in the tables Table-410 to Table-413
The value of UQI is always less than 1 The greatest value of UQI for a particular
standard deviation of Gaussian noise is identified and is highlighted The UQI values
Chapter-4 Development of Transform-Domain Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 141
of proposed filters and some existing high performing filters under different noise
conditions for various images are plotted in Fig 46
The method noise of the proposed transform-domain filters are compared with
existing transform-domain filters and the values are tabulated in Table-414 The
filtering performance is better if the method noise is very low since it talks of little
distortion when a non-noisy image is passed through a filter Therefore a least value
of method noise for a particular noise standard deviation is highlighted to show the
best performer
The filters are simulated on three different computing systems SYSTEM-1
SYSTEM-2 and SYSTEM-3 presented in Table-11 in Section-15 The execution
time of the different filters is given in Table-415 The filter having less execution
time is usually required for online and real-time applications The least value of
execution time is highlighted
For subjective evaluation the filtered output images are shown in figures
Fig 47 to Fig 414 The test images Lena and Pepper are used for subjective
evaluation A smooth region and a complex region of Lena image are taken for
critical analysis The performance of various filters for smooth regions is shown in
Fig 413 whereas that for complex regions is shown in Fig 414
Conclusions are drawn in Section 45
Chapter-4 Development of Transform-Domain Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 142
Table-42 Filtering performance of mean filter and various transform-domain filters in terms
of PSNR (dB) operated on Lena image under various noise conditions (σn varies from 5 to 50)
Peak-Signal-to-Noise Ratio PSNR (dB)
Standard deviation of AWGN Sl
No
Denoising
Filters
5 10 15 20 25 30 35 40 45 50
Test Image Lena
1 Mean [3times3] 3388 3270 3127 2978 2848 2728 2626 2530 2445 2362
2 Mean [5times5] 2977 2959 2931 2892 2848 2805 2748 2696 2649 2593
3 Mean [7times7] 2766 2760 2750 2737 2721 2701 2677 2649 2623 2589
4 VisuShrink 3165 3056 2960 2875 2791 2678 2541 2395 2257 2148
5 SureShrink 2980 2961 2928 2882 2839 2793 2745 2701 2664 2621
6 BayesShrink 3747 3364 3158 3020 2918 2840 2777 2711 2664 2607
7 OracleShrink 3613 3170 2880 2651 2452 2290 2148 2021 1910 1815
8 OracleThresh 3534 2997 2645 2385 2183 2013 1865 1741 1631 1542
9 NeighShrink 3870 3445 3197 3011 2880 2769 2676 2608 2542 2497
10 SmoothShrink 3234 3041 2893 2743 2606 2488 2381 2289 2203 2131
11 LAWML [3times3] 3839 3413 3161 2978 2847 2741 2648 2572 2508 2458
12 LAWML[5times5] 3860 3459 3226 3066 2941 2853 2774 2709 2656 2602
13 LAWML [7times7] 3853 3458 3234 3086 2969 2884 2800 2741 2689 2638
14 GS-DCT 3376 3313 3188 3098 3001 2911 2746 2706 2689 2611
15 TV-DWT 3465 3376 3229 3056 296 2844 2736 2667 2558 2477
16 RM-DWT 3910 3472 3236 3069 2948 2858 2781 2723 2655 2602
Chapter-4 Development of Transform-Domain Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 143
Table-43 Filtering performance of mean filter and various transform-domain filters in
terms of PSNR (dB) operated on Pepper image under various noise conditions (σn varies from 5 to 50)
Peak-Signal-to-Noise Ratio PSNR (dB)
Standard deviation of AWGN Sl
No
Denoising
Filters
5 10 15 20 25 30 35 40 45 50
Test Image Pepper
1 Mean [3times3] 3190 3116 3015 2899 2788 2682 2586 2495 2415 2345
2 Mean [5times5] 3061 3039 3001 2955 2902 2840 2781 2722 2656 2601
3 Mean [7times7] 2862 2855 2841 2818 2793 2771 2732 2696 2658 2618
4 VisuShrink 2794 2740 2667 2587 2534 2475 2401 2321 2233 2137
5 SureShrink 2671 2667 2658 2642 2625 2596 2564 2529 2496 2454
6 BayesShrink 3743 3369 3145 2990 2898 2824 2745 2669 2598 2505
7 OracleShrink 3648 3200 2895 2666 2474 2307 2163 2040 1930 1835
8 OracleThresh 3532 3017 2694 2450 2236 2044 1889 1762 1654 1564
9 NeighShrink 3829 3437 3194 3017 2868 2755 2652 2578 2509 2451
10 SmoothShrink 2672 2588 2452 2319 2190 2079 1974 1882 1803 1728
11 LAWML [3times3] 3837 3428 3181 3003 2861 2738 2641 2565 2501 2447
12 LAWML[5times5] 3877 3464 3246 3084 2952 2843 2754 2679 2610 2560
13 LAWML [7times7] 3842 3463 3245 3088 2967 2857 2767 2695 2621 2575
14 GS-DCT 3379 3310 3259 3100 2976 2855 2766 2621 2610 2562
15 TV-DWT 3278 3183 3075 297 2865 2772 2675 2593 2507 2438
16 RM-DWT 3918 3481 3189 3083 2971 2852 2748 2687 2523 2454
Chapter-4 Development of Transform-Domain Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 144
Table-44 Filtering performance of mean filter and various transform-domain filters in
terms of PSNR (dB) operated on Goldhill image under various noise conditions (σn varies from 5 to 50)
Peak-Signal-to-Noise Ratio PSNR (dB)
Standard deviation of AWGN Sl
No
Denoising
Filters
5 10 15 20 25 30 35 40 45 50
Test Image Goldhill
1 Mean [3times3] 3154 3082 2983 2877 2769 2666 2573 2483 2401 2332
2 Mean [5times5] 2815 2802 2779 2748 2713 2669 2625 2574 2525 2477
3 Mean [7times7] 2648 2644 2634 262 2607 2583 2556 2525 2495 2453
4 VisuShrink 2971 2864 2778 2693 2591 2484 2370 2247 2135 2026
5 SureShrink 2744 2738 2718 2690 2660 2623 2589 2545 2512 2462
6 BayesShrink 3648 3234 3020 2868 2750 2654 2582 2517 2458 2409
7 OracleShrink 3302 2945 2707 2547 2416 2293 2182 2087 2000 1921
8 OracleThresh 3371 2914 2656 2455 2293 2158 2030 1919 1818 1724
9 NeighShrink 3737 3305 3063 2902 2779 2675 2595 2527 2465 2411
10 SmoothShrink 2813 2681 2522 2372 2237 2119 2013 1916 1837 1762
11 LAWML [3times3] 3655 3278 3037 2877 2742 2644 2558 2477 2420 2361
12 LAWML[5times5] 3722 3302 3078 2920 2803 2710 2629 2556 2492 2443
13 LAWML [7times7] 3689 3302 3078 2927 2811 2724 2640 2573 2511 2443
14 GS-DCT 3325 3161 3089 2956 2821 2716 2623 2518 2474 2401
15 TV-DWT 2782 2693 2645 2594 254 2488 2434 2379 2327 2277
16 RM-DWT 3812 3331 3076 2922 2800 2719 2635 2555 2497 2442
Chapter-4 Development of Transform-Domain Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 145
Table-45 Filtering performance of mean filter and various transform-domain filters in terms
of PSNR (dB) operated on Barbara image under various noise conditions (σn varies from 5 to 50)
Peak-Signal-to-Noise Ratio PSNR (dB)
Standard deviation of AWGN Sl
No
Denoising
Filters
5 10 15 20 25 30 35 40 45 50
Test Image Barbara
1 Mean [3times3] 2652 2602 2568 2525 2475 2419 2364 2306 2250 2195
2 Mean [5times5] 2381 2376 2368 2357 2343 2325 2304 2284 2256 2231
3 Mean [7times7] 2353 2351 2347 2341 2332 2321 2307 2292 2275 2253
4 VisuShrink 2661 2572 2475 2391 2325 2261 2199 2135 2074 1989
5 SureShrink 2434 2430 2423 2412 2397 2380 2358 2333 2312 2286
6 BayesShrink 3591 3138 2904 2748 2634 2539 2453 2368 2311 2271
7 OracleShrink 3101 2628 2507 2442 2384 2325 2256 2188 2115 2044
8 OracleThresh 3403 2743 2519 2376 2229 2095 1983 1880 1787 1708
9 NeighShrink 3750 3292 3033 2857 2725 2611 2527 2455 2385 2326
10 SmoothShrink 2767 2587 2453 2319 2197 2084 1982 1892 1809 1739
11 LAWML [3times3] 3713 3257 3002 2821 2687 2581 2491 2419 2352 2295
12 LAWML[5times5] 3727 3278 3030 2865 2742 2642 2560 2483 2421 2371
13 LAWML [7times7] 3716 3276 3029 2865 2744 2647 2566 2494 2433 2378
14 GS-DCT 3376 3195 3085 2995 2808 2649 2544 2439 2416 2321
15 TV-DWT 2712 2693 2645 2594 254 2488 2434 2379 2327 2277
16 RM-DWT 3793 3310 3012 2834 2689 2588 2496 2431 2372 2325
Chapter-4 Development of Transform-Domain Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 146
Table-46 Filtering performance of mean filter and various transform-domain filters in
terms of RMSE operated on Lena image under various noise conditions (σn varies from 5 to 50)
Root-Mean-Squared Error (RMSE)
Standard deviation of AWGN Sl
No
Denoising
Filters
5 10 15 20 25 30 35 40 45 50
Test Image Lena
1 Mean [3times3] 515 590 696 827 960 1102 1240 1385 1527 1680
2 Mean [5times5] 828 845 873 913 960 1009 1077 1144 1207 1288
3 Mean [7times7] 1055 1063 1075 1091 1111 1137 1169 1207 1244 1294
4 VisuShrink 666 756 844 931 1025 1168 1367 1618 1896 2150
5 SureShrink 825 843 876 923 970 1023 1081 1137 1187 1247
6 BayesShrink 341 530 672 788 886 969 1042 1124 1187 1267
7 OracleShrink 398 663 925 1205 1515 1826 2150 2489 2828 3155
8 OracleThresh 436 809 1213 1637 2065 2512 2978 3435 3899 4320
9 NeighShrink 296 483 642 796 925 1052 1171 1266 1366 1438
10 SmoothShrink 615 769 912 1084 1269 1453 1644 1828 2018 2193
11 LAWML [3times3] 306 501 669 827 961 1086 1209 1319 1420 1505
12 LAWML[5times5] 299 475 621 747 863 955 1046 1127 1198 1275
13 LAWML [7times7] 302 475 615 730 835 921 1015 1086 1153 1223
14 GS-DCT 558 562 649 720 805 893 1080 1131 1153 1261
15 TV-DWT 472 523 619 756 844 965 1092 1183 1341 1472
16 RM-DWT 282 468 614 744 856 949 1037 1109 1199 1275
Chapter-4 Development of Transform-Domain Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 147
Table-47 Filtering performance of mean filter and various transform-domain filters in
terms of RMSE operated on Pepper image under various noise conditions (σn varies from 5 to 50)
Root-Mean-Squared Error (RMSE)
Standard deviation of AWGN Sl
No
Denoising
Filters
5 10 15 20 25 30 35 40 45 50
Test Image Pepper
1 Mean [3times3] 647 705 792 905 1029 1162 1298 1442 1581 1714
2 Mean [5times5] 751 770 805 849 902 969 1037 1110 1198 1276
3 Mean [7times7] 945 952 968 994 1023 1049 1097 1144 1195 1251
4 VisuShrink 1022 1088 1183 1297 1378 1475 1607 1762 1951 2177
5 SureShrink 1177 1183 1195 1217 1241 1283 1332 1386 1440 1512
6 BayesShrink 342 527 682 815 906 987 1081 1180 1281 1425
7 OracleShrink 382 640 910 1184 1477 1790 2113 2435 2764 3083
8 OracleThresh 437 790 1146 1518 1943 2424 2897 3353 3797 4212
9 NeighShrink 310 487 644 790 938 1069 1203 1310 1419 1517
10 SmoothShrink 1174 1295 1515 1766 2049 2328 2627 2921 3199 3487
11 LAWML [3times3] 307 492 654 803 946 1090 1219 1330 1432 1524
12 LAWML[5times5] 293 472 607 732 852 966 1070 1166 1263 1338
13 LAWML [7times7] 305 473 608 728 837 950 1054 1145 1247 1315
14 GS-DCT 521 564 598 718 828 952 1055 1247 1263 1335
15 TV-DWT 585 653 739 834 941 1048 1172 1288 1422 1540
16 RM-DWT 280 463 648 732 833 956 1077 1156 1396 1512
Chapter-4 Development of Transform-Domain Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 148
Table-48 Filtering performance of mean filter and various transform-domain filters in
terms of RMSE operated on Goldhill image under various noise conditions (σn varies from 5 to 50)
Root-Mean-Squared Error (RMSE)
Standard deviation of AWGN Sl
No
Denoising
Filters
5 10 15 20 25 30 35 40 45 50
Test Image Goldhill
1 Mean [3times3] 675 733 822 929 1052 1184 1318 1462 1607 174
2 Mean [5times5] 997 1012 1041 1077 1122 1180 1241 1316 1393 1472
3 Mean [7times7] 1209 1214 1229 1248 1267 1303 1344 1393 1442 1513
4 VisuShrink 833 943 1041 1148 1291 1460 1665 1918 2182 2474
5 SureShrink 1082 1090 1115 1152 1192 1244 1294 1361 1414 1498
6 BayesShrink 382 615 788 938 1075 1201 1304 1406 1505 1592
7 OracleShrink 569 859 1129 1358 1579 1819 2068 2307 255 2792
8 OracleThresh 526 890 1198 1510 1819 2125 2463 2799 3144 3503
9 NeighShrink 345 567 749 902 1041 1172 1285 1390 1492 1588
10 SmoothShrink 1000 1164 1398 1661 1941 2223 2512 2808 3076 3353
11 LAWML [3times3] 379 585 772 929 1085 1214 1341 1472 1572 1682
12 LAWML[5times5] 351 569 737 884 1011 1126 1236 1344 1447 1531
13 LAWML [7times7] 364 569 737 877 1002 1108 1220 1318 1415 1531
14 GS-DCT 554 669 727 848 990 1118 1244 1404 1477 1607
15 TV-DWT 1036 1148 1213 1286 1369 1453 1547 1648 175 1853
16 RM-DWT 316 550 738 882 1015 1114 1227 1346 1438 1533
Chapter-4 Development of Transform-Domain Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 149
Table-49 Filtering performance of mean filter and various transform-domain filters in terms
of RMSE operated on Barbara image under various noise conditions (σn varies from 5 to 50)
Root-Mean-Squared Error (RMSE)
Standard deviation of AWGN Sl
No
Denoising
Filters
5 10 15 20 25 30 35 40 45 50
Test Image Barbara
1 Mean [3times3] 1203 1275 1326 1393 1475 1574 1677 1792 1912 2037
2 Mean [5times5] 1644 1654 1669 1690 1718 1754 1797 1838 1899 1954
3 Mean [7times7] 1698 1702 1710 1722 1741 1762 1790 1822 1858 1905
4 VisuShrink 1191 1319 1475 1625 1754 1888 2027 2182 2341 2582
5 SureShrink 1547 1554 1566 1586 1614 1646 1688 1738 1780 1834
6 BayesShrink 408 687 900 1077 1229 1371 1513 1669 1782 1866
7 OracleShrink 717 1237 1422 1533 1638 1754 1899 2053 2233 2424
8 OracleThresh 507 1084 1402 1654 1959 2285 2600 2927 3258 3568
9 NeighShrink 340 576 776 950 1106 1261 1390 1510 1637 1752
10 SmoothShrink 1054 1297 1513 1766 2032 2314 2603 2887 3177 3443
11 LAWML [3times3] 354 599 804 990 1156 1306 1448 1574 1700 1815
12 LAWML[5times5] 349 585 779 941 1085 1217 1338 1462 1570 1663
13 LAWML [7times7] 353 586 779 941 1082 1210 1329 1443 1549 1650
14 GS-DCT 523 644 731 811 1005 1207 1363 1538 1579 1762
15 TV-DWT 1123 1148 1213 1286 1369 1453 1547 1648 1751 1853
16 RM-DWT 323 564 795 976 1153 1295 1440 1552 1661 1754
Chapter-4 Development of Transform-Domain Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 150
Table-410 Filtering performance of mean filter and various transform-domain filters in terms
of UQI operated on Lena image under various noise conditions (σn varies from 5 to 50)
Universal Quality Index (UQI)
Standard deviation of AWGN Sl
No
Denoising
Filters
5 10 15 20 25 30 35 40 45 50
Test Image Lena
1 Mean [3times3] 09941 09922 09892 09849 09797 09732 09663 09579 09488 09376
2 Mean [5times5] 09845 09838 09827 09811 09791 09769 09736 09700 09665 09613
3 Mean [7times7] 09743 09739 09733 09725 09714 09701 09683 09659 09636 09601
4 VisuShrink 09902 09874 09843 09809 09769 09704 09607 09473 09321 09178
5 SureShrink 09848 09841 09828 09808 09788 09764 09734 09704 09675 09636
6 BayesShrink 09943 09938 09900 09863 09826 09790 09755 09711 09675 09621
7 OracleShrink 09965 09903 09811 09680 09500 09283 09018 08712 08372 08021
8 OracleThresh 09959 09858 09685 09439 09133 08759 08329 07873 07399 06953
9 NeighShrink 09981 09949 09910 09861 09812 09757 09698 09642 09582 09530
10 SmoothShrink 09729 09658 09521 09336 09118 08867 08687 08284 07984 07661
11 LAWML [3times3] 09979 09945 09902 09850 09797 09740 09676 09613 09547 09484
12 LAWML[5times5] 09980 09950 09915 09877 09835 09797 09755 09712 09670 09622
13 LAWML [7times7] 09980 09951 09916 09882 09845 09811 09773 09731 09693 09649
14 GS-DCT 09944 09937 09911 09896 09856 09813 09740 09720 09626 09578
15 TV-DWT 09968 09938 09925 09877 09843 09788 09724 09652 09570 09481
16 RM-DWT 09985 09954 09917 09878 09844 09808 09766 09692 09654 09596
Chapter-4 Development of Transform-Domain Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 151
Table-411 Filtering performance of mean filter and various transform-domain filters in terms
of UQI operated on Pepper image under various noise conditions (σn varies from 5 to 50)
Universal Quality Index (UQI)
Standard deviation of AWGN Sl
No
Denoising
Filters
5 10 15 20 25 30 35 40 45 50
Test Image Pepper
1 Mean [3times3] 09927 09912 09889 09856 09814 09762 09702 09631 09557 09476
2 Mean [5times5] 09900 09894 09884 09871 09853 09831 09805 09776 09737 09699
3 Mean [7times7] 09839 09836 09830 09821 09809 09799 09779 09758 09734 09706
4 VisuShrink 09817 09793 09756 09710 09676 09634 09575 09502 09408 09289
5 SureShrink 09751 09749 09743 09732 09720 09700 09675 09645 09613 09568
6 BayesShrink 09980 09952 09919 09883 09855 09826 09789 09745 09696 09617
7 OracleShrink 09975 09928 09855 09753 09617 09437 09222 08974 08697 08400
8 OracleThresh 09967 09893 09775 09610 09372 09049 08683 08294 07885 07484
9 NeighShrink 09983 09959 09928 09891 09845 09798 09743 09692 09636 09579
10 SmoothShrink 09734 09693 09583 09439 09257 09054 08817 08561 08305 08022
11 LAWML [3times3] 09984 09958 09925 09887 09843 09791 09736 09683 09630 09575
12 LAWML[5times5] 09987 09885 09876 09862 09843 09821 09795 09761 09713 09675
13 LAWML [7times7] 09988 09961 09935 09907 09876 09838 09800 09761 09726 09689
14 GS-DCT 09971 09960 09954 09921 09883 09822 09754 09721 09689 09635
15 TV-DWT 09953 09932 09908 09878 09839 09797 09741 09684 09613 09544
16 RM-DWT 09991 09971 09885 09868 09853 09833 09798 09752 09708 09639
Chapter-4 Development of Transform-Domain Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 152
Table-412 Filtering performance of mean filter and various transform-domain filters in terms
of UQI operated on Goldhill image under various noise conditions (σn varies from 5 to 50)
Universal Quality Index (UQI)
Standard deviation of AWGN Sl
No
Denoising
Filters
5 10 15 20 25 30 35 40 45 50
Test Image Goldhill
1 Mean [3times3] 09939 09928 09909 09884 09850 09809 09762 09705 0964 09575
2 Mean [5times5] 09866 09861 09853 09841 09827 09807 09784 09754 09722 09687
3 Mean [7times7] 09801 09799 09793 09785 09777 09762 09744 09722 09699 09665
4 VisuShrink 09908 09882 09856 09826 09784 09730 09659 09562 09454 09328
5 SureShrink 09843 09840 09831 09819 09804 09785 09765 09736 09712 09673
6 BayesShrink 09981 09950 09917 09881 09842 09801 09761 09719 09673 09627
7 OracleShrink 09957 09901 09828 09750 09660 09546 09412 09266 09105 08926
8 OracleThresh 09964 09895 09810 09699 09563 09404 09206 08981 08732 08443
9 NeighShrink 09984 09957 09925 09891 09854 09813 09773 09731 09684 09638
10 SmoothShrink 09878 09816 09736 09627 09494 09340 09162 08959 08760 08541
11 LAWML [3times3] 09982 09955 09921 09884 09841 09798 09751 09696 09648 09592
12 LAWML[5times5] 09984 09956 09927 09895 09861 09826 09787 09744 09699 09656
13 LAWML [7times7] 09986 09957 09928 09896 09863 09831 09791 09754 09711 09658
14 GS-DCT 09958 09949 09939 09913 09881 09845 09789 09756 09703 09648
15 TV-DWT 09976 09954 09935 09902 09873 09841 09779 09768 09718 09654
16 RM-DWT 09992 09961 09926 09889 09859 09788 09759 09698 09659 09599
Chapter-4 Development of Transform-Domain Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 153
Table-413 Filtering performance of mean filter and various transform-domain filters in terms
of UQI operated on Barbara image under various noise conditions (σn varies from 5 to 50)
Universal Quality Index (UQI)
Standard deviation of AWGN Sl
No
Denoising
Filters
5 10 15 20 25 30 35 40 45 50
Test Image Barbara
1 Mean [3times3] 09753 09739 09718 09688 09649 09601 09545 09478 09403 09318
2 Mean [5times5] 09560 09554 09545 09532 09515 09491 09462 09433 0939 09346
3 Mean [7times7] 09525 09521 09516 09507 09494 0948 09458 09433 09407 09371
4 VisuShrink 09777 09726 09661 09596 09540 09479 09417 09342 09261 09138
5 SureShrink 09613 09609 09602 09590 09573 09552 09526 09493 09463 09424
6 BayesShrink 09974 09927 09874 09817 09759 09696 09624 09534 09461 09401
7 OracleShrink 09919 09756 09674 09618 09560 09492 09400 09294 09158 09005
8 OracleThresh 09960 09817 09690 09569 09398 09188 08961 08702 08422 08136
9 NeighShrink 09982 09949 09907 09859 09808 09747 09691 09631 09560 09491
10 SmoothShrink 09813 09726 09630 09501 09344 09159 08949 08721 08477 08233
11 LAWML [3times3] 09974 09944 09900 09846 09789 09728 09663 09598 09524 09433
12 LAWML[5times5] 09976 09946 09904 09860 09813 09763 09710 09650 09589 09517
13 LAWML [7times7] 09981 09947 09905 09861 09814 09765 09713 09656 09598 09521
14 GS-DCT 09945 09933 09913 09867 09823 09764 09701 09645 09532 09512
15 TV-DWT 09801 09783 09755 09724 09685 09643 09593 09537 09478 09413
16 RM-DWT 09989 09951 09898 09859 09807 09759 09700 09647 09573 09511
Chapter-4 Development of Transform-Domain Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 154
Table-414 Method Noise MN of mean filter and various transform-domain
filters operated on different test images
Sl No Images Denoising
Filters
Lena Pepper Goldhill Barbara
1 Mean [3times3]
262 290 410 668
2 Mean [5times5]
443 408 642 946
3 Mean [7times7]
573 520 793 1035
4 VisuShrink
318 423 471 637
5 SureShrink
517 673 770 1007
6 BayesShrink
00232 00273 00194 00190
7 OracleShrink
00285 00267 00242 00238
8 OracleThresh
00285 00267 00242 00238
9 NeighShrink
408times10-10
466times10-10
334times10-10
497times10-10
10 SmoothShrink
660 752 64515 790
11 LAWML [3times3]
408times10-10
466times10-10
334times10-10
497times10-10
12 LAWML[5times5]
408times10-10
466times10-10
334times10-10
497times10-10
13 LAWML [7times7]
408times10-10
466times10-10
334times10-10
497times10-10
14 GS-DCT
05737 072675 067065 07930
15 TV-DWT
201 226 341 479
16 RM-DWT
408times10-10
466times10-10
334times10-10
497times10-10
Chapter-4 Development of Transform-Domain Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 155
Table-415 Execution time (seconds) TE taken by mean filter and various transform-domain filters for Lena image
Execution time (seconds) in three different hardware
platforms Sl No Denoising Filters
SYSTEM-1
SYSTEM-2
SYSTEM-3
1 Mean [3times3] 318 701 2313
2 Mean [5times5] 323 712 2349
3 Mean [7times7] 327 720 2376
4 VisuShrink 0540 119 392
5 SureShrink 060 134 442
6 BayesShrink 188 415 1369
7 OracleShrink 2 440 1452
8 OracleThresh 197 435 1435
9 NeighShrink 414 912 3009
10 SmoothShrink 108 239 788
11 LAWML [3times3] 367 809 2669
12 LAWML[5times5] 370 815 2689
13 LAWML [7times7] 374 823 2715
14 GS-DCT 1381 3038 7025
15 TV-DWT 04261 09375 309
16 RM-DWT 515 1134 3742
Chapter-4 Development of Transform-Domain Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 156
PSNR values for Lena Image
PS
NR
(d
B)
PSNR values for Pepper Image
PS
NR
(d
B)
PS
NR
(d
B)
PSNR values for Goldhill Image
PS
NR
(d
B)
PSNR values for Barbara Image
(a) (b)
(c) (d)
Fig 44 Performance comparison of various filters in terms of PSNR (dB) under different noise levels of AWGN on the images
(a) Lena
(b) Pepper
(c) Goldhill
(d) Barbara
σn
σn σn
σn
Chapter-4 Development of Transform-Domain Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 157
RMSE values for Lena Image
RM
SE
RM
SE
RMSE values for Pepper Image
RM
SE
RMSE values for Goldhill Image RMSE values for Barbara Image
RM
SE
(a) (b)
(c) (d)
Fig 45 Performance comparison of various filters in terms of RMSE values under different noise levels of AWGN on the images
(a) Lena
(b) Pepper
(c) Goldhill
(d) Barbara
σn σn
σn σn
Chapter-4 Development of Transform-Domain Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 158
UQ
I
UQI values for Lena Image UQI values for Pepper Image
UQ
I
UQ
I
UQI values for Goldhill Image
UQ
I
UQI values for Barbara Image
(a) (b)
(c) (d)
Fig 46 Performance comparison of various filters in terms of UQI values under
different noise levels of AWGN on the images
(a) Lena (b) Pepper
(c) Goldhill (d) Barbara
σn σn
σn σn
Chapter-4 Development of Transform-Domain Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 159
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
(j)
(k)
Fig 47 Performance of Various Filters for Lena Image with AWGN σn = 15
(a) Original image (b) Noisy image
(c) ndash (n) Results of various filtering schemes
(c) Mean (d) VisuShrink (e) SureShrink (f) BayesShrink (g) OracleShrink
(h) OracleThresh (i) NeighShrink (j) SmoothShrink (k) LAWML (l) GS-DCT
(m) TV-DWT (n) RM-DWT
(l)
(m)
(n)
Chapter-4 Development of Transform-Domain Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 160
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
(j)
(k)
Fig 48 Performance of Various Filters for Lena Image (Smooth Region) with AWGN
σn = 15
(a) Original image (b) Noisy image
(c) ndash (n) Results of various filtering schemes
(c) Mean (d) VisuShrink (e) SureShrink (f) BayesShrink (g) OracleShrink
(h) OracleThresh (i) NeighShrink (j) SmoothShrink (k) LAWML (l) GS-DCT
(m) TV-DWT (n) RM-DWT
(l)
(m)
(n)
Chapter-4 Development of Transform-Domain Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 161
(a) (b) (c) (d) (e)
(f) (g) (h) (i) (j)
Fig 49 Performance of Various Filters for Lena Image (Complex Region) with AWGN σn = 15
(a) Original image (b) Noisy image
(c) ndash (n) Results of various filtering schemes
(c) Mean (d) VisuShrink (e) SureShrink (f) BayesShrink (g) OracleShrink
(h) OracleThresh (i) NeighShrink (j) SmoothShrink (k) LAWML (l) GS-DCT
(m) TV-DWT (n) RM-DWT
(h) (i) (j)
(m) (k)
(l)
(m) (n)
Chapter-4 Development of Transform-Domain Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 162
(a) (b) (c)
(d)
(e) (f) (g) (h)
(i) (j) (k)
Fig 410 Performance of Various Filters for Pepper Image with AWGN σn = 15
(a) Original image (b) Noisy image
(c) ndash (n) Results of various filtering schemes
(c) Mean (d) VisuShrink (e) SureShrink (f) BayesShrink (g) OracleShrink
(h) OracleThresh (i) NeighShrink (j) SmoothShrink (k) LAWML (l) GS-DCT
(m) TV-DWT (n) RM-DWT
(l)
(m) (n)
Chapter-4 Development of Transform-Domain Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 163
(a) (b) (c)
(d)
(e)
(f)
(g)
(h)
(i)
(j)
(k)
Fig 411 Performance of Various Filters for Lena Image with AWGN σn = 40 (a) Original image (b) Noisy image
(c) ndash (n) Results of various filtering schemes
(c) Mean (d) VisuShrink (e) SureShrink (f) BayesShrink (g) OracleShrink
(h) OracleThresh (i) NeighShrink (j) SmoothShrink (k) LAWML (l) GS-DCT
(m) TV-DWT (n) RM-DWT
(l)
(m) (n)
Chapter-4 Development of Transform-Domain Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 164
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
(j)
(k)
Fig 412 Performance of Various Filters for Lena Image (Smooth Region) with AWGN σn = 40
(a) Original image (b) Noisy image
(c) ndash (n) Results of various filtering schemes
(c) Mean (d) VisuShrink (e) SureShrink (f) BayesShrink (g) OracleShrink
(h) OracleThresh (i) NeighShrink (j) SmoothShrink (k) LAWML (l) GS-DCT
(m) TV-DWT (n) RM-DWT
(l)
(m) (n)
Chapter-4 Development of Transform-Domain Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 165
(a)
(b) (c)
(d) (e)
(g) (h) (i) (j)
(k)
Fig 413 Performance of Various Filters for Lena Image (Complex Region) with AWGN σn = 40
(a) Original image (b) Noisy image
(c) ndash (n) Results of various filtering schemes
(c) Mean (d) VisuShrink (e) SureShrink (f) BayesShrink (g) OracleShrink
(h) OracleThresh (i) NeighShrink (j) SmoothShrink (k) LAWML (l) GS-DCT
(m) TV-DWT (n) RM-DWT
(f)
(m) (n) (l)
Chapter-4 Development of Transform-Domain Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 166
Fig 414 Performance of Various Filters for Pepper Image with AWGN σn = 40
(a) Original image (b) Noisy image
(c) ndash (n) Results of various filtering schemes
(c) Mean (d) VisuShrink (e) SureShrink (f) BayesShrink (g) OracleShrink
(h) OracleThresh (i) NeighShrink (j) SmoothShrink (k) LAWML (l) GS-DCT
(m) TV-DWT (n) RM-DWT
(a) (b) (c)
(d)
(e)
(f)
(g)
(h)
(i)
(j)
(k)
(l)
(m) (n)
Chapter-4 Development of Transform-Domain Filters
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 167
45 Conclusion
Three transform-domain filters GS-DCT TV-DWT and RM-DWT are
proposed for suppression of AWGN from images These filters are found to perform
well as compared to other existing filters
From tables Table-42 to Table-45 it is observed that the developed filters
RM-DWT and GS-DCT have higher PSNR values as compared to other filters at low
and moderate noise conditions respectively Under such noise conditions the filters
have smaller RMSE values which can be seen from tables Table-46 to Table-49
These filters also give superior performance in terms of UQI values which can be
observed from tables Table-410 to Table-413 From Table-414 it can be seen that
this two developed filters yield relatively less method noise
It is observed from these tables that the other proposed filter TV-DWT shows
moderate performance in terms of PSNR RMSE and UQI But its execution-time is
minimal as depicted in Table-415 Further it yields reasonably low method noise as
shown in Table-414 Thus the TV-DWT is a very good candidate for real-time
applications
From subjective evaluations it can be seen that the wavelet-domain filters
introduce artifacts in the smooth regions of the filtered image However they are
effective up to some extent in preserving the complex regions at the time of filtering
These are evident from Fig 412 and Fig 413 The proposed filter RM-DWT is
found to be the best in filtering smooth and complex regions with quite little distortion
and giving the best visual quality among all filters compared here
Chapter 5
Development of
Some Color Image
Denoising Filters
Chapter-5 Development of Some Color Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 169
Preview
Most of the denoising techniques available in literature are developed and
tested only for gray images [62-106] Recently a few color image denoising filters are
reported in the literature [8137-142] Hence there is sufficient scope for developing
very good color image filters Efforts are made in this research work to develop
novel color image filters both in spatial-domain and in transform-domain
Since the circular spatial filter (CSF) and region merging based DWT-domain
(RM-DWT) filter are found in the preceding two chapters to be very efficient in
suppressing AWGN from gray images necessary modifications are made to develop
their multi-channel versions to cater to the need of color image processing
In this chapter two multi-channel filters Multi-channel Circular Spatial Filter
(MCSF) and Multi-channel Region Merging based DWT-domain (MRM-DWT) Filter
are developed for suppression of additive noise from color images The developed
filters MCSF and MRM-DWT are based on three-channel-processing (eg RGB-
5
Chapter-5 Development of Some Color Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 170
processing YCbCr-processing etc) and hence are necessarily 3-Channel CSF and 3-
Channel RM-DWT respectively
The filtering performance is compared with Multi-channel versions of existing
filters (i) mean filter (simplest and oldest filter) [1] and (ii) locally adaptive window
maximum likelihood (LAWML) filter [105] (best performer among the existing
wavelet-domain filters examined in Chaper-2)
The organization of this chapter is given below
Multi-Channel Color Image Filtering
Multi-Channel Mean Filter
Multi-Channel LAWML Filter
Development of Multi-Channel Circular Spatial Filter
Development of Multi-Channel Region Merging based DWT-domain
Filter
Simulation Results
Conclusion
Chapter-5 Development of Some Color Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 171
51 Multi-Channel Color Image Filtering
Multi-channel filters can be employed for denoising color images where each
color component of noisy image is applied to an independent channel processor The
denoising can be performed either in the basic RGB-color space or in any other color
space C such as YCbCr CMY CIE Lab etc [18] The block diagram of a multi-
channel filter is shown in Fig 51 A Type-I filter (RGB-color image filter) is
illustrated in Fig 51 (a) while a Type-II filter (any other color-space) is shown in
Fig 51 (b) A combination of a pre-processing transformation (RGB-to-other color
space) at the front end and a corresponding inverse transformation for post-processing
distinguishes a Type-II filter from Type-I filter
Chapter-5 Development of Some Color Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 172
(a)
Filter R-Channel
G-Channel
B-Channel
R-Channel
G-Channel
B-Channel
Input
Color Image
(RGB)
Output
Color Image
(RGB)
Filter
Filter
Fig 51 Block Diagram of a Multi-Channel Filter
(a) Type-I Filter (RGB-Color Space)
(b) Type-II Filter (Color Space C other than RGB)
Filter R-Channel
G-Channel
RG
B ndash
C
T
ran
sfo
rma
tio
n
C ndash
RG
B
T
ran
sfo
rma
tio
n
B-Channel
(b)
R-Channel
G-Channel
B-Channel Filter
Filter
Input
Color Image
(RGB)
Output Color Image
(RGB)
Chapter-5 Development of Some Color Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 173
Helbert et al [137] Lian et al [139] Kim et al [140] and Luisier et al [141]
have shown that the RGB and YCbCr color spaces are found to be quite effective
color representation spaces for image (2-D) and video (3-D) denoising applications
Since the performance of denoising filters degrades in other color spaces more
concentrated efforts are made in this research work to develop color image denoising
filters only in RGB and YCbCr color spaces Nevertheless two other standard color
spaces CMY and CIE Lab are also employed initially to study their performance
An RGB to YCbCr-color space conversion [6] is given by
029900000 058700000 014400000
016873000 033126400 050000000
050000000 041866800 008131200
Y R
Cb G
Cr B
= minus minus minus minus
(51)
where Y is the luminance component of the color image and the Cb and Cr are the
blue-chrominance and red-chrominance of color image in YCbCr-color space
The conversion of RGB to CMY-color space is performed using the following
expression [1]
1
1
1
C R
M G
Y B
= minus
(52)
The RGB to CIE Lab-color space conversion is given by [153154]
1
3
1 1
3 3
1 1
3 3
116 16
500
200
n n
n n
YL
Yn
X Ya
X Y
Y Zb
Y Z
= minus
= minus
= minus
(53)
Chapter-5 Development of Some Color Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 174
where the tristimulus values Xn Yn Zn are those of nominally white object color
stimulus and the values X Y and Z are defined by
0412 0358 0180
0213 0715 0072
0019 0119 0950
X R G B
Y R G B
Z R G B
= + +
= + +
= + +
(54)
Table 51 illustrates the performance of the denoising filters in four color
spaces RGB YCbCr CMY and CIE Lab It is observed that all filters exhibit their
best performance in YCbCr-color space Further it may be concluded that RGB is
the second-best color representation Hence CSF and RM-DWT filters are developed
for the basic color space RGB and the best color space YCbCr The performance of
various filters in terms of CPSNR (dB) is demonstrated as a bar plot in Fig 52 The
best CPSNR value for a particular standard deviation of AWGN irrespective of
window size of a filter is considered for the bar plot
Thus it is observed from Table-51 and Fig 52 that YCbCr-color space is the
most effective color representation space for image denoising applications Hence
only YCbCr-color space is considered for Type-II filter design hereafter
A brief introduction to the multi-channel versions of existing filters MF and
LAWML are given in Section 52 and Section 53 respectively The developed multi-
channel CSF (MCSF) is presented in the Section 54 Section 55 describes the
developed multi-channel RM-DWT (MRM-DWT) filter
Chapter-5 Development of Some Color Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 175
Table-51 Filtering performance of color image denoising filters in different color spaces in terms of
CPSNR (dB) [Test Image Lena]
RGB color space
YCbCr color space
CMY color space
CIE LAB color space
Standard deviation of AWGN
Standard deviation of AWGN
Standard deviation of AWGN
Standard deviation of AWGN
Sl
No
Denoising
Filters
10
25
40
10
25
40
10
25
40
10
25
40
1 M-MF [3times3] 3350 2868 2572 3745 3326 3003 3311 2849 2555 3240 2789 2499
2 M-MF [5times5] 3029 2888 2701 3437 3322 3159 2990 2869 2684 2919 2809 2628
3 M-MF [7times7] 2820 2771 2660 3242 3195 3110 2781 2753 2643 2710 2692 2587
4 M-LAWML [3times3] 3425 2925 2583 3897 3416 3159 3386 2916 2566 3315 2846 2510
5 M-LAWML [5times5] 3455 3011 2712 3857 3341 3008 3416 2993 2695 3345 2932 2639
6 M-LAWML [7times7] 3496 3048 2755 3824 3266 2793 3457 3028 2738 3386 2969 2682
7 MCSF [3times3] 3357 2654 2245 3764 3044 2659 3318 2631 2228 3247 2575 2172
8 MCSF [5times5] 3330 3049 2686 3751 3417 3080 3291 3030 2669 3220 2970 2613
9 MCSF [7times7] 3101 2998 2835 3458 3357 3204 3062 2979 2818 2991 2919 2762
10 MRM-DWT 3502 3011 2765 3987 3388 3149 3463 2992 2748 3392 2932 2692
Chapter-5 Development of Some Color Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 176
Fig 52 Bar plot showing the filtering performance in terms of CPSNR (dB)
in different color spaces of various filters on Lena image corrupted
with AWGN of the standard deviation
(a) σn=10 (low noise)
(b) σn=25 (moderate noise)
(c) σn=40 (high noise)
YC
bC
r
RG
B
CM
Y
CIE
La
b
CP
SN
R (
dB
)
(a)
CM
Y
RG
B
YC
bC
r
CIE
La
b
CP
SN
R (
dB
)
(b)
YC
bC
r
RG
B
CIE
La
b
CM
Y
CP
SN
R (
dB
) (c)
Chapter-5 Development of Some Color Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 177
52 Multi-Channel Mean Filter
The mean filter is the simplest filter used for suppressing AWGN from gray
images For denoising color images the mean filter can be modified to multi-channel
mean filter (M-MF) by employing the lsquomeanrsquo operation in three independent channels
of color space (eg RGB YCbCr CMY CIE Lab etc) separately Its multi-channel
versions Type-I M-MF (RGB-color space) and Type-II M-MF (YCbCr-color
space) are developed here in accordance with Fig 51 (a) and Fig 51 (b)
respectively for color image denoising These two filters are represented in block
schematic in Fig 53
The performance of these filters is examined by extensive simulation work
presented in Section-56
Chapter-5 Development of Some Color Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 178
Fig 53 Block Diagram of a Multi-Channel Mean Filter
(a) Type-I Filter (RGB-Color Space)
(b) Type-II Filter (Color Space YCbCr)
Input
Color Image
(RGB)
Mean
Filter R-Channel
G-Channel
RG
B ndash
YC
bC
r
T
ran
sfo
rma
tio
n
YC
bC
r ndash
RG
B
T
ran
sfo
rma
tio
n
Output
Color Image
(RGB)
B-Channel
(b)
R-Channel
G-Channel
B-Channel
Y
Cb
Cr
Y
Cb
Cr
Mean
Filter
Mean
Filter
(a)
Mean
Filter
R-Channel
G-Channel
B-Channel
R-Channel
G-Channel
B-Channel
Mean
Filter
Mean
Filter
Input Color Image
(RGB)
Output Color Image
(RGB)
Chapter-5 Development of Some Color Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 179
53 Multi-Channel LAWML Filter
The locally adaptive window maximum likelihood (LAWML) filter [105] is a
wavelet-domain filter that performs well for suppressing additive noise The filtering
performance of LAWML has already been examined and found to be very promising
for gray images Therefore its multi-channel versions Type-I M-LAWML (RGB-
color space) and Type-II M-LAWML (YCbCr color space) are developed here in
accordance with Fig 51 (a) and Fig 51 (b) respectively for color image denoising
These two filters are represented in block schematic in Fig 54
The performance of these filters is examined by extensive simulation work
presented in Section-56
Chapter-5 Development of Some Color Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 180
Input
Color Image
(RGB)
LAWML
Filter R-Channel
G-Channel
RG
B ndash
YC
bC
r
T
ran
sfo
rma
tio
n
YC
bC
r ndash
RG
B
T
ran
sfo
rma
tio
n
Output
Color Image
(RGB)
B-Channel
(b)
R-Channel
G-Channel
B-Channel
Y
Cb
Cr
Y
Cb
Cr
LAWML
Filter
LAWML
Filter
(a)
LAWML
Filter
R-Channel
G-Channel
B-Channel
R-Channel
G-Channel
B-Channel
LAWML
Filter
LAWML
Filter
Input Color Image
(RGB)
Output Color Image
(RGB)
Fig 54 Block Diagram of a Multi-Channel LAWML Filter
(a) Type-I Filter (RGB-Color Space)
(b) Type-II Filter (Color Space YCbCr)
Chapter-5 Development of Some Color Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 181
54 Development of Multi-Channel Circular Spatial Filter
The Circular Spatial Filter (CSF) is a spatial-domain filter that performs very
well for suppressing AWGN from gray images The filtering operation for
suppressing AWGN is explained in Chaper-3 The CSF is found to be quite efficient
in suppressing AWGN under moderate and high noise conditions yielding less
distortion to the filtered image The filtering performance of CSF has already been
examined and found to be very promising for gray images Therefore its multi-
channel versions Type-I MCSF (RGB-color space) and Type-II MCSF (YCbCr-
color space) are developed here [P6] in accordance with Fig 51 (a) and Fig 51 (b)
respectively for color image denoising These two filters are represented in block
schematic in Fig 55
The performance of these filters is examined by extensive simulation work
presented in Section-56
Chapter-5 Development of Some Color Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 182
Input
Color Image
(RGB)
CSF
Filter R-Channel
G-Channel
RG
B ndash
YC
bC
r
T
ran
sfo
rma
tio
n
YC
bC
r ndash
RG
B
T
ran
sfo
rma
tio
n
Output
Color Image
(RGB)
B-Channel
(b)
R-Channel
G-Channel
B-Channel
Y
Cb
Cr
Y
Cb
Cr
CSF
Filter
CSF
Filter
(a)
CSF
Filter
R-Channel
G-Channel
B-Channel
R-Channel
G-Channel
B-Channel
CSF
Filter
CSF
Filter
Input Color Image
(RGB)
Output Color Image
(RGB)
Fig 55 Block Diagram of a Multi-Channel CSF Filter
(a) Type-I Filter (RGB-Color Space)
(b) Type-II Filter (Color Space YCbCr)
Chapter-5 Development of Some Color Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 183
55 Development of Multi-Channel Region Merging based
DWT-domain Filter
The noise suppression capability of the Region Merging based DWT-domain
(RM-DWT) filter has been examined for the gray image in Chapter-4 It has been
observed that it performs very well for low noise conditions For denoising color
images its multi-channel versions Type-I MRM-DWT (RGB-color space) and
Type-II MRM-DWT filters are developed here in accordance with Fig 51 (a) and
Fig 51 (b) respectively These two filters are represented in block schematic in
Fig 56
The performance of these filters is examined by extensive simulation work
presented in Section-56
Chapter-5 Development of Some Color Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 184
Input
Color Image
(RGB)
RM-DWT
Filter R-Channel
G-Channel
RG
B ndash
YC
bC
r
T
ran
sfo
rma
tio
n
YC
bC
r ndash
RG
B
T
ran
sfo
rma
tio
n
Output Color Image
(RGB)
B-Channel
(b)
R-Channel
G-Channel
B-Channel
Y
Cb
Cr
Y
Cb
Cr
RM-DWT
Filter
RM-DWT
Filter
(a)
RM-DWT
Filter
R-Channel
G-Channel
B-Channel
R-Channel
G-Channel
B-Channel
RM-DWT
Filter
RM-DWT
Filter
Input
Color Image
(RGB)
Output Color Image
(RGB)
Fig 56 Block Diagram of a Multi-Channel RM-DWT Filter
(a) Type-I Filter (RGB-Color Space)
(b) Type-II Filter (Color Space YCbCr)
Chapter-5 Development of Some Color Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 185
56 Simulation Results
Extensive simulation is carried out to study the performance of the multi-
channel filters M-MF M-LAWML MCSF and MRM-DWT The performance of
these filters is studied in RGB- and YCbCr-color spaces The performance measures
color-peak-signal-to-noise ratio (CPSNR) root-mean-squared error (RMSE) and
universal quality index (UQI) method noise (MN ) and execution time (TE) are
evaluated and presented in tables Table-52 to Table-518
The simulation work is performed on color test images Lena (512times512times3
pixels) and Pepper (512times512times3 pixels) corrupted with AWGN of standard deviation
σn = 5 10 15 20 25 30 35 40 45 and 50 The noise level of additive noise is
categorized as low (noise standard deviation σnle10) moderate (10ltσnle30) and high
(30ltσnle50)
The CPSNR values of multi-channel filters for RGB-color space are given in
Table-52 and Table-53 and for YCbCr-color space are given in Table-58 and Table-
59 The largest CPSNR value for a particular standard deviation of Gaussian noise is
highlighted to show the best performance
The RMSE values of multi-channel filters for RGB-color space are given in
the tables Table-54 to Table-55 For YCbCr-color space the RMSE values of multi-
channel filters are given in the tables Table-510 to Table-511 The smallest RMSE
value (best performance) for a particular standard deviation of Gaussian noise is
highlighted
The UQI values of various multi-channel filters for RGB-color space are given
in the tables Table 56 to Table 57 For YCbCr-color space the performances of
different multi-channel filters in terms of UQI values are given in Table-512 to
Table-513 The maximum value of UQI for a particular standard deviation of
Gaussian noise is identified and is highlighted as the best performance
The method noise of various multi-channel filters for the images Lena and
Pepper is presented in the table Table 514 to Table 515
Chapter-5 Development of Some Color Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 186
The filters are simulated on three different computing systems SYSTEM-1
SYSTEM-2 and SYSTEM-3 presented in Table-11 in Section-15 The execution
time taken for different filtering schemes is given in the Table-516 and Table-517
Fig 57 illustrates the resulting CPSNR of different multi-channel filters in
RGB- and YCbCr-color spaces for Lena image that is corrupted with different levels
of AWGN The best performance measure for a particular standard deviation of
AWGN irrespective of window size of a filter is shown in the figures The execution
time (TE) of various filters is shown as bar plot in Fig 58 The TE of a filter with
larger window size (for worst-case analysis) is taken in the bar plot
For subjective evaluation the filtered output images of various multi-channel
filters are shown in the figures Fig 59 to Fig 520 The images corrupted with
AWGN of standard deviation σn = 15 (moderate-noise) and σn = 40 (high-noise) are
applied to different filters and the resulted output images are shown
It has been observed from Table-51 that the filters perform very well in
YCbCr-color space It needs further investigations whether the Type-II versions
(YCbCr-color space) exhibit good filtering characteristics in flat and smooth regions
as well as complex regions of an image To examine the distortion and artifacts the
different multi-channel filters in YCbCr-color space are applied on a smooth region
and a complex region of color Lena image corrupted with AWGN of σn = 15 and σn =
40 and the filtering performances are shown in the figures Fig 517 to Fig 520 to
demonstrate the effectiveness of the filters
In Fig 521 the magnified (zoomed) versions of output-images of the filters
M-LAWML MCSF and MRM-DWT of complex regions that are already
demonstrated in Fig 520 are shown In Fig 521 six regions (containing textures
and fine details) are chosen which are identified with green circles for critical
analysis
Conclusions are drawn in Section 57
Chapter-5 Development of Some Color Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 187
Table-52 Filtering performance of Type-I color image denoising filters in RGB-color space in
terms of CPSNR (dB) operated on Lena image under various noise conditions (σn varies
from 5 to 50)
CPSNR (dB)
Standard deviation of AWGN Sl
No Denoising Filters
5 10 15 20 25 30 35 40 45 50
Test Image Lena
1 M-MF [3times3] 3470 3350 3227 3078 2868 2778 2686 2572 2495 2458
2 M-MF[5times5] 3051 3029 2977 2902 2888 2855 2783 2701 2659 2599
3 M-MF[7times7] 2829 2820 2789 2776 2761 2714 2689 2660 2645 2591
4 M-LAWML [3times3] 3501 3425 3263 3078 2925 2777 2662 2583 2513 2476
5 M-LAWML[5times5] 3513 3455 3336 3161 3011 2893 2769 2712 2682 2623
6 M-LAWML [7times7] 3537 3496 3344 3179 3048 2905 2867 2755 2698 2658
7 MCSF [3times3] 3488 3357 3077 2845 2654 2477 2355 2245 2189 2083
8 MCSF [5times5] 3402 3388 3375 3179 3049 2876 2774 2686 2595 2541
9 MCSF [7times7] 3331 3101 3085 3039 2998 2952 2942 2835 2789 2733
10 MRM-DWT 3587 3502 3373 3175 3046 2908 2876 2765 2698 2661
Table-53 Filtering performance of Type-I color image denoising filters in RGB-color space in
terms of CPSNR (dB) operated on Pepper image under various noise conditions (σn varies
from 5 to 50)
CPSNR (dB)
Standard deviation of AWGN Sl
No Denoising Filters
5 10 15 20 25 30 35 40 45 50
Test Image Pepper
1 M-MF [3times3] 3346 3176 3087 2942 2831 2725 2629 2538 2458 2388
2 M-MF[5times5] 3271 3097 3065 3009 2956 2894 2835 2776 2713 2673
3 M-MF[7times7] 3162 2914 2916 2859 2834 2812 2773 2737 2734 2682
4 M-LAWML [3times3] 3538 3501 3254 3076 2934 2811 2714 2638 2574 2520
5 M-LAWML[5times5] 3579 3543 3325 3163 3031 2922 2833 2758 2689 2639
6 M-LAWML [7times7] 3593 3545 3327 3170 3049 2939 2849 2777 2703 2657
7 MCSF [3times3] 3443 3346 3039 281 2623 2471 2342 223 2134 2044
8 MCSF [5times5] 3462 3464 3327 3174 3032 2902 2788 269 2597 2517
9 MCSF [7times7] 3432 3313 3278 3131 3078 3012 2948 2879 2817 2783
10 MRM-DWT 3596 3548 3318 3167 3053 2941 2856 2781 2712 2656
Chapter-5 Development of Some Color Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 188
Table-54 Filtering performance of Type-I color image denoising filters in RGB-color space
in terms of RMSE operated on Lena image under various noise conditions (σn varies from 5
to 50)
RMSE
Standard deviation of AWGN Sl
No Denoising Filters
5 10 15 20 25 30 35 40 45 50
Test Image Lena
1 M-MF [3times3] 469 538 620 737 938 1041 1157 1319 1442 1505
2 M-MF[5times5] 760 779 828 902 917 952 1035 1137 1194 1279
3 M-MF[7times7] 981 992 1028 1067 1049 1120 1153 1192 1213 1291
4 M-LAWML [3times3] 452 494 595 737 879 1042 1190 1303 1412 1474
5 M-LAWML[5times5] 446 477 547 669 796 912 1052 1123 1162 1244
6 M-LAWML [7times7] 434 455 542 656 763 899 939 1069 1141 1195
7 MCSF [3times3] 459 534 737 963 1201 1472 1694 1923 2051 2317
8 MCSF [5times5] 507 551 523 656 762 930 1046 1157 1285 1367
9 MCSF [7times7] 550 717 720 765 808 852 862 975 1028 1096
10 MRM-DWT 412 452 660 692 796 896 930 1056 1141 1191
Table-55 Filtering performance of Type-I color image denoising filters in RGB color space
in terms of RMSE operated on Pepper image under various noise conditions (σn varies
from 5 to 50)
RMSE
Standard deviation of AWGN Sl
No Denoising Filters
5 10 15 20 25 30 35 40 45 50
Test Image Pepper
1 M-MF [3times3] 541 658 729 862 979 1106 1236 1372 1505 1631
2 M-MF[5times5] 590 721 748 798 848 911 978 1043 1122 1175
3 M-MF[7times7] 669 890 888 948 9762 1001 1047 10915 1095 1162
4 M-LAWML [3times3] 434 452 601 738 870 1002 1120 12233 1316 1401
5 M-LAWML[5times5] 414 431 554 668 778 882 977 10655 1153 1221
6 M-LAWML [7times7] 407 430 553 663 762 865 959 10424 1135 1196
7 MCSF [3times3] 484 541 770 1003 1244 1482 1722 19568 2185 2424
8 MCSF [5times5] 473 472 553 659 777 902 1029 11522 1282 1406
9 MCSF [7times7] 490 631 656 693 737 795 856 92692 995 1035
10 MRM-DWT 406 429 559 665 758 863 951 10376 1123 1198
Chapter-5 Development of Some Color Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 189
Table-56 Filtering performance of Type-I color image denoising filters in RGB-color space in
terms of UQI operated on Lena image under various noise conditions (σn varies from 5 to 50)
UQI
Standard deviation of AWGN Sl
No Denoising Filters
5 10 15 20 25 30 35 40 45 50
Test Image Lena
1 M-MF [3times3] 09954 09936 09906 09863 09811 09746 09677 09593 09502 09392
2 M-MF[5times5] 09871 09853 09842 09826 09806 09784 09751 09715 09682 09628
3 M-MF[7times7] 09768 09755 09749 09741 09733 09717 09699 09675 09652 09617
4 M-LAWML [3times3] 09966 09959 09916 09864 09811 09754 0969 09627 09561 09498
5 M-LAWML[5times5] 09978 09965 09932 09892 09852 09812 09772 09727 09685 09637
6 M-LAWML [7times7] 09977 09966 09932 09898 09861 09827 09788 09747 09709 09665
7 MCSF [3times3] 09972 09963 09863 09756 09625 09466 09286 09081 08868 08628
8 MCSF [5times5] 09945 09939 09934 09899 09861 09828 09725 09655 09572 09484
9 MCSF [7times7] 09912 09903 09855 09844 09829 09805 09789 09751 09716 09675
10 MRM-DWT 09982 09973 09915 09881 09837 09786 09788 09747 09708 09663
Table-57 Filtering performance of Type-I color image denoising filters in RGB-color space in
terms of UQI operated on Pepper image under various noise conditions (σn varies from 5 to 50)
UQI
Standard deviation of AWGN Sl
No Denoising Filters
5 10 15 20 25 30 35 40 45 50
Test Image Pepper
1 M-MF [3times3] 09917 09901 09873 09836 09788 09731 09663 09587 09506 09410
2 M-MF[5times5] 09886 09878 09867 09849 09827 09800 09770 09731 09688 09639
3 M-MF[7times7] 09820 09815 09807 09794 09780 09760 09738 09708 09678 09641
4 M-LAWML [3times3] 09980 09950 09912 09867 09816 09758 09702 09639 09576 09505
5 M-LAWML[5times5] 09978 09906 09897 09883 09864 09842 09816 09782 09747 0971
6 M-LAWML [7times7] 09991 09983 09957 09929 09898 09861 09822 09783 09735 09697
7 MCSF [3times3] 09987 09983 099 09817 0971 09582 09433 09267 09089 08883
8 MCSF [5times5] 09979 09971 09968 09934 09898 09847 09797 09735 09671 0959
9 MCSF [7times7] 09921 09913 09906 09895 09889 09862 09838 09810 09785 09766
10 MRM-DWT 09993 09986 09961 09929 09890 09861 09821 09776 09731 09695
Chapter-5 Development of Some Color Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 190
Table-58 Filtering performance of Type-II color image denoising filters in YCbCr-color space
in terms of CPSNR (dB) operated on Lena image under various noise conditions (σn varies
from 5 to 50)
CPSNR (dB)
Standard deviation of AWGN Sl
No Denoising Filters
5 10 15 20 25 30 35 40 45 50
Test Image Lena
1 M-MF [3times3] 3863 3745 3602 3460 3326 3209 3099 3003 2917 2838
2 M-MF[5times5] 3456 3437 3407 3366 3322 3267 3216 3159 3100 3046
3 M-MF[7times7] 3249 3242 3230 3217 3195 3172 3143 3110 3076 3040
4 M-LAWML [3times3] 4173 3897 3683 3537 3416 3323 3236 3159 3088 3019
5 M-LAWML[5times5] 4145 3857 3608 3456 3341 3224 3099 3008 2938 2840
6 M-LAWML [7times7] 4129 3824 3555 3385 3266 3107 2963 2793 2782 2694
7 MCSF [3times3] 4078 3864 3455 3224 3044 2895 2767 2659 2567 2484
8 MCSF [5times5] 3976 3781 3774 3617 3417 3276 3174 3080 2991 2913
9 MCSF [7times7] 3786 3458 3432 3398 3357 3343 3260 3204 3150 3095
10 MRM-DWT 4372 3987 3652 3508 3388 3308 3224 3149 3076 3016
Table-59 Filtering performance of Type-II color image denoising filters in YCbCr-color space
in terms of CPSNR (dB) operated on Pepper image under various noise conditions (σn
varies from 5 to 50)
CPSNR (dB)
Standard deviation of AWGN Sl
No Denoising Filters
5 10 15 20 25 30 35 40 45 50
Test Image Pepper
1 M-MF [3times3] 3656 3581 3475 3364 3253 3152 3052 2967 2884 2812
2 M-MF[5times5] 3520 3494 3454 3403 3346 3286 3222 3156 3094 3030
3 M-MF[7times7] 3324 3312 3294 3271 3241 3206 3170 3126 3083 3032
4 M-LAWML [3times3] 4121 3811 3611 3453 3333 3224 3131 3047 2960 2881
5 M-LAWML[5times5] 4105 3781 3575 3390 3261 3127 3028 2929 2835 2760
6 M-LAWML [7times7] 4087 3747 3505 3354 3195 3047 2926 2812 2724 2595
7 MCSF [3times3] 4018 3743 3446 3220 3042 2893 2772 2665 2572 2491
8 MCSF [5times5] 3945 3821 3696 3540 3418 3282 3174 3077 2985 2904
9 MCSF [7times7] 3832 3565 3524 3474 3414 3355 3290 3221 3156 3087
10 MRM-DWT 4212 3895 3676 3535 3402 3314 3212 3130 3050 2974
Chapter-5 Development of Some Color Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 191
Table-510 Filtering performance of Type-II color image denoising filters in YCbCr-color
space in terms of RMSE operated on Lena image under various noise conditions (σn varies
from 5 to 50)
RMSE
Standard deviation of AWGN Sl
No Denoising Filters
5 10 15 20 25 30 35 40 45 50
Test Image Lena
1 M-MF [3times3] 298 342 403 474 554 633 719 803 887 971
2 M-MF[5times5] 477 487 504 529 556 592 622 671 718 764
3 M-MF[7times7] 605 610 618 628 644 661 683 710 738 770
4 M-LAWML [3times3] 208 287 367 434 499 555 614 671 728 788
5 M-LAWML[5times5] 215 300 400 477 544 623 719 798 866 969
6 M-LAWML [7times7] 219 312 425 517 593 712 841 1023 1036 1146
7 MCSF [3times3] 232 334 477 623 766 912 1054 1194 1327 1460
8 MCSF [5times5] 262 327 330 391 498 586 659 735 814 891
9 MCSF [7times7] 326 475 490 509 534 543 597 637 678 722
10 MRM-DWT 166 258 389 449 515 565 617 681 738 793
Table-511 Filtering performance of Type-II color image denoising filters in YCbCr-color
space in terms of RMSE operated on Pepper image under various noise conditions (σn
varies from 5 to 50)
RMSE
Standard deviation of AWGN Sl
No Denoising Filters
5 10 15 20 25 30 35 40 45 50
Test Image Pepper
1 M-MF [3times3] 378 413 466 530 602 676 759 837 921 1001
2 M-MF[5times5] 443 456 478 507 541 580 624 673 723 779
3 M-MF[7times7] 555 563 574 590 611 636 663 697 732 777
4 M-LAWML [3times3] 221 316 399 478 549 623 693 763 844 924
5 M-LAWML[5times5] 225 328 415 514 597 696 780 875 975 1063
6 M-LAWML [7times7] 230 341 450 536 644 763 878 1001 1108 1285
7 MCSF [3times3] 249 342 482 625 768 912 1048 1185 1319 1448
8 MCSF [5times5] 271 313 361 433 498 582 659 737 820 900
9 MCSF [7times7] 309 420 441 467 500 535 577 625 673 729
10 MRM-DWT 199 287 370 435 507 561 631 694 761 830
Chapter-5 Development of Some Color Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 192
Table-512 Filtering performance of Type-II color image denoising filters in YCbCr-color space
in terms of UQI operated on Lena image under various noise conditions (σn varies from 5 to 50)
UQI
Standard deviation of AWGN Sl
No
Denoising
Filters
5 10 15 20 25 30 35 40 45 50
Test Image Lena
1 M-MF [3times3] 09926 09903 09865 09813 09747 09671 09579 09475
09366 09245
2 M-MF[5times5] 09807 09799 09784 09764 09739 09704 09667 09623 09570 09515
3 M-MF[7times7] 09686 09681 09673 09663 09646 09627 09601 09572 09540 09504
4
M-LAWML
[3times3] 09977 09945 09910 09870 09834 09796 09751 09705 09656 09598
5
M-
LAWML[5times5] 09975 09939 09894 09848 09803 09739 09659 09577 09506 09384
6
M-LAWML [7times7] 09974 09935 09880 09820 09764 09665 09533 09280 09288 09131
7 MCSF [3times3] 09943 09908 09815 09687 09533 09354 09149 08928 08701 08457
8 MCSF [5times5] 09924 09920 09918 09871 09837 09717 09641 09559 09462 09361
9 MCSF [7times7] 09912 09901 09896 09861 09819 09798 09776 09727 09668 09613
10 MRM-DWT 09982 09953 09873 09832 09789 09788 09744 09699 09644 09596
Table-513 Filtering performance of Type-II color image denoising filters in YCbCr color space in
terms of UQI operated on Pepper image under various noise conditions (σn varies from 5 to 50)
UQI
Standard deviation of AWGN Sl
No Denoising Filters
5 10 15 20 25 30 35 40 45 50
Test Image Pepper
1 M-MF [3times3] 09917 09901 09873 09836 09787 09731 09661 09588 09501 09411
2 M-MF[5times5] 09886 09879 09866 09849 09827 09802 09769 09731 09689 09640
3 M-MF[7times7] 09820 09815 09806 09795 09780 09760 09739 09710 09680 09641
4 M-LAWML [3times3] 09956 09932 09904 09872 09837 09806 09752 09703 09641 09571
5 M-LAWML[5times5] 09955 09929 09908 09855 09812 09750 09689 09613 09524 09423
6 M-LAWML [7times7] 09954 09925 09884 09843 09783 09704 09607 09501 09385 09177
7 MCSF [3times3] 09960 09931 09865 09774 09661 09528 09380 09213 09035 08850
8 MCSF [5times5] 09950 09943 09922 09888 09849 09801 09744 09681 09605 09526
9 MCSF [7times7] 09903 09897 09886 09872 09853 09831 09804 09769 09732 09686
10 MRM-DWT 09976 09950 09920 09889 09852 09812 09762 09711 09653 09585
Chapter-5 Development of Some Color Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 193
Table-514 Method Noise MN of various Type-I multi-channel filters in RGB-color
space operated on different test images
Sl
No
Images
Denoising Filters Lena Pepper
1 M-MF [3times3] 265 308
2 M-MF[5times5] 446 425
3 M-MF[7times7] 573 563
4 M-LAWML [3times3] 379times10-10
456times10-10
5 M-LAWML[5times5] 379times10-10
456times10-10
6 M-LAWML [7times7] 379times10-10
456times10-10
7 MCSF [3times3] 124 150
8 MCSF [5times5] 275 270
9 MCSF [7times7] 438 400
10 MRM-DWT 379times10-10
456times10-10
Table-515 Method Noise MN of various Type-II multi-channel filters in
YCbCr-color space operated on different test images
Sl
No
Images
Denoising Filters Lena Pepper
1 M-MF [3times3] 265 308
2 M-MF[5times5] 446 425
3 M-MF[7times7] 573 563
4 M-LAWML [3times3] 379times10-10
456times10-10
5 M-LAWML[5times5] 379times10-10
456times10-10
6 M-LAWML [7times7] 379times10-10
456times10-10
7 MCSF [3times3] 124 150
8 MCSF [5times5] 275 270
9 MCSF [7times7] 438 400
10 MRM-DWT 379times10-10
456times10-10
Chapter-5 Development of Some Color Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 194
Table-516 Execution Time (seconds) TE taken by various Type-I multi-channel filters in
RGB-color space for Lena image
Sl No Images Denoising
Filters
SYSTEM-1 SYSTEM-2 SYSTEM-3
1 M-MF [3times3] 855 1539 4309
2 M-MF[5times5] 8966 1614 4519
3 M-MF[7times7] 945 1701 4762
4 M-LAWML [3times3] 1188 2139 5989
5 M-LAWML[5times5] 1198 2157 6039
6 M-LAWML [7times7] 1245 2242 6277
7 MCSF [3times3] 8711 1568 4390
8 MCSF [5times5] 928 1672 4681
9 MCSF [7times7] 1001 1803 5048
10 MRM-DWT 1307 2353 6588
Table-517 Execution Time (seconds) TE taken by various Type-II multi-channel filters in YCbCr-color space for Lena image
Sl No Images
Denoising
Filters
SYSTEM-1 SYSTEM-2 SYSTEM-3
1 M-MF [3times3] 1042 1564 4848
2 M-MF[5times5] 1104 1656 5133
3 M-MF[7times7] 1150 1726 5350
4 M-LAWML [3times3] 1624 2436 7551
5 M-LAWML[5times5] 1688 2532 7849
6 M-LAWML [7times7] 1792 2688 8332
7 MCSF [3times3] 1067 1601 4963
8 MCSF [5times5] 1148 1722 5338
9 MCSF [7times7] 1210 1816 5629
10 MRM-DWT 1984 2976 9225
Chapter-5 Development of Some Color Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 195
Fig 58 Bar plot showing the execution time (seconds) of various multi-channel
filters in YCbCr-color space on three different hardware platforms
SYSTEM-1 SYSTEM-2 SYSTEM-3
Ex
ecu
tio
n T
ime
in s
econ
ds
Fig 57 Performance comparison of various multi-channel filters in terms of CPSNR [dB]
for the various standard deviation of AWGN operated on Lena image
(e) in RGB-color space
(f) in YCbCr-color space
CP
SN
R [
dB
]
Standard deviation of AWGN (σn) Standard deviation of AWGN (σn)
CP
SN
R [
dB
] (a) (b)
CPSNR values in RGB-color space CPSNR values in YCbCr-color space
Chapter-5 Development of Some Color Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 196
(a) (b) (c)
(d) (e) (f)
Fig 59 Performance of Various Filters in RGB-Color Space
for Color Lena Image with AWGN of σn = 15
(a) Original image
(b) Noisy image
(c) Type-I M-MF ndash output image
(d) Type-I M-LAWML ndash output image
(e) Type-I MCSF ndash output image
(f) Type-I MRM-DWT ndash output image
Chapter-5 Development of Some Color Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 197
(a) (b) (c)
(d) (e) (f)
Fig 510 Performance of Various Filters in RGB-Color Space
for Color Lena Image with AWGN of σn = 40
(a) Original image
(b) Noisy image
(c) Type-I M-MF ndash output image
(d) Type-I M-LAWML ndash output image
(e) Type-I MCSF ndash output image
(f) Type-I MRM-DWT ndash output image
Chapter-5 Development of Some Color Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 198
(a) (b) (c)
(d) (e) (f)
Fig 511 Performance of Various Filters in RGB-Color Space for Color Pepper Image with AWGN of σn = 15
(a) Original image
(b) Noisy image
(c) Type-I M-MF ndash output image
(d) Type-I M-LAWML ndash output image
(e) Type-I MCSF ndash output image
(f) Type-I MRM-DWT ndash output image
Chapter-5 Development of Some Color Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 199
(a) (b) (c)
(d) (e) (f)
Fig 512 Performance of Various Filters in RGB-Color Space
for Color Pepper Image with AWGN of σn = 40
(a) Original image
(b) Noisy image
(c) Type-I M-MF ndash output image
(d) Type-I M-LAWML ndash output image
(e) Type-I MCSF ndash output image
(f) Type-I MRM-DWT ndash output image
Chapter-5 Development of Some Color Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 200
(a) (b) (c)
(d) (e) (f)
Fig 513 Performance of Various Filters in YCbCr-Color Space
for Color Lena Image with AWGN of σn = 15
(a) Original image
(b) Noisy image
(c) Type-II M-MF ndash output image
(d) Type-II M-LAWML ndash output image
(e) Type-II MCSF ndash output image
(f) Type-II MRM-DWT ndash output image
Chapter-5 Development of Some Color Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 201
(a) (b) (c)
(d) (e) (f)
Fig 514 Performance of Various Filters in YCbCr-Color Space
for Color Lena Image with AWGN of σn = 40
(a) Original image
(b) Noisy image (c) Type-II M-MF ndash output image
(d) Type-II M-LAWML ndash output image (e) Type-II MCSF ndash output image
(f) Type-II MRM-DWT ndash output image
Chapter-5 Development of Some Color Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 202
(a) (b) (c)
(d) (e) (f)
Fig 515 Performance of Various Filters in YCbCr-Color Space
for Color Pepper Image with AWGN of σn = 15
(a) Original image (b) Noisy image
(c) Type-II M-MF ndash output image (d) Type-II M-LAWML ndash output image
(e) Type-II MCSF ndash output image (f) Type-II MRM-DWT ndash output image
Chapter-5 Development of Some Color Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 203
(a) (b) (c)
(d) (e) (f)
Fig 516 Performance of Various Filters in YCbCr-Color Space
for Color Pepper Image with AWGN of σn = 40
(a) Original image
(b) Noisy image (c) Type-II M-MF ndash output image
(d) Type-II M-LAWML ndash output image (e) Type-II MCSF ndash output image
(f) Type-II MRM-DWT ndash output image
Chapter-5 Development of Some Color Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 204
(a)
(b)
(c)
(d)
(e)
(f)
Fig 517 Performance of Various Filters in YCbCr-Color Space for Color Lena Image (Smooth Region) with AWGN of σn = 15
(a) Original image
(b) Noisy image
(c) Type-II M-MF ndash output image
(d) Type-II M-LAWML ndash output image
(e) Type-II MCSF ndash output image
(f) Type-II MRM-DWT ndash output image
Chapter-5 Development of Some Color Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 205
(a) (b) (c)
(d) (e) (f)
Fig 518 Performance of Various Filters in YCbCr-Color Space
for Color Lena Image (Complex Region) with AWGN of σn = 15
(a) Original image
(b) Noisy image
(c) Type-II M-MF ndash output image (d) Type-II M-LAWML ndash output image
(e) Type-II MCSF ndash output image (f) Type-II MRM-DWT ndash output image
Chapter-5 Development of Some Color Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 206
(a)
(b)
(c)
(d)
(e)
(f)
Fig 519 Performance of Various Filters in YCbCr-Color Space
for Color Lena Image (Smooth Region) with AWGN of σn = 40
(a) Original image
(b) Noisy image
(c) Type-II M-MF ndash output image
(d) Type-II M-LAWML ndash output image
(e) Type-II MCSF ndash output image
(f) Type-II MRM-DWT ndash output image
Chapter-5 Development of Some Color Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 207
(a) (b) (c)
(d) (e) (f)
Fig 520 Performance of Various Filters in YCbCr-Color Space
for Color Lena Image (Complex Region) with AWGN of σn = 40
(a) Original image
(b) Noisy image (c) Type-II M-MF ndash output image
(d) Type-II M-LAWML ndash output image (e) Type-II MCSF ndash output image
(f) Type-II MRM-DWT ndash output image
Chapter-5 Development of Some Color Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 208
Fig 521 Zoomed versions of Fig 520 (a) (d) (e) (f) showing six various regions
containing texture and fine details in complex regions of color Lena image
(a) Original image
(b) Type-II M-LAWML ndash output image
(c) Type-II MCSF ndash output image
(d) Type-II MRM-DWT ndash output image
(c)
2
1
3
4
5
6
(a)
2
1
3
4
5
6
(d)
2
1
3
4
5
6
(b)
2
1
3
4
5
6
Chapter-5 Development of Some Color Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 209
57 Conclusion
The performance of multi-channel filters Multi-Channel Mean Filter (M-MF)
Multi-Channel LAWML (M-LAWML) Filter Multi-Channel Circular Spatial Filter
(MCSF) and Multi-Channel Region Merging based DWT-domain (MRM-DWT)
Filter are studied in RGB- and YCbCr-color spaces It is observed that the filtering
performance is better in YCbCr-color space for all filters
From Table-52 and Table-53 (for RGB-color space) and Table-58 and
Table-59 (for YCbCr-color space) it is observed that the CPSNR values are higher
for MCSF under moderate and high noise conditions When the noise level is low the
MRM-DWT performs better than other multi-channel filters
From Table-54 and Table-55 (for RGB-color space) and Table-510 and
Table-511 (for YCbCr-color space) it is observed that the RMSE values are smaller
for MCSF under moderate and high noise conditions When the noise level is low the
RMSE values are smaller for MRM-DWT
The UQI values of various multi-channel filters are given in the Table 56 and
Table-57 (for RGB-color space) and in Table-512 and Table-513 (for YCbCr-color
space) From the tables it is observed that the MRM-DWT filter is found to be
effective in terms of UQI under low noise conditions Under moderate and high noise
conditions the UQI values are higher for MCSF
Considering the performance measures CPSNR RMSE and UQI it can be
concluded that the MRM-DWT is efficient in noise suppression under low noise
conditions whereas the MCSF filter suppresses additive noise quite effectively under
moderate and high noise conditions effectively
The filtering performance in terms of method noise is shown in Table-514
(RGB-color space) and Table-515 (YCbCr-color space) From these tables it is
observed that the method noise is low in case of MRM-DWT and M-LAWML So
these filters yield less distortion to the original noise-free image while filtering
Chapter-5 Development of Some Color Image Denoising Filters
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 210
operation is done These tables also illustrate that the performance MCSF in terms of
method noise is moderate
The execution time (TE) of various filters is shown in Table-516 (RGB-color
space) and Table-517 (YCbCr-color space) From these tables it is seen that the
execution time of MCSF is smaller than other multi-channel filters (except M-MF)
and is close to the simplest M-MF
The subjective evaluation should also be taken into consideration to judge the
filtering performance The filtering performances of various multi-channel filters on a
smooth region and a complex region of Lena image are shown in the figures
Fig 517 to Fig 520 From these figures it is observed that the wavelet-domain
multi-channel filter M-LAWML yield a lot of artifacts in the smooth region The
other wavelet-domain filter MRM-DWT also yields artifacts but it is less than
M-LAWML filter The MCSF does not introduce artifacts in the smooth region In
Fig 521 some textures and detailed structures are identified in a complex region
From the figure it is seen that the developed filter MCSF retains the detailed
information and texture effectively as compared to other multi-channel filters This is
quite obvious when the regions 5 and 6 are examined in details Only the proposed
filter MCSF is found to be capable of preserving the details in these regions On the
other hand the other two high-performing filters M-LAWML and MRM-DWT yield
high blurring in these regions
Hence it is concluded that the proposed filter MCSF [P6] is found to be a
high performing filter for suppression of AWGN from color images
Chapter 6
Conclusion
Chapter-6 Conclusion
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 212
Preview
In this thesis various spatial-domain and transform-domain filters for
suppression of additive white Gaussian noise (AWGN) available in literature are
studied and their performances are analyzed Considering the limitations of the
existing filters efforts have been made to develop two spatial-domain filters (i)
adaptive window Wiener filter (AWWF) [P1] and (ii) circular spatial filter (CSF) [P2]
and three transform-domain filters (i) Gaussian shrinkage based DCT-domain
filter (GS-DCT) [P3] (ii) Total variation based DWT-domain (TV-DWT) filter [P4]
and Region Merging based DWT-domain (RM-DWT) filter [P5] The performances of
the proposed filters are compared with existing spatial-domain and transform-domain
filters The objective evaluation metrics peak-signal-to-noise ratio (PSNR) root-
mean-squared error (RMSE) universal quality index (UQI) method noise (MN ) and
execution time (TE) are considered for comparing their filtering performances
In this research work two multi-channel filters multi-channel circular spatial
filter (MCSF) and multi-channel region merging based DWT-domain (RM-DWT)
filter are developed for suppression of additive noise from color images The
6
Chapter-6 Conclusion
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 213
developed filters are based on three-channel processing (eg RGB-processing
YCbCr-processing etc) and hence are necessarily 3-channel CSF and 3-channel RM-
DWT respectively The objective evaluation metrics color-peak-signal-to-noise ratio
(CPSNR) root-mean-squared error (RMSE) universal quality index (UQI) method
noise ( MN ) and execution time (TE) are considered for comparing filter performances
All the developed filters are compared against some well-known filters
available in literature
The following topics are covered in this chapter
Comparative Analysis
Conclusion
Scope for Future Work
61 Comparative Analysis
The filtering performances of developed filters for gray and color images are
analyzed here
611 Comparative Analysis of Developed Filters for Denoising Gray
Images
The proposed spatial-domain filters and transform-domain filters are simulated
on test images Lena Pepper Goldhill and Barbara of sizes 512times512 pixels each
corrupted with AWGN of standard deviation σn = 5 10 15 20 25 30 35 40 45 and
50 The noise level of AWGN is categorized as low (noise standard deviation
Chapter-6 Conclusion
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 214
σnle10) moderate (10ltσnle30) and high (30ltσnle50) The proposed filters are
compared with the existing spatial-domain filters mean filter median filter alpha-
trimmed mean (ATM) filter Wiener filter anisotropic diffusion (AD) filter total
variation (TV) filter Lee filter Bilateral filter and non-local means (NL-Means) filter
and existing wavelet-domain filters VisuShrink SureShrink BayesShrink
OracleShrink OracleThresh NeighShrink SmoothShrink and locally adaptive
window maximum likelihood (LAWML) To check the filtering performance of the
proposed filters as well as the existing filters the performance-measures PSNR
RMSE UQI MN and TE are evaluated for all cases To give a concise presentation of
all simulation results so as to have a precise comparative study the performance-
measures of the proposed filters as well as some high-performing existing filters are
shown in Table-61 and Table-62 only for three cases of noise level σn = 10 σn = 20
and σn = 40 just to give an insight to low moderate and high noise power conditions
respectively Here Lena is taken as test image
Table-61 shows the performance of the various filters in terms of PSNR
RMSE and UQI whereas Table-62 shows method noise and execution time of
different filters The execution time is evaluated for Pentium IV Duo Processor
(Clock 28 GHz RAM 1 GB Windows XP 32 bit OS) ie the hardware platform
SYSTEM-2 presented in Table-11 Section-15 Since the TV filter is iterative in
nature its execution time is necessarily very high and hence is not considered
Therefore it is not included in Table-62
Chapter-6 Conclusion
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 215
Table-61 Filtering performance of various filters in terms of PSNR (dB) RMSE and UQI
operated on Lena image under various noise conditions ( σn = 10 20 and 40)
Noise standard deviation σn
σn = 10
σn = 20
σn = 40
Denoising Filters PSNR RMSE UQI PSNR RMSE UQI PSNR RMSE UQI
Mean 3270 589 09922 2978 826 09849 2696 1142 09700
ATM 3271 589 09922 2983 821 09851 2703 1134 09710
Wiener 3401 507 09943 3019 787 09861 2655 1198 09671
TV 3322 555 09931 3025 782 09864 2585 1298 09633
Lee 3347 540 09936 2974 828 09847 2677 1167 09688
Bilateral 3258 596 09921 2977 826 09849 2671 1175 09686
BayesShrink 3364 527 09938 3020 787 09863 2711 1124 09711
NeighShrink 3445 481 09949 3011 795 09861 2608 1264 09642
Ex
isti
ng
Fil
ters
LAWML 3459 474 09950 3086 729 09882 2732 1086 09721
AWWF 3336 545 09934 3056 754 09865 2688 1152 09690
CSF 3287 578 09949 3031 777 09866 2749 1076 09735
GS-DCT 3310 563 09902 3098 719 09896 2710 1124 09720
TV-DWT 3376 522 09936 3056 754 09855 2667 1180 09652 Pro
po
sed
Fil
ters
RM-DWT 3472 466 09954 3022 785 09815 2734 1083 09725
Chapter-6 Conclusion
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 216
Table-62 Filtering performance various filters in terms of Method Noise MN and
Execution Time TE on Lena image ( σn = 0 and σn = 40 for first and second column
respectively)
Denoising Filters Method Noise Execution Time (sec)
Mean 262 720
ATM 262 1784
Wiener 186 1614
TV 211 -------
Lee 00118 1508
Bilateral 288 1347
BayeShrink 00232 415
NeighShrink 408times10-10 912
Ex
isti
ng
F
ilte
rs
LAWML 408times10-10
809
AWWF 183 2417
CSF 122 729
GS-DCT 05737 3038
TV-DWT 2014 09375
Pro
po
sed
Fil
ters
RM-DWT 408times10-10 1134
Chapter-6 Conclusion
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 217
It is observed that at low noise conditions the proposed filter RM-DWT
outperforms all other filters Its PSNR is 3472 dB whereas the existing filter
LAWML gives a PSNR of 3459 dB for σn = 10
Under moderate noise conditions the proposed filter GS-DCT gives superior
performance The PSNR value of the filter at σn = 20 is 3098 dB The PSNR of
LAWML is very close to GS-DCT with a value of 3086 dB at σn = 20
Under high noise conditions the proposed filter CSF gives best performance
among all filters considered here for comparison It yields a PSNR of 2749 dB and a
UQI of 09735 at σn = 40 that are best among all other filters considered here
The method noise of RM-DWT LAWML and NeighShrink filters are same
and found to be 408times10-10 ie quite negligible and hence are best suited for very low
noise conditions
From Table-62 it is observed that the developed filter TV-DWT takes
minimum execution time which is found to be 09375 sec However the developed
filter CSF takes execution time of 729 sec which is close to the execution time of
the simplest mean filter
Chapter-6 Conclusion
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 218
612 Comparative Analysis of Developed Filters for Denoising Color
Images
The simulation work is performed on color test image Lena (512times512times3
pixels) and Pepper (512times512times3 pixels) corrupted with AWGN of standard deviation
σn = 5 10 15 20 25 30 35 40 45 and 50 The filtering performances of multi-
channel filters are examined on various color spaces (eg RGB YCbCr CMY and
CIE Lab) The filtering performance is compared with multi-channel versions of
existing filters (i) mean filter [1] (simplest and oldest filter) and (ii) locally adaptive
window maximum likelihood (LAWML) filter [105] (best performer among the
existing wavelet-domain filters examined in Chapter-2) The performance of various
filters in YCbCr-color space in terms of CPSNR RMSE and UQI is given in
Table-63 Here color Lena image corrupted with AWGN of σn = 10 (low noise) σn =
20 (moderate noise) and σn = 40 (high noise) is taken to test the filter performance
Table-64 shows the method noise and execution time of various filters in YCbCr-
color space operated on Lena image
Chapter-6 Conclusion
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 219
Table-63 Filtering performance of various filters in terms of CPSNR (dB) RMSE and UQI
operated on Lena image under various noise conditions ( σn = 10 20 and 40) in YCbCr-color
space
Noise standard deviation
σn = 10 σn = 20 σn = 40
Denoising
Filters
CPSNR
RMSE
UQI
CPSNR
RMSE
UQI
CPSNR
RMSE
UQI
M-MF [3times3] 3745 342 09903 3460 474 09813 3003 803 09475
M-MF [5times5] 3437 487 09799 3366 529 09764 3159 671 09623
M-MF [7times7] 3242 610 09681 3217 628 09663 3110 710 09572
M-LAWML[3times3] 3897 287 09945 3537 434 09870 3159 671 09705
M-LAWML[5times5] 3857 300 09939 3456 477 09848 3008 798 09577
Ex
isti
ng
F
ilte
rs
M-LAWML[7times7] 3824 312 09935 3385 517 09820 2793 1023 09280
MCSF [3times3] 3864 334 09908 3224 623 09687 2659 1194 08928
MCSF [5times5] 3781 327 09920 3617 391 09871 3080 735 09559
MCSF [7times7] 3458 475 09901 3398 509 09861 3204 637 09727
Pro
po
sed
Fil
ters
MRM-DWT 3987 258 09953 3508 449 09832 3149 681 09699
Chapter-6 Conclusion
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 220
Table-64 Filtering performance various filters in terms of Method
Noise MN and Execution Time TE on Lena image in YCbCr-color space
Denoising Filters
Method Noise
Execution Time
M-MF [3times3] 265 1564
M-MF [5times5] 446 1656
M-MF [7times7] 573 1726
M-LAWML[3times3] 379times10
-10
2436
M-LAWML[5times5] 379times10
-10 2532
Ex
isti
ng
F
ilte
rs
M-LAWML[7times7] 379times10
-10 2688
MCSF [3times3] 12495 1601
MCSF [5times5] 2754 1722
MCSF [7times7] 4386 1816
Pro
po
sed
Fil
ters
MRM-DWT 379times10
-10 2976
From Table-63 it is observed that the proposed filter MRM-DWT performs
better under low noise conditions whereas MCSF gives better performance under
moderate and high noise conditions From Table-64 it is seen that the wavelet-
domain filters MRM-DWT and M-LAWML have lower method noise as compared
to other methods The execution time is lowest in case of simplest M-MF The
proposed MCSF has got execution time of 1601 sec which is close to that of M-MF
Chapter-6 Conclusion
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 221
62 Conclusion
The developed image denoising filters AWWF [P1] CSF [P2] GS-DCT
[P3] TV-DWT [P4] RM-DWT [P5] and MCSF [P6] are examined with extensive
simulation and the results are presented in the tables Table-61 to Table-64
From the results presented in Table-61 it is observed that
(i) The RM-DWT filter performs very efficiently for low-noise power
(ii) The GS-DCT filter performs very efficiently for moderate-noise power
(iii) The CSF filter performs very efficiently for high-noise power
for gray images This conclusion is derived on the concept of yielding high values of
PSNR UQI and low RMSE so that the filtered output contains very low noise power
On the other hand if method noise and execution time parameters are considered
then some other filters should be regarded as best performers Thus for the online and
real-time applications that need low MN and TE values it is observed that
(i) The RM-DWT is the best filter yielding minimum method noise
(ii) The TV-DWT is the best filter having minimum execution time
(iii) The CSF is an excellent filter having moderate values of both MN and TE
These observations are quite evident from Table-62 If an overall comparison is
drawn amongst all filters against all the performance measures ie to consider the
noise suppression capability (PSNR RMSE UQI) as well as the system-nonlinearity
(method noise) and the system-complexity (execution time) then for gray images it
is quite obvious that
(i) The proposed filter Circular Spatial Filter (CSF) [P2] is the best
performing filter under moderate and high noise conditions
(ii) The proposed filter RM-DWT [P5] is the best filter under low noise
conditions
Chapter-6 Conclusion
Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 222
It is observed from Table-63 that
(i) The MRM-DWT performs well under low noise conditions
(ii) The MCSF performs well under moderate and high noise conditions
for suppressing additive noise for color images
The results presented in Table-64 show that the multi-channel version of the
existing scheme LAWML ie M-LAWML yields minimal method noise and is thus
seen to be a very good candidate for color image denoising applications under very
low noise conditions Of course it does not have high significance since the noise
power level in practical situation is seldom so low
Finally it may be concluded that the proposed filter CSF [P2] and its
multi-channel version MCSF [P6] are the best performers considering all
performance measures
63 Scope for Future Work
Some new directions of research in the field of image denoising are not yet
fully explored There is sufficient scope to develop very effective filters in the
directions mentioned below
(a) Fuzzy logic and neural network may be employed for optimizing the tuning
parameters needed in the different filters
(b) The widow size of different filters can be made adaptive for efficient
denosing The shape of the window can also be varied and made adaptive to
develop very effective filters
(c) Some other transforms such as DHT curvelet and slantlet can be used for
image denoising
(d) Very few filters are developed based on blind techniques Independent
component analysis can be a very good candidate for blind denoising
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 223
REFERENCES [1] RC Gonzalez and RE Woods Digital Image Processing 2nd ed Englewood
Cliffs NJ Prentice-Hall 2002
[2] AK Jain Fundamentals of Digital Image Processing Englewood Cliffs NJ
Prentice-Hall 1989
[3] J W Tukey Experimental Data Analysis Reading M A Addison-Wesley
1971
[4] J Astola and P Kuosmanen Fundamentals of Nonlinear Digital Filtering
Boca Raton FL CRC Press 1997
[5] I Pitas and AN Venetsanopoulos Nonlinear Digital Filters Principles and
Applications Norwell MA Kluwer 1990
[6] WK Pratt Digital Image Processing NY John Wiley amp Sons 2001
[7] RS Blum Z Liu Multi-Sensor Image Fusion and Its Applications Boca
Raton Taylor amp Francis 2006
[8] R Lukac and KN Plataniotis Color Image Processing Methods and
Applications Boca Raton FL CRC Press 2007
[9] JS Lim Two-Dimensional Signal and Image Processing Englewood Cliffs
NJ Prentice-Hall 1990
[10] S Mallat A Wavelet Tour of Signal Processing 2nd ed Academic Press Inc
1999
[11] G Strang and T Nguyen Wavelets and Filter Banks Wellesley-Cambridge
Press 1996
[12] JC Goswami and AK Chan Fundamentals of Wavelets Theory Algorithms
and Applications Wiley 1999
[13] Y Meyer R D Ryan Wavelets Algorithms amp Applications Society for
Industrial and Applied Mathematics Philadelphia 1993
[14] I Daubechies Ten Lectures on Wavelets Society for Industrial and Applied
Mathematics Philadelphia 1992
REFERENCES
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 224
[15] KR Rao and P Yip Discrete Cosine Transform Algorithms Advantages
Applications Academic Press Boston 1990
[16] Norbert Wiener Extrapolation Interpolation and Smoothing of Stationary
Time Series New York Wiely 1949
[17] N Ahmed T Natarajan and KR Rao ldquoDiscrete Cosine Transformrdquo IEEE
Transactions on Computers vol C-23 no 1 pp 90-93 1974
[18] S Mallat ldquoA Theory for Multiresolution Signal Decomposition The Wavelet
Representationrdquo IEEE Transactions on Pattern Analysis and Machine
Intelligence vol 11 no7 pp 674-692 1989
[19] M Vetterli C Herley ldquoWavelets and Filter Banks Theory and Designrdquo
IEEE Transactions on Signal Processing vol 40 no 9 1992
[20] D Stanhill YY Zeevi ldquoTwo-Dimensional Orthogonal and Symmetrical
Wavelets and Filter-Banksrdquo IEEE Acoustics Speech and Signal Processing
vol 3 pp 1499-1502 1996
[21] T Cooklev A Nishihara ldquoBiorthogonal coifletsrdquo IEEE Transactions on
Signal Processing vol 47 no 9 pp 2582-2588 1999
[22] J Canny ldquoA computational approach to edge detectionrdquo IEEE Transactions
on Pattern Analysis and Machine Intelligence vol 8 no 6 pp 679-698 1986
[23] L S Davis ldquoA survey on edge detection techniquesrdquo Computer Graphics and
Image Processing vol 4 pp 248-270 1975
[24] F Russo ldquoColor edge detection in presence of Gaussian noise using nonlinear
prefilteringrdquo IEEE Transactions on Instrumentation and Measurement vol
54 no 1 pp 352-358 2005
[25] P Bao L Zhang X Wu ldquoCanny edge detection enhancement by scale
multiplicationrdquo IEEE Transactions on Pattern Analysis and Machine
Intelligence vol 27 no 9 pp 1485-1490 2005
[26] P Hsiao C Chen H Wen S Chen ldquoReal-time realization of noise-immune
gradient-based edge detectorrdquo Proc IEE Computers and Digital Techniques
vol 153 no 4 pp 261-269 2006
[27] T Chaira AK Ray ldquoA new measure using intuitionistic fuzzy set theory and
its application to edge detectionrdquo Applied Soft Computing vol 8 no 2 pp
919-927 2008
REFERENCES
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 225
[28] T Chen K K Ma and L H Chen ldquoTri-state median filter for image
denoisingrdquo IEEE Trans on Image Processing vol 8 pp1834-1838
December 1999
[29] P S Windyga ldquoFast impulsive noise removalrdquo IEEE Trans on image
Processing vol10 no 1 pp173-179 January 2001
[30] F Russo ldquoEvolutionary neural fuzzy system for noise cancellation in image
processingrdquo IEEE Trans Inst amp Meas vol 48 no 5 pp 915-920 Oct 1999
[31] F Farbiz M B Menhaj SA Motamedi and MT Haganrdquo A new fuzzy logic
filter for image enhancementrdquo IEEE Trans on Syst Meas Cybernetics ndash Part
B Cybernetro vol30 no1 pp 110-119 Feb 2000
[32] H-L Eng and K-K Ma ldquo Noise adaptive soft switching median filterrdquo IEEE
Trans on Image Processing vol10 no2 pp 242-251 Feb 2001
[33] T Chen and HR Wu ldquoAdaptive impulse detection using center-weighted
median filtersrdquo IEEE Signal Processing Letters vol 8 no 1 pp1-3 Jan
2001
[34] KN Plataniotis S Vinayagamoorthy D Androutsos AN Venetsanopoulos
ldquoAn adaptive nearest neighbor multichannel filterrdquo IEEE Transactions on
Circuits and Systems for Video Technology vol 6 no 6 pp 699-703 1996
[35] S Schulte S Morillas V Gregori E E Kerre ldquoA new fuzzy color correlated
impulse noise reduction methodrdquo IEEE Transactions on Image Processing
vol 16 no 10 pp 2565-2575 2007
[36] H Zhou KZ Mao ldquoAn impulsive noise color image filter using learning-
based color morphological operationsrdquo Digital Signal Processing vol 18 pp
406-421 2008
[37] Y Li GR Arce J Bacca ldquoWeighted median filters for multichannel
signalsrdquo IEEE Transactions on Image Processing vol 54 no 11 pp 4271-
4281 2006
[38] Z Ma D Feng HR Wu ldquoA neighborhood evaluated adaptive vector filter
for suppression of impulse noise in color imagesrdquo Real-Time Imaging vol
11 no 6 pp 403-416 2005
REFERENCES
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 226
[39] I Aizenberg C Butakoff D Paliy ldquoImpulsive noise removal using threshold
Boolean filtering based on the impulse detecting functionsrdquo IEEE Signal
Processing Letters vol 12 no 1 pp 63-66 2005
[40] L Khriji M Gabbouj ldquoAdaptive fuzzy order statistics-rational hybrid filters
for color image processingrdquo Fuzzy Sets and System vol 128 no 1 pp 35-
46 2002
[41] S Meher G Panda B Majhi MR Meher ldquoFuzzy weighted rank-ordered
mean (FWROM) filters for efficient noise suppressionrdquo Proc of National
Conference on Communication NCC-2005 Indian Institute of Technology
Kharagpur 2005
[42] S Meher Development of Some Novel Nonlinear and Adaptive Digital Image
Filters for Efficient Noise Suppression Doctoral Dissertation National
Institute of Technology Rourkela India
[43] R Garnett T Huegerich C Chui W He ldquoA universal noise removal
algorithm with an impulse detectorrdquo IEEE Transactions on Image Processing
vol14 no 11 2005
[44] R Li YJ Zhang ldquoA hybrid filter for the cancellation of mixed Gaussian
noise and impulse noiserdquo Proceedings of the Joint Conference of the Fourth
International Conference on Information Communications and Signal
Processing and Fourth Pacific Rim Conference on Multimedia ICICS-PCM
2003
[45] R Manthalkar PK Biswas BN Chatterji ldquoRotation invariant texture
classification using even symmetric Gabor filterrdquo Pattern Recognition Letters
vol 24(12) pp 2061-2068 2003
[46] M Damian E Cernadas A Formella M Delgado P Sa-Otero ldquoAutomatic
detection and classification of grains of pollen based on shape and texturerdquo
IEEE Transactions on Systems Man and Cybernetics-Part C Applications
and Reviews vol 36 no 4 pp 531-542 2006
[47] M Mellor B Hong M Brady ldquoLocally rotation contrast and scale invariant
descriptors for texture analysisrdquo IEEE Transactions on Pattern Analysis and
Machine Intelligence vol 30 no 1 pp 52-61 2008
REFERENCES
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 227
[48] I Epifanio P Soille ldquoMorphological texture features for unsupervised and
supervised segmentations of natural landscapesrdquo IEEE Transactions on
Geoscience and Remote Sensing vol 45 no 4 pp 1074-1083 2007
[49] G Zhao M Pietikaumlinen ldquoDynamic texture recognition using local binary
patterns with an application to facial expressionsrdquo IEEE Transactions on
Pattern Analysis and Machine Intelligence vol 29 no 6 pp 915-928 2007
[50] Z Wang J Yong ldquoTexture analysis and classification with linear regression
model based on wavelet transformrdquo IEEE Transactions on Image Processing
vol17 no 8 pp 1421-1430 2008
[51] X Xie M Mirmehdi ldquoTEXEMS Texture exemplars for defect detection on
random textured surfacesrdquo IEEE Transactions on Pattern Analysis and
Machine Intelligence vol 29 no 8 pp 1454-1464 2007
[52] A Ravichandran and B Yegnanarayana ldquoStudies on object recognition from
degraded images using neural networkrdquo Neural Networks vol 8 no 3 pp
481-488 1995
[53] A Diplaros T Gevers I Patras ldquoCombining color and shape information for
illumination-viewpoint invariant object recognitionrdquo IEEE Transactions on
Image Processing vol15 no 1 pp 1-11 2006
[54] S Naik CA Murthy ldquoDistinct multicolored region descriptors for object
recognitionrdquo IEEE Transactions on Image Processing vol29 no 7 pp 1291-
1296 2007
[55] T Seree L Wolf S Bileschi M Riesenhuber T Poggio ldquoRobust object
recognition with cortex-like mechanismsrdquo IEEE Transactions on Pattern
Analysis and Machine Intelligence vol 29 no 3 pp 411-426 2007
[56] IB Ayed A Mitiche ldquoA region merging prior for variational level set image
segmentationrdquo IEEE Transactions on Image Processing vol17 no 12 pp
2301-2311 2008
[57] A Safou P Maragos ldquoGeneralized flooding and multicue PDE-based image
segmentationrdquo IEEE Transactions on Image Processing vol17 no 3
pp 364-376 2008
REFERENCES
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 228
[58] Q Li N Mitianoudis T Stathaki ldquoSpatial kernel K-harmonic means
clustering for multi-spectral image segmentationrdquo IET Image Processing vol
1 no 2 pp 156-167 2007
[59] YK Singh SK Parui ldquoISITRA A generalized way of signal decomposition
and reconstructionrdquo Digital Signal Processing Elsevier vol 16 no 1
pp 3-23 2006
[60] H G Longotham and AC Bovik ldquoTheory of order statistics filters and their
relationship to linear FIR filtersrdquo IEEE Trans on Acoust Speech Signal
Processing vol ASSP-37 no2 pp 275-287 February 1989
[61] N C Gallagher and G L Wise ldquoA Theoretical analysis of the properties of
median filtersrdquo IEEE Trans Accoust Speech Signal Processing vol ASSP-
29 pp 1136-1141 Dec 1981
[62] I H Jang and N C Kim ldquoLocally adaptive Wiener filtering in wavelet
domain for image restorationrdquo Proc IEEE R-10 Conference on Speech and
Image Technologies for Computing and Telecommunications TENCON-97
vol 1 pp 25-28 1997
[63] G Angelopoulos and I Pitas ldquoMultichannel Wiener filters in color image
restorationrdquo IEEE Transactions on Circuits and Systems for Video
Technology vol 4 no 1 1994
[64] L Shao R M Lewitt JS Karp and G Muehllehner ldquoCombination of
Wiener filtering and singular value decomposition filtering for volume
imaging PETrdquo IEEE Transactions on Nuclear Science vol 42 no 4 1995
[65] A P Wikin ldquoScale-space filteringrdquo Proc Int Joint Conf Artif Intell IJCAI
pp 1019-1021 1983
[66] J J Koenderink ldquoThe structure of imagesrdquo J Biol Cybern vol 50 pp 363-
370 1984
[67] P Perona and J Malik ldquoScale space and edge detection using anisotropic
diffusionrdquo in Proc IEEE Comput Soc Workshop Comput Vision Miami
FL pp 16-22 1987
[68] P Perona and J Malik ldquoScale space and edge detection using anisotropic
diffusionrdquo IEEE Trans Pattern Anal Machine Intell vol 12 no 7 pp 629-
639 1990
REFERENCES
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 229
[69] L I Rudin S Osher and E Fatemi ldquoNonlinear total variation based noise
removal algorithmsrdquo Physica D vol 60 pp 259-268 1992
[70] C Tomasi R Manduchi ldquoBilateral filtering for gray and color imagesrdquo
Proceedings of IEEE international conference on computer vision pp 839-
846 1998
[71] BM Oh M Chen J Dorsey F Durand ldquoImage-based modeling and photo
editingrdquo Proceedings of SIGGRAPHrsquo01 pp 433-442 2001
[72] F Durand J Dorsey ldquoFast bilateral filtering for the display of high-dynamic-
range imagesrdquo ACM Transactions on Graphics vol 21 no 3 pp 257-266
2002
[73] E Eisemann F Durand ldquoFlash photography enhancement via intrinsic
relightingrdquo ACM Transactions on Graphics vol 23 no 3 pp 673-678 2004
[74] G Petschnigg M Agrawala H Hoppe R Szeliski M Cohen K Toyama
ldquoDigital photography with flash and no-flash image pairsrdquo ACM Transactions
on Graphics vol 23 no 3 pp 664-672 2004
[75] TR Jones F Durand M Desbrun ldquoNon-iterative feature-preserving mesh
smoothingrdquo ACM Transactions on Graphics vol 22 no 3 pp 943-949
2003
[76] S Fleishman I Drori D Cohen-Or ldquoBilateral mesh denoisingrdquo ACM
Transactions on Graphics vol 22 no 3 pp 950-953 2003
[77] WCK Wong ACS Chung SCH Yu ldquoTrilateral filtering for biomedical
imagesrdquo Proceedings of IEEE international symposium on biomedical
imaging pp 820-823 2004
[78] EP Bennett L McMillan ldquoVideo enhancement using per-pixel virtual
exposuresrdquo ACM Transactions on Graphics vol 24 no 3 pp 845-852 2005
[79] JS Lee ldquoDigital image enhancement and noise filtering by use of local
statisticsrdquo IEEE Transactions on Pattern Analysis and Machine Intelligence
vol 2 no 3 pp 165-168 1980
[80] JS Lee ldquoRefined filtering of image noise using local statisticsrdquo Computer
Graphics and Image Processing vol 15 no 4 pp 380-389 1981
[81] JS Lee ldquoSpeckle suppression and analysis for synthetic aperture radar
imagesrdquo Optical Engineering vol 25 no 5 pp 636-643 1986
REFERENCES
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 230
[82] X Wang ldquoLee filter for multiscale image denoisingrdquo Proceedings of
international conference on signal processing vol 1 2006
[83] C Hengzhi Y Xianchuan Z Junlan ldquoA new algorithm fusing the fractal
interpolation and the enhanced lee filter and its application to the SAR imagersquos
denoisingrdquo Proceedings of world congress on intelligent control and
automation pp 6778-6782 2008
[84] J Zhu R Chen Y Hong ldquoA novel adaptive filtering algorithm for SAR
speckle reductionrdquo Proceedings of Asian and Pacific conference on synthetic
aperture radar pp 327-330 2007
[85] L Klaine B Vozel K Chehdi ldquoAn integro-differential method for adaptive
filtering of additive or multiplicative noiserdquo Proceedings of IEEE
international conference on acoustics speech and signal processing pp 1001-
1004 2005
[86] B Waske M Barun G Menz ldquoA segment-based speckle filter using
multisensoral remote sensing imageryrdquo IEEE Geoscience and Remote
Sensing Letters vol 4 no 2 pp 231-235 2007
[87] A Baraldi F Parmiggiani ldquoAn alternative form of the Lee filter for speckle
suppression in SAR imagesrdquo Graphical Models and Image Processing vol
57 no 1 pp 75-78 1995
[88] A Buades B Coll and J Morel ldquoA non-local algorithm for image
denoisingrdquo Proc IEEE international conference on computer vision and
pattern recognition pp 60-65 2005
[89] A Buades B Coll and J Morel ldquoOn image denoising methodsrdquo Technical
Report 2004-15 CMLA 2004
[90] A Efros and T Leung ldquoTexture synthesis by non parametric samplingrdquo Proc
international conference computer vision pp 1033-1038 1999
[91] A Buades B Coll J Morel ldquoNon-local movie and image denoisingrdquo
International Journal of Computer Vision 76 no 2 pp 123-139 2008
[92] A Baudes B Coll JM Morel ldquoDenoising image sequences does not require
motion estimationrdquo Proceedings IEEE international conference on advanced
video and image based surveillance pp 70-74 2005
REFERENCES
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 231
[93] M Mahmoudi G Sapiro ldquoFast image and video denoising via non local
means of similar neighborhoodrdquo IEEE Signal Processing Letters vol 12 no
12 pp 839-842 2005
[94] MV Jose CC Jose JL Juan GM Gracian MB Luis R Montserrat
ldquoMRI denoising using non-local meansrdquo Medical Image Analysis vol 12 no
4 pp 514-523 2008
[95] P Coupe P Yger C Barillot ldquoFast non-local means denoising for 3D MR
imagesrdquo Proc of medical image computing and computer assisted
intervention LNCS 2879 9no2 pp 33-40 2006
[96] M Ebrahimi ER Vrscay ldquoSolving the inverse problem of image zooming
using self examplesrdquo Image Analysis and Recognition LNCS 4633 Springer
pp 117-130 2007
[97] G Gilboa S Osher ldquoNon local linear image regularization and supervised
segmentationrdquo SIAM Journal on Multiscale Modeling and Simulation vol 6
no 2 pp 597-630 2007
[98] DL Donoho IM Johnstone ldquoDe-noising by soft-thresholdingrdquo IEEE
Transactions on Information Theory vol 41 no 3 pp 613ndash27 1995
[99] DL Donoho IM Johnstone ldquoIdeal spatial adaptation via wavelet
shrinkagerdquo Biometrika vol 81 no 3 pp 425-55 1994
[100] DL Donoho IM Johnstone ldquoAdapting to unknown smoothness via wavelet
shrinkagerdquo Journal of the American Statistical Association vol 90(432) pp
1200-1224 1995
[101] F Luisier T Blu M Unser ldquoA new SURE approach to image denosing
interscale orthonormal wavelet thresholdingrdquo IEEE Transactions on Image
Processing vol 16 (3) pp 593-606 2007
[102] S Chang B Yu M Vetterli ldquoAdaptive wavelet thresholding for image
denoising and compressionrdquo IEEE Transactions on Image Processing vol 9
no 9 pp 1532-1546 2000
[103] GY Chen TD Bui A Krzyzak ldquoImage denoising using neighboring
wavelet coefficientsrdquo proceedings of IEEE international conference on
acoustics speech and signal processing rsquo04 pp 917-920 2004
REFERENCES
Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 232
[104] M Mastriani and AE Giraldez ldquoSmoothing of coefficients in wavelet domain
for speckle reduction in synthetic aperture radar imagesrdquo Journal of Graphics
Vision and Image Processing vol 7(special issue) pp 1-8 2007
[105] MK Mihcak I Kozintsev K Ramchandran P Moulin ldquoLow-complexity
image denoising based on statistical modeling of wavelet coefficientsrdquo IEEE
Signal Processing Letters vol 6 no 12 pp300-303 1999
[106] M Crouse R Nowak R Baraniuk ldquoWavelet based statistical signal
processing using hidden Markov modelsrdquo IEEE Transactions on Signal
Processing vol 46(4) pp886-902 1998
[107] M Marta S Grgic M Grgic ldquoPicture quality measures in image compression
systemsrdquo Proceedings EUROCON rsquo03 p 233-7 2003
[108] Z Wang AC Bovik ldquoA universal image quality indexrdquo IEEE Signal
Processing Letters vol 9 no 3 pp81-84 2002
[109] PGJ Barten Contrast sensitivity of human eye and its effects on image
quality SPIE Washington 1999
[110] T Rabie ldquoRobust estimation approach for blind denoisingrdquo IEEE
Transactions on Image Processing vol 14 no 11 pp 1755-1765 2005
[111] F Russo ldquoAutomatic enhancement of noisy images using objective evaluation
of image qualityrdquo IEEE Transactions on Instrumentation and Measurement
vol 54 no 4 pp 1600-1606 2005
[112] S Tan L Jio ldquoA unified iterative denoising algorithm based on natural image
statistical models derivation and examplesrdquo Optics Express vol 16 (2) pp
1056-1068 2008
[113] D V Ville M Nachtegael DV Weken EE Kerre W Philips I Lemahieu
ldquoNoise reduction by fuzzy image filteringrdquo IEEE Transactions on Fuzzy
Systems vol11 no 4 pp 429-436 2003
[114] C Kervrann J Boulanger ldquoOptimal spatial adaptation for patch-based image
denoisingrdquo IEEE Transactions on Image Processing vol 15 no 10 pp 2866-
2878 2006
[115] DD Muresan TW Parks ldquoAdaptive principal components and image
denoisingrdquo Proc IEEE international conference on image processing ICIP
2003 vol 1 pp I-101-I-104 2003