Research Article Improving Image Quality in Medical Images …downloads.hindawi.com/journals/ijbi/2013/797924.pdf · 2019-07-31 · We propose a method for improving image quality

Hindawi Publishing CorporationInternational Journal of Biomedical ImagingVolume 2013 Article ID 797924 11 pageshttpdxdoiorg1011552013797924

Research ArticleImproving Image Quality in Medical Images Usinga Combined Method of Undecimated Wavelet Transform andWavelet Coefficient Mapping

Du-Yih Tsai1 Eri Matsuyama1 and Hsian-Min Chen2

1 Department of Radiological Technology Graduate School of Health Sciences Niigata University 2-746 Asahimachi-doriNiigata 951-8518 Japan

2Department of Biomedical Engineering College of Engineering Hungkuang University Taichung 43302 Taiwan

Correspondence should be addressed to Du-Yih Tsai tsaiclgniigata-uacjp

Received 5 August 2013 Revised 30 October 2013 Accepted 8 November 2013

Academic Editor J C Chen

Copyright copy 2013 Du-Yih Tsai et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

We propose a method for improving image quality in medical images by using a wavelet-based approach The proposed methodintegrates two components image denoising and image enhancement In the first component a modified undecimated discretewavelet transform is used to eliminate the noise In the second component a wavelet coefficient mapping function is applied toenhance the contrast of denoised images obtained from the first componentThis methodology can be used not only as a means forimproving visual quality of medical images but also as a preprocessing module for computer-aided detectiondiagnosis systemsto improve the performance of screening and detecting regions of interest in images To confirm its superiority over existingstate-of-the-art methods the proposed method is experimentally evaluated via 30 mammograms and 20 chest radiographs Itis demonstrated that the proposed method can further improve the image quality of mammograms and chest radiographs ascompared to two other methods in the literature These results reveal the effectiveness and superiority of the proposed method

1 Introduction

Denoising and contrast enhancement operations are two ofthe most common and important techniques for medicalimage quality improvement Because of their importancethere has been an enormous amount of research dedicated tothe subject of noise removal and image enhancement [1ndash4]

With regard to image denoising some approaches usingdiscrete wavelet transform (DWT) have been proposed [5ndash7] The DWT is very efficient from a computational pointof view but it is shift variant Therefore its denoisingperformance can change drastically if the starting positionof the signal is shifted In order to achieve shift invarianceresearchers have proposed the undecimated DWT (UDWT)[8ndash10] Mencattini et al reported a UDWT-based methodfor the reduction of noise in mammographic images [11]The reported method was robust and effective However themethod was not advantageous in terms of computationalaspects Zhao et al proposed an image denoising method

based on Gaussian and non-Gaussian distribution assump-tions for wavelet coefficients [12] Huang et al reportedon a denoising method which involves directly selectingthe thresholds for denoising by evaluating some statisticalproperties of the noise [13] Recently Matsuyama et alproposed a modified UDWT approach to mammographicdenoising [14] The results demonstrated that the methodcould further improve image quality and decrease imageprocessing time

As regard to the improvement of contrast enhancementvarious image enhancement techniques have been proposed[15ndash20] These techniques can be divided into several cat-egories including histogram equalization [15 16] region-based [17] fuzzy [18] genetic algorithm [19] and adaptivemethodology [20] Wavelet-based approaches to enhance-ment of digital images have been also reported [21ndash25] Tsaiet al proposed a method which employs an exponential-type mapping function to the wavelet coefficients of digitalchest images and then reconstructs an enhanced image with

2 International Journal of Biomedical Imaging

the mapped wavelet coefficients [22 23] Lee et al useda sigmoid-type mapping function for wavelet coefficientweighting adjustment to improve the contrast of medicalimages [25] The method was applied to chest radiographsmammograms and chest CT images The method showed astatistically significant superiority over the exponential-typemapping function

In this study we expanded upon the previously suggestedmodified UDWT method [14] and combined it with thesigmoid-type mapping function [25] By combining the twomethods together in sequence an effective algorithm forboth image denoising and enhancement could be obtainedOriginal images were first denoised using the modifiedUDWT followed by image enhancement using the waveletcoefficientmapping function Finally a denoised and contrastenhanced image was reconstructed by the inverse wavelettransform In this study we investigated the effectiveness ofthe proposed method by comparing it with two methods inthe literature [14 25]

2 Methods and Materials

21 Combined Method of Undecimated Discrete WaveletTransform and Wavelet Coefficient Mapping Figure 1 showsa flowchart of our proposed method In the first phasedenoising was applied to original images using our newlyadopted UDWT In the second phase image enhancementwas performed using a sigmoid-type transfer function forwavelet coefficient mapping Sections 211 and 212 describethe two phases of the proposed method respectively

211 Extended Undecimated Discrete Wavelet TransformMethod The UDWT is a wavelet transform algorithmdesigned to overcome the lack of translation invariance ofthe DWT Unlike the DWT the UDWT does not incorporatethe downsampling operationsThus the approximation coef-ficients (low-frequency coefficients) and detailed coefficients(high-frequency coefficients) at each level are the same lengthas the original signalThe basic algorithm of the conventionalUDWT is that it applies the transform at each point ofthe image and saves the detailed coefficients and uses theapproximation coefficients for the next level The size of thecoefficients array does not diminish from level to level Thisdecomposition operation is further iterated up to a higherlevel There are major differences between the modifiedUDWT method [14] and the conventional UDWT methodFirst the conventional UDWT decomposes the originalimage (level 0) into one low-frequency band and three high-frequency bands for each resolution level with the samesize as the original image The decompositions are usuallyconducted up to resolution level 4 In contrast the modifiedUDWTmethod only needs to perform the computation up toresolution level 2 and repeat the computation only one time[14 26] Second the conventional UDWT thresholded thedetailed coefficients at all 4 levels with the same thresholdingvalue while the modified UDWTmethod utilizes the hierar-chical correlation of the coefficients between level 1 and level2 of the three detailed coefficients for thresholding In other

words the thresholding values vary and are dependent on thenature of the noise

The extended UDWT method adopted in the presentstudywas based on themodifiedUDWT [14]Themethodweused mainly consisted of the following steps (see Figure 1)

(1) Perform two-dimensional UDWT to the originalimage to obtain wavelet coefficients up to level 2

(2) Calculate the hierarchical correlations of the detailedcoefficients between level 1 and level 2 for the threesubbands The correlations for the three detailedsubbands are given as

1003816100381610038161003816Coeflev 1 (119901 119902) times Coeflev 2 (119901 119902)

1003816100381610038161003816 (1)

where 119901 and 119902 are the new coordinates after wavelettransform Coeflev 1 and Coeflev 2 are wavelet coeffi-cients of level 1 and level 2 respectively

(3) Determine threshold values for each detailed sub-band The determination procedure is as follows

(a) Generate a correlation image ImgCor(119901 119902) foreach detailed subband

ImgCor (119901 119902)

=

10038161003816100381610038161003816

Coeflev1

(119901 119902) times Coeflev2

(119901 119902)

10038161003816100381610038161003816

(2)

(b) Find themaximumvalue in each row in the hor-izontal (119909-) direction of the obtained correlationimage for each of the three detailed subbands

(c) Compute the mean of the maximum valuesobtained from all rows in the 119909-direction ofthe correlation image The mean is denoted byMeanmax

(d) Eliminate those correlation values greater than08 times Meanmax These excluded values are con-sidered signal data The value of 08 was deter-mined empirically through experiments

(e) Compute the standard deviation 120590 from theremaining correlation values

(f) Determine the threshold value by use of thefollowing formula

THR = 16 times 120590 (3)

The value of 16 was determined empiricallythrough experiments

(4) Apply the determined threshold values to the correla-tion values

New Coeflev 1 (119901 119902)

=

Coeflev 1 (119901 119902) if 1003816100381610038161003816Coeflev 1 times Coeflev 2

1003816100381610038161003816ge THR

0 otherwise(4)

International Journal of Biomedical Imaging 3

H detail H detailHorizontal

Vertical

Diagonal

Level 1

Level 1 Level 2

|L1Htimes L2H|

|L1Vtimes L2V|

|L1Dtimes L2D|

wavelet transform

Originalimage

Thresholding

Thresholding

Thresholding

V detail V detail

D detail D detail

Approximation ApproximationApproximation

NewH detail

NewV detail

NewD detail

Sigm

oid-

type

tran

sfer f

unct

ion

for

wav

elet c

oeffi

cien

t map

ping

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times

times

times =

=

=

Two-dimensional undecimated

Inve

rse t

wo-

dim

ensio

nal w

avele

t tra

nsfo

rm

Figure 1 A flowchart summarizing the processing procedure for the proposed algorithm

where New Coeflev 1(119901 119902) is the newly obtainedmodified coefficient for level 1 The modified coeffi-cients of the horizontal vertical and diagonal sub-bands are respectively obtained It should be notedthat the threshold operation was only applied to thedetailed components The reason is that the detailedcomponents mainly contain the noise and high-frequency information whereas the approximationcomponent thatmainly contains low-frequency infor-mation remains unchanged

(5) Perform the inverse wavelet transform to reconstructthe denoised image with the approximation coeffi-cient of level 1 and the three newly obtained detailedcoefficients of level 1

In a previous study [14] we evaluated six comparativelypopular wavelet basis functions namely discrete FIR approx-imation of Meyer wavelet (dmey) Daubechies order 2 (db2)Symlets order 7 (sym7) Coiflets order 1 (coif1) Coiflets order5 (coif5) and biorthogonal 68 (bior68) as candidates forselection as the most suitable basis function for the UDWTThe evaluation results showed that wavelet-processed imageswith db2 basis function provided the best results among thesix basis functions Thus we selected db2 basis function forthe proposed method [14 25 26]

212 Wavelet Coefficient Mapping A sigmoid-type transfercurve with a one-to-one mapping function was used forenhancement of image contrast [25] The mapping functionwas determined based on the following considerations (a)wavelet coefficients having high values are heavily weighted

because they carry more useful information (b) the coeffi-cients at low levels are heavily weighted because they carrydetailed information such as edge information and (c) theapproximation coefficients are not manipulated to preventimage distortion [23 25]

The input coefficient 119908

119895

input(119898 119899) of level 119895 at position(119898 119899) was manipulated using the sigmoid-type transfercurves of wavelet coefficients The mapping function is givenby

119908

119895

output (119898 119899)

= 119886 times

1

1 + 1 exp [(119908

119895

input (119898 119899) minus 119888) 119887]

times 119908

119895

input (119898 119899)

(5)

where 119908

119895

output(119898 119899) represents output coefficient a b and 119888

are constants and are determined depending on the extentof enhancement to be added In practice (6) is used as themapping function instead of (5) In (6) the values of thecoefficients are expressed in terms of percentage for the easeof computation

119908

119895

output = 119886 times

1

1 + [1 exp ((119908

119895

input minus 119888) 119887)]

times 119908

119895

input []

(6)

Here 119908119895input is the input value expressed in terms of percent-age This value makes the mean of the absolute values of the


coefficients at level 119895 equal to 50 Notation 119908

119895

output is thecorresponding output value expressed in terms of percentageBy utilization of percentage the constants a b and c couldbe used independent of image characteristics The value ofconstant a was obtained using (7)

119886 = 2 minus

(119895 minus 1)

119873

(7)

where 119873 represents the maximum decomposition levelConsequently the lower the wavelet decomposition level jthe greater the gradient of the transfer curve becomes Asa result the wavelet coefficients at low-decomposition levelsthat contain information about edges of an image are highlyweighted The constant 119888 was determined by use of (8)

119888 = 119889 + 119887 times log119890(119886 minus 10) (8)

where 119889 is a constant used for determining the inflectionpoint of the sigmoid curve and 119887 represents a constant usedfor determining the gradient of the sigmoid curveThe valuesof 119887 and 119889 used in this study were 20 and 25 respectively [23]

22 Image Data To evaluate and validate our proposedmethod we used two standard digital databases a mam-mogram database and a chest radiograph database Theformer was from theMammographic Image Analysis Society(MIAS) [27] and the latter was from the Japanese Society ofRadiological Technology [28] Patient informed consent wasnot required A total of 30 mammograms obtained from thedatabase were used for investigation of the effectiveness of theproposed method The matrix size of each image was 1024 times

1024 pixels with 8-bit gray-level resolution The matrix sizeof each chest radiograph was 2048 times 2048 pixels with 12-bitgray-level resolution From the radiograph database 20 chestimages were used for the present study

Other than the described image data we also preparedanother data set by purposely adding a zero-mean Gaussiannoise with a standard deviation of 001 to the obtained 30mammograms and 20 chest radiographs The purpose ofusing the images with external added noise was to clearlydemonstrate the effectiveness of the proposed method bycomparing the pixel-value profiles along the horizontal direc-tion of processed images As for visual perceptual evaluationin order to keep visual evaluation clinically practical imageswithout adding external noise were used for visual assess-ment

23 Visual Perceptual Evaluation Avisual perceptual evalua-tionwas designed for performance analysisWe used Scheffersquosmethod of paired comparison to evaluate the preference ofoverall image quality [29 30]The visual evaluationwasmadeby five experienced radiological technologists (ranging from20 to 25 years of experience) In the case of mammogramsthe obtained 30 mammograms from the data set wereprocessed using the proposed method the modified UDWTmethod and the sigmoid-type wavelet coefficient mappingmethod Thus a total of 90 images were used for imagequality evaluation All images were evaluated on a pair of

widely used medical 3M monochrome liquid-crystal displaymonitors Each observer reviewed the images independentlyThe reading time was limited to less than 20 seconds for eachreading The observers independently evaluated one pair ofimages which were shown on the monitors one at a timeusing a 5-point grading scale (minus2 points to +2 points) If theimage shown on the left was much better than that shownon the right in terms of overall image quality the left imagewas given +2 points the left image was given +1 point whenit was slightly better than the right one the left image wasgiven 0 points when both images were of the same imagequality Conversely if the image shown on the left was muchpoorer than that shown on the right in terms of overall imagequality the left image was given minus2 points the left image wasgiven minus1 point when it was slightly poorer than the right oneComparisons were made by use of three possible combina-tions that is modified UDWTsigmoid mapping modifiedUDWTproposed method and sigmoid mappingproposedmethod combinations Each pair of images was determinedrandomly In addition the two paired images (left side versusright side) were arranged on a random basis

The same procedures were performed for the case of chestradiographs

24 Quantitative Evaluation In order to compare objectivelythe performance of the proposed algorithm against twopublished algorithms [14 25] in this study we adoptedfour image quality metrics The 4 metrics are the mean-to-standard-deviation (MSR) the contrast to noise ratio (CNR)contrast improvement ratio (CIR) and peak signal-to-noiseratio (PSNR) They are briefly described as follows

TheMSR [31 32] in a desired region of interest (DROI) isdefined as

MSR =

120583119889

120590119889

(9)

where 120583119889and 120590

119889are the mean and standard deviation

computed in the DROI The CNR [31 32] is defined as

CNR =

10038161003816100381610038161003816

120583119889minus 120583120583

10038161003816100381610038161003816

radic05 (1205902

119889+ 1205902

120583)

(10)

where 120583120583and 120590

120583are the mean and the standard deviation

computed in an undesired region of interest (UROI) suchas background Both the MSR and CNR measurements areproportional to the medical image quality

TheCIR [33] is a quantitativemeasurement of the contrastimprovement and is defined as

CIR =

sum119894sum119895

10038161003816100381610038161003816

119888 (119894 119895) minus 119888

1015840(119894 119895)

210038161003816100381610038161003816

sum119894sum119895119888(119894 119895)

2 (11)

where 119888(119894 119895) and 119888

1015840(119894 119895) are the local contrast values of

original and enhanced images respectivelyThe local contrast119888(119894 119895) is defined by the difference of mean values in two

International Journal of Biomedical Imaging 5Table 1 Results of mammogram scoring for the three combinationsby the five observers

Combination Observera b c d e Sum

Sigmoid UDWT minus11 minus087 0 minus12 minus12 minus437Sigmoid Proposed minus157 minus14 minus167 minus147 minus16 minus771UDWT Proposed minus133 minus127 minus147 minus13 minus15 minus687

Table 2 Results of chest radiograph scoring for the three combina-tions by the five observers


Sigmoid UDWT minus1 minus04 minus01 minus095 minus125 minus37Sigmoid Proposed minus17 minus14 minus135 minus14 minus165 minus75UDWT Proposed minus15 minus135 minus15 minus14 minus155 minus73

rectangular windows centered on a pixel at the coordinate(119894 119895) In detail the 119888(119894 119895) is given by

119888 (119894 119895) =

1003816100381610038161003816119901 (119894 119895) minus 119886 (119894 119895)

1003816100381610038161003816

1003816100381610038161003816119901 (119894 119895) + 119886 (119894 119895)

1003816100381610038161003816

(12)

where 119901 and 119886 are the average values of pixels within a 3 times 3region and a 7 times 7 surrounding neighborhood respectivelyThe greater the CIR value the better the enhancement result

The PSNR [34] in decibels is adopted for measuring theperformance of denoising and is given by

PSNR = 10 log10

119872 times 119873 times 119879

2

sum119894sum119895[119889 (119894 119895) minus 119889

1015840(119894 119895)]

2 (13)

where 119872 times 119873 is the size of the image 1198792 is the maximumpossible value that can be obtained by the image signal 119889(119894 119895)and 119889

1015840(119894 119895) are the pixel-values of original and processed

images respectively The higher the PSNR value the betterthe performance of denoising

3 ResultsIn this study we used 30 mammograms and 20 chestradiographs to evaluate the proposed method by comparingit to two other existing methods a modified UDWTmethod[14] and a sigmoid-type wavelet coefficient (STWC)mappingmethod [25] The results of a previous study showed thatby use of a modified UDWT method the computationtime can be reduced to approximately 110 that of theconventional UDWT method In addition the results ofvisual assessment indicated that the images processed withthe modified UDWT method showed statistically signifi-cant superior image quality over those processed with theconventional UDWT method [14] The STWC mappingmethod demonstrated that it offers considerably improvedenhancement capability as compared to the conventionalenhancement methods such as the fast Fourier transformmethod the conventional wavelet-based method and theconventional exponential-type wavelet coefficient mappingmethod [25]

Figure 2 shows two sets of example images of mammo-grams and chest radiographs Original images are shown in

the upper row of the figure and corresponding images areshown in the lower row with external noise added Figure 3illustrates an example of image processing results obtainedfrom the mammogram shown in Figure 2(e) Figures 3(a)3(b) and 3(c) are resulting images processed by using theproposed method the modified UDWT method and theSTWCmapping method respectively

Figure 4 shows the 119909-direction profiles of the processedimages traced from the lines indicated on the images ofFigures 3(a)ndash3(c) Figures 4(a)ndash4(c) illustrate the profiles ofthe images processed by the proposed method the modifiedUDWT method and STWC mapping method respectivelyThe 119909-direction profile of the original image traced from theline indicated on the image of Figure 2(e) is also shown in thefigures for comparison Figures 4(d)ndash4(f) show themagnifiedviews of the profiles corresponding to the positions indicatedby the dotted circles in Figures 4(a)ndash4(c) respectively Thepixel-value profile of the image obtained with the proposedmethod and that of the image obtained with the modifiedUDWT method are shown in Figure 4(g) The pixel-valueprofile of the image obtained with the proposed method andthat of the image obtained with the STWC mapping methodare shown in Figure 4(h) It is obvious from Figure 4(g) thatthe pixel-value profile of the image processed by the proposedmethod is much more enhanced at the edges than that ofthe image processed by the modified UDWT method Itis also apparent from Figure 4(h) that the noise has beensignificantly reduced by employing the proposed method

Similarly Figure 5 illustrates an example of image pro-cessing obtained from the chest radiograph shown inFigure 2(g) Figures 5(a) 5(b) and 5(c) are resulting imagesprocessed by using the proposed method the modifiedUDWT method and the STWC mapping method respec-tively

Figure 6 shows the 119909-direction profiles of the processedimages traced from the lines indicated on the images ofFigures 5(a)ndash5(c) Figures 6(a)ndash6(c) illustrate the profiles ofthe images processed by the proposed method the modifiedUDWT method and the STWC mapping method respec-tively The 119909-direction profile of the original image tracedfrom the line indicated on the image of Figure 2(g) is alsoshown in the figures for comparison Figures 6(d)-6(f) showthe magnified views of the profiles corresponding to thepositions indicated by the dotted circles in Figures 6(a)ndash6(c) The pixel-value profile of the image obtained with theproposed method and that of the image obtained with themodified UDWT method are shown in Figure 6(g) Thepixel-value profile of the image obtained with the proposedmethod and that of the image obtained with the STWCmappingmethod are shown in Figure 6(h) It is obvious fromFigure 6(g) that the pixel-value profile of the image processedby the proposedmethod is muchmore enhanced at the edgesthan that of the image processed by the modified UDWTmethod It is also apparent from Figure 6(h) that the noisehas been significantly reduced by employing the proposedmethod

The results of scoring for the three combinations by thefive observers are listed in Tables 1 and 2 for mammogramsand chest radiographs respectively As described earlier if


(a) (b) (c) (d)

(e) (f) (g) (h)

Figure 2 Examples of images used for this study Images shown in the upper row are original images (a) and (b) are two mammograms and(c) and (d) are two chest radiographs The corresponding images are in the lower row with external added noise

(a) (b) (c)

Figure 3 Image processing results for mammograms (a) Image processed by the proposed method (b) image processed by the modifiedUDWTmethod and (c) image processed by the sigmoid-type wavelet coefficient mapping method

the left image of the paired images (two-image combination)was poorer than the right image in terms of overall imagequality it received a negative score Table 1 summarizes thevisual results for the case of mammograms As indicated bythe preference scores shown in the rightmost column of thetable the images processed by the proposed method werejudged to have the best quality Figure 7 illustrates visualevaluation results using Scheffersquos method of paired compar-isons The results are shown by a preference ranking map forthe three image groups namely the proposed method themodified UDWT method and the STWC mapping method

The figures shown on the horizontal line of the map areaverage preference degrees of the three groups The averagepreference degrees were obtained from the average maineffects by use of the data shown in Table 1 The imagesprocessed by the proposedmethod show the highest rankingfollowed by those processed by the modified UDWTmethodand those processed by the STWC mapping method A two-tailed F test was used to measure statistical significance Thedifference between the processed images of the proposedmethod and those of the modified UDWT method wasstatistically significant (119875 lt 005)The difference between the


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Figure 4 An example showing pixel-value profiles from original and processed mammograms (a)ndash(c) Original versus processed by theproposed method the modified UDWT method and the sigmoid-type wavelet coefficient mapping method respectively The profiles weremeasured along the horizontal lines (black lines) as shown in Figures 3(a)ndash3(c) (d)ndash(f) Correspondingmagnified profiles indicated by circlesas shown in (a)ndash(c) respectively (g) Profiles of two processed images the solid line indicates the profile of an image processed by themodifiedUDWTmethod and the dotted line indicates that by the proposed method (h) Profiles of two processed images the solid line indicates theprofile of an image processed by the sigmoid-type wavelet coefficient mapping method and the dotted line indicates that by the proposedmethod

processed images of the proposed method and those of theSTWCmappingmethodwas also statistically significant (119875 lt

001) However there was no significant difference betweenthe processed images of the modified UDWT method andthose of the STWCmapping method

Table 2 summarizes the visual results for the case of chestradiographs As shown in the rightmost column of the tablethe images processed by the proposedmethodwere judged to

have the best quality Figure 8 shows visual evaluation resultsusing Scheffersquos method of paired comparisons As shown inthe figure the images processed by the proposed methodshow the highest ranking followed by those processed by themodified UDWTmethod and those processed by the STWCmapping method The difference between the processedimages of the proposed method and those of the modifiedUDWT method and the difference between the processed


(a) (b) (c)

Figure 5 Image processing results for chest radiographs (a) Image processed by the proposed method (b) image processed by the modifiedUDWTmethod and (c) image processed by the sigmoid-type wavelet coefficient mapping method

Table 3 Comparison of image processing methods in terms of 4quantitative quality metrics for mammograms

Method MSR CNR CIR PSNRUDWT 580 818 028 3835Sigmoid 609 764 029 3639Proposed 624 824 067 3798

Table 4 Comparison of image processing methods in terms of 4quantitative quality metrics for chest radiographs


images of the proposed method and those of the STWCmapping method were statistically significant (119875 lt 001)However there was no significant difference between theprocessed images of the modified UDWT method and thoseof the STWCmapping method

Tables 3 and 4 summarize the quantitative evaluationresults for the proposed method and two published methodsin terms ofMSR CNR CIR and PSNRmetrics As describedin Section 24 the MSR and CNR measurements are propor-tional to the medical image quality It is obvious from thetables that bothMSR andCNRvalues of the images processedby the proposed method give the best results as comparedto those processed by the other two methods The CIR isa metric used for evaluating the contrast improvement Itis noted from the results shown in Tables 3 and 4 that theproposed method shows the greatest value followed by thesigmoid mapping and modified UDWT The reason why theproposedmethod is superior to the sigmoidmappingmethodis due to the fact that the images processed by the proposedmethod have been denoised prior to mapping operationIn the case of PSNR measurement the results listed in thetables show that the modified UDWT method was slightly

better than both the proposed method and sigmoid mappingmethod from the point of viewof denoising performanceThereason might be because some residual (unremoved) noisehas also enhanced at enhancement operation This results inthe decrease of PSNR value However the images processedby the proposed method showed the best overall imagequality in terms of both denoising and contrast enhancementwhen looking into the values of the MSR and CNR as shownin Tables 3 and 4

4 Discussion and Conclusion

In this study we proposed an algorithm which combinesthe modified UDWT method and the sigmoid-type waveletcoefficient mapping methodThe results of visual evaluationas illustrated in Figures 7 and 8 suggested that the proposedmethod was significantly superior to the two previouslyreported methods It is apparent from Figures 4(g) and4(h) and Figures 6(g) and 6(h) that the proposed methodcombines the advantages of the two methods denoising andcontrast enhancement The results of the quantitative evalu-ation also showed that the proposed method outperformedover the two other methods

By using our proposed method the computation timecan be reduced to 2 seconds (personal computer DELLOPTIPLEX 960) approximately 110 of the computing timecompared to the conventional UDWT method The reasonfor enabling reduction of processing time lies in the followingfact in the conventional UDWTmethod the decompositionand composition processes are usually conducted up toresolution level 4 That is the method needs to processa total of 12 images (3 detailed coefficients for each ofthe 4-resolution levels) for wavelet transforms and inversetransforms and it results in time consumption In contrastthe proposed method only needs to perform the process upto resolution level 2 and repeat the calculation one timeTherefore only 6 images (3 detailed components for each ofthe 2-resolution levels) were required for processing As a


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x-axis position

(h)

Figure 6 An example showing pixel-value profiles from original and processed chest radiographs (a)ndash(c) Original versus processed by theproposed method the modified UDWT method and the sigmoid-type wavelet coefficient mapping method respectively The profiles weremeasured along the horizontal lines (black lines) as shown in Figures 5(a)ndash5(c) (d)ndash(f) Correspondingmagnified profiles indicated by circlesas shown in (a)ndash(c) respectively (g) Profiles of two processed images the solid line indicates the profile of an image processed by themodifiedUDWTmethod and the dotted line indicates that by the proposed method (h) Profiles of two processed images the solid line indicates theprofile of an image processed by the sigmoid-type wavelet coefficient mapping method and the dotted line indicates that by the proposedmethod

result the computing time using the proposed method canbe much reduced

This study has several limitations First we only appliedthe proposed method to mammograms and chest radio-graphs In order to validate the versatility of the proposedalgorithm application of the proposed method to otherimages obtained from different modalities such as ultra-sound digital radiography and SPECT is needed Second thevalue shown in (3) used for determining threshold value and

that shown in (8) used for determining the gradient of thesigmoid curve were empirically selected A method for auto-mated selection is desirable Finally our dataset containedonly 30 mammograms and 20 chest radiographs A largerdataset may enable us to better evaluate the performance ofthe proposed method

In summary we proposed a method for improving imagequality inmedical images by using a wavelet-based approachThe proposed method integrated two components image


0 05 10minus05minus10

mdash

Sigmoid UDWT Proposed

lowastlowastlowastlowast

lowastlowast P lt 001

lowast P lt 005

mdash No significant difference

Figure 7 Preference ranking map for the three image groupsSTWC-mapping-method-processed modified-UDWT-processedand proposed-method-processed mammograms


mdash





Figure 8 Preference ranking map for the three image groupsSTWC-mapping-method-processed modified-UDWT-processedand proposed-method-processed chest radiographs

denoising and image enhancement In the first componenta modified undecimated discrete wavelet transform was usedto eliminate the noise In the second component a waveletcoefficient mapping function was applied to enhance thecontrast of denoised images obtained from the first compo-nentWe examined the performance of the proposedmethodby comparing it with two previously reported methodsThe results of visual assessment indicated that the imagesprocessed by the proposed UDWT method showed statis-tically significant superior image quality over the other twomethods The results of quantitative assessment also showedthat the proposed UDWT method outperformed over thetwo other methods Our research results demonstrated thesuperiority and effectiveness of the proposed method Thismethodology can be used not only as a means for improvingvisual quality of medical images but also as a preprocessingmodule for computer-aided detectiondiagnosis systems toimprove the performance of screening and detecting regionsof interest in images

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research was supported in part by a Grant-in-Aid forScientific Research (23602004) from the Japan Society forthe Promotion of Sciences (JSPS) The authors also would

like to thank the observers for their participation in visualevaluation

References

[1] A Mencattini M Salmeri R Lojacono M Frigerio and FCaselli ldquoMammographic images enhancement and denoisingfor breast cancer detection using dyadic wavelet processingrdquoIEEETransactions on Instrumentation andMeasurement vol 57no 7 pp 1422ndash1430 2008

[2] J Scharcanski and C R Jung ldquoDenoising and enhancing digitalmammographic images for visual screeningrdquo ComputerizedMedical Imaging and Graphics vol 30 no 4 pp 243ndash254 2006

[3] D-Y Tsai Y Lee and R Chiba ldquoAn improved adaptive neigh-borhood contrast enhancement method for medical imagesrdquoin Proceedings of the 3rd IASTED International Conference onMedical Engineering pp 59ndash63 BioMed February 2005

[4] B-W Yoon andW-J Song ldquoImage contrast enhancement basedon the generalized histogramrdquo Journal of Electronic Imaging vol16 no 3 Article ID 033005 2007

[5] I K Fodor and C Kamath ldquoDenoising through waveletshrinkage an empirical studyrdquo Journal of Electronic Imagingvol 12 no 1 pp 151ndash160 2003

[6] C B R Ferreira and D L Borges ldquoAnalysis of mammogramclassification using awavelet transformdecompositionrdquoPatternRecognition Letters vol 24 no 7 pp 973ndash982 2003

[7] D Cho T D Bui and G Chen ldquoImage denoising based onwavelet shrinkage using neighbor and level dependencyrdquo Inter-national Journal of Wavelets Multiresolution and InformationProcessing vol 7 no 3 pp 299ndash311 2009

[8] J E Fowler ldquoThe redundant discrete wavelet transform andadditive noiserdquo IEEE Signal Processing Letters vol 12 no 9 pp629ndash632 2005

[9] J-L Starck J Fadili and FMurtagh ldquoThe undecimated waveletdecomposition and its reconstructionrdquo IEEE Transactions onImage Processing vol 16 no 2 pp 297ndash309 2007

[10] X-Y Wang H-Y Yang and Z-K Fu ldquoA new wavelet-basedimage denoising using undecimated discrete wavelet transformand least squares support vector machinerdquo Expert Systems withApplications vol 37 no 10 pp 7040ndash7049 2010

[11] A Mencattini G Rabottino M Salmeri R Lojacono andB Sciunzi ldquoDenoising and enhancement of mammographicimages under the assumption of heteroscedastic additive noiseby an optimal subband thresholdingrdquo International Journal ofWavelets Multiresolution and Information Processing vol 8 no5 pp 713ndash741 2010

[12] P Zhao Z Shang and C Zhao ldquoImage denoising based onGaussian and non-Gaussian assumptionrdquo International Journalof Wavelets Multiresolution and Information Processing vol 10no 2 Article ID 1250014 2012

[13] Z Huang B Fang X He and L Xia ldquoImage denoising basedon the dyadicwavelet transform and improved thresholdrdquo Inter-national Journal of Wavelets Multiresolution and InformationProcessing vol 7 no 3 pp 269ndash280 2009

[14] EMatsuyama D-Y Tsai Y Lee et al ldquoAmodified undecimateddiscrete wavelet transform based approach to mammographicimage denoisingrdquo Journal of Digital Imaging vol 26 pp 748ndash758 2013

[15] W Kim J You and J Jeong ldquoContrast enhancement usinghistogram equalization based on logarithmic mappingrdquoOpticalEngineering vol 51 no 6 Article ID 067002 2012


[16] A Papadopoulos D I Fotiadis and L Costaridou ldquoImprove-ment of microcalcification cluster detection in mammographyutilizing image enhancement techniquesrdquoComputers in Biologyand Medicine vol 38 no 10 pp 1045ndash1055 2008

[17] R M Rangayyan L Shen Y Shen et al ldquoImprovement of sen-sitivity of breast cancer diagnosis with adaptive neighborhoodcontrast enhancement of mammogramsrdquo IEEE Transactions onInformation Technology in Biomedicine vol 1 no 3 pp 161ndash1701997

[18] J Jiang B Yao andAMWason ldquoIntegration of fuzzy logic andstructure tensor towards mammogram contrast enhancementrdquoComputerized Medical Imaging and Graphics vol 29 no 1 pp83ndash90 2005

[19] S Hashemi S Kiani N Noroozi and M E MoghaddamldquoAn image contrast enhancement method based on geneticalgorithmrdquo Pattern Recognition Letters vol 31 no 13 pp 1816ndash1824 2010

[20] D-Y Tsai Y Lee and R Chiba ldquoAn improved adaptive neigh-borhood contrast enhancement method for medical imagesrdquoin Proceedings of the 3rd IASTED International Conference onMedical Engineering pp 59ndash63 February 2005

[21] R N Strickland and H Hahn ldquoWavelet transforms for detect-ingmicrocalcifications inmammogramsrdquo IEEE Transactions onMedical Imaging vol 15 no 2 pp 218ndash229 1996

[22] D-Y Tsai Y Lee and S Sakaguchi ldquoA preliminary study ofwavelet-coefficient transfer curves for the edge enhancement ofmedical imagesrdquoTransactions of the Japanese Society forMedicaland Biological Engineering vol 40 no 2 pp 86ndash90 2002

[23] D-Y Tsai andY Lee ldquoAmethod ofmedical image enhancementusing wavelet-coefficient mapping functionsrdquo in Proceedings ofthe International Conference on Neural Networks and SignalProcessing (ICNNSP rsquo03) pp 1091ndash1094 December 2003

[24] P Heinlein J Drexl and W Schneider ldquoIntegrated wavelets forenhancement of microcalcifications in digital mammographyrdquoIEEE Transactions on Medical Imaging vol 22 no 3 pp 402ndash413 2003

[25] Y Lee D -Y Tsai and T Suzuki ldquoContrast enhancementof medical images using sigmoid-type transfer curves forwavelet coefficient weighting adjustmentrdquoMedical Imaging andInformation Science vol 25 no 3 pp 48ndash53 2008

[26] E Matsuyama D Y Tsai Y Lee and N Takahashi ldquoCompar-ison of a discrete wavelet transform method and a modifiedundecimated discrete wavelet transform method for denoisingof mammogramsrdquo in Proceedings of 34th Annual InternationalConference of the IEEE EMBS pp 3403ndash3406 2013

[27] Mammographic Image Analysis Society httppeipaessexacukinfomiashtml

[28] Japanese Society of Radiological Technology 2012 httpwwwjsrtorjpjsrt-dbengphp

[29] H Scheffe The Analysis of Variance John Wiley amp Sons NewYork NY USA 1959

[30] G C Canavos and J A Koutrouvelis An Introduction to theDesign amp Analysis of Experiments Pearson Prentice Hall 2008

[31] P Bao and L Zhang ldquoNoise reduction for magnetic resonanceimages via adaptive multiscale products thresholdingrdquo IEEETransactions on Medical Imaging vol 22 no 9 pp 1089ndash10992003

[32] G Cincotti G Loi and M Pappalardo ldquoFrequency decom-position and compounding of ultrasound medical images withwavelet packetsrdquo IEEE Transactions onMedical Imaging vol 20no 8 pp 764ndash771 2001

[33] Y-P Wang Q Wu K R Castleman and Z Xiong ldquoChromo-some image enhancement using multiscale differential opera-torsrdquo IEEE Transactions on Medical Imaging vol 22 no 5 pp685ndash693 2003

[34] F Luisier T Blu andMUnser ldquoA new SURE approach to imagedenoising interscale orthonormal wavelet thresholdingrdquo IEEETransactions on Image Processing vol 16 no 3 pp 593ndash6062007

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



the mapped wavelet coefficients [22 23] Lee et al useda sigmoid-type mapping function for wavelet coefficientweighting adjustment to improve the contrast of medicalimages [25] The method was applied to chest radiographsmammograms and chest CT images The method showed astatistically significant superiority over the exponential-typemapping function

In this study we expanded upon the previously suggestedmodified UDWT method [14] and combined it with thesigmoid-type mapping function [25] By combining the twomethods together in sequence an effective algorithm forboth image denoising and enhancement could be obtainedOriginal images were first denoised using the modifiedUDWT followed by image enhancement using the waveletcoefficientmapping function Finally a denoised and contrastenhanced image was reconstructed by the inverse wavelettransform In this study we investigated the effectiveness ofthe proposed method by comparing it with two methods inthe literature [14 25]

2 Methods and Materials

21 Combined Method of Undecimated Discrete WaveletTransform and Wavelet Coefficient Mapping Figure 1 showsa flowchart of our proposed method In the first phasedenoising was applied to original images using our newlyadopted UDWT In the second phase image enhancementwas performed using a sigmoid-type transfer function forwavelet coefficient mapping Sections 211 and 212 describethe two phases of the proposed method respectively

211 Extended Undecimated Discrete Wavelet TransformMethod The UDWT is a wavelet transform algorithmdesigned to overcome the lack of translation invariance ofthe DWT Unlike the DWT the UDWT does not incorporatethe downsampling operationsThus the approximation coef-ficients (low-frequency coefficients) and detailed coefficients(high-frequency coefficients) at each level are the same lengthas the original signalThe basic algorithm of the conventionalUDWT is that it applies the transform at each point ofthe image and saves the detailed coefficients and uses theapproximation coefficients for the next level The size of thecoefficients array does not diminish from level to level Thisdecomposition operation is further iterated up to a higherlevel There are major differences between the modifiedUDWT method [14] and the conventional UDWT methodFirst the conventional UDWT decomposes the originalimage (level 0) into one low-frequency band and three high-frequency bands for each resolution level with the samesize as the original image The decompositions are usuallyconducted up to resolution level 4 In contrast the modifiedUDWTmethod only needs to perform the computation up toresolution level 2 and repeat the computation only one time[14 26] Second the conventional UDWT thresholded thedetailed coefficients at all 4 levels with the same thresholdingvalue while the modified UDWTmethod utilizes the hierar-chical correlation of the coefficients between level 1 and level2 of the three detailed coefficients for thresholding In other

words the thresholding values vary and are dependent on thenature of the noise

The extended UDWT method adopted in the presentstudywas based on themodifiedUDWT [14]Themethodweused mainly consisted of the following steps (see Figure 1)

(1) Perform two-dimensional UDWT to the originalimage to obtain wavelet coefficients up to level 2

(2) Calculate the hierarchical correlations of the detailedcoefficients between level 1 and level 2 for the threesubbands The correlations for the three detailedsubbands are given as

1003816100381610038161003816Coeflev 1 (119901 119902) times Coeflev 2 (119901 119902)

1003816100381610038161003816 (1)

where 119901 and 119902 are the new coordinates after wavelettransform Coeflev 1 and Coeflev 2 are wavelet coeffi-cients of level 1 and level 2 respectively

(3) Determine threshold values for each detailed sub-band The determination procedure is as follows

(a) Generate a correlation image ImgCor(119901 119902) foreach detailed subband

ImgCor (119901 119902)

=

10038161003816100381610038161003816

Coeflev1

(119901 119902) times Coeflev2

(119901 119902)

10038161003816100381610038161003816

(2)

(b) Find themaximumvalue in each row in the hor-izontal (119909-) direction of the obtained correlationimage for each of the three detailed subbands

(c) Compute the mean of the maximum valuesobtained from all rows in the 119909-direction ofthe correlation image The mean is denoted byMeanmax

(d) Eliminate those correlation values greater than08 times Meanmax These excluded values are con-sidered signal data The value of 08 was deter-mined empirically through experiments

(e) Compute the standard deviation 120590 from theremaining correlation values

(f) Determine the threshold value by use of thefollowing formula

THR = 16 times 120590 (3)

The value of 16 was determined empiricallythrough experiments

(4) Apply the determined threshold values to the correla-tion values

New Coeflev 1 (119901 119902)

=

Coeflev 1 (119901 119902) if 1003816100381610038161003816Coeflev 1 times Coeflev 2

1003816100381610038161003816ge THR

0 otherwise(4)



Vertical

Diagonal

Level 1

Level 1 Level 2

|L1Htimes L2H|

|L1Vtimes L2V|

|L1Dtimes L2D|

wavelet transform

Originalimage

Thresholding

Thresholding

Thresholding

V detail V detail

D detail D detail


NewH detail

NewV detail

NewD detail

Sigm

oid-

type

tran

sfer f

unct

ion

for

wav

elet c

oeffi

cien

t map

ping

Finalimage

times

times

times =

=

=


Inve

rse t

wo-

dim

ensio

nal w

avele

t tra

nsfo

rm








119895


119908

119895

output (119898 119899)

= 119886 times

1

1 + 1 exp [(119908

119895

input (119898 119899) minus 119888) 119887]

times 119908

119895

input (119898 119899)

(5)

where 119908

119895



119908

119895


1

1 + [1 exp ((119908

119895

input minus 119888) 119887)]

times 119908

119895

input []

(6)




119895


119886 = 2 minus

(119895 minus 1)

119873

(7)


119888 = 119889 + 119887 times log119890(119886 minus 10) (8)










MSR =

120583119889

120590119889

(9)

where 120583119889and 120590



CNR =

10038161003816100381610038161003816

120583119889minus 120583120583

10038161003816100381610038161003816

radic05 (1205902

119889+ 1205902

120583)

(10)

where 120583120583and 120590




CIR =

sum119894sum119895

10038161003816100381610038161003816

119888 (119894 119895) minus 119888

1015840(119894 119895)

210038161003816100381610038161003816

sum119894sum119895119888(119894 119895)

2 (11)

where 119888(119894 119895) and 119888










119888 (119894 119895) =

1003816100381610038161003816119901 (119894 119895) minus 119886 (119894 119895)

1003816100381610038161003816

1003816100381610038161003816119901 (119894 119895) + 119886 (119894 119895)

1003816100381610038161003816

(12)



PSNR = 10 log10

119872 times 119873 times 119879

2

sum119894sum119895[119889 (119894 119895) minus 119889

1015840(119894 119895)]

2 (13)












(a) (b) (c) (d)

(e) (f) (g) (h)


(a) (b) (c)





50

100

150

200Pi

xel v

alue

OriginalProposed

x-axis position

(a)

UDWT

50

100

150

200

Pixe

l val

ue

Original

x-axis position

(b)

Sigmoid

50

100

150

200

Pixe

l val

ue

Original

x-axis position

(c)

135

140

145

150

155

160

165

Pixe

l val

ue

OriginalProposed

x-axis position

(d)

135

140

145

150

155

160

165Pi

xel v

alue

OriginalUDWT

x-axis position

(e)

135

140

145

150

155

160

165

Pixe

l val

ue

OriginalSigmoid

x-axis position

(f)

135

140

145

150

155

160

165

Pixe

l val

ue

UDWTProposed

x-axis position

(g)

135

140

145

150

155

160

165

Pixe

l val

ue

SigmoidProposed

x-axis position

(h)







(a) (b) (c)













2000

2500

3000

3500

4000

4500Pi

xel v

alue

OriginalProposed

x-axis position

(a)

2000

2500

3000

3500

4000

4500

Pixe

l val

ue

OriginalUDWT

x-axis position

(b)

Sigmoid

2000

2500

3000

3500

4000

4500

Pixe

l val

ue

Original

x-axis position

(c)

2200

2400

2600

2800

3000

3200

Pixe

l val

ue

OriginalProposed

x-axis position

(d)

2200

2400

2600

2800

3000

3200Pi

xel v

alue

OriginalUDWT

x-axis position

(e)

Sigmoid

2200

2400

2600

2800

3000

3200

Pixe

l val

ue

Original

x-axis position

(f)

2200

2400

2600

2800

3000

3200

Pixe

l val

ue

UDWTProposed

x-axis position

(g)

Sigmoid

2200

2400

2600

2800

3000

3200

Pixe

l val

ue

Proposed

x-axis position

(h)








mdash




lowast P lt 005




mdash









Acknowledgments



References






































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











Vertical

Diagonal

Level 1

Level 1 Level 2

|L1Htimes L2H|

|L1Vtimes L2V|

|L1Dtimes L2D|

wavelet transform

Originalimage

Thresholding

Thresholding

Thresholding

V detail V detail

D detail D detail


NewH detail

NewV detail

NewD detail

Sigm

oid-

type

tran

sfer f

unct

ion

for

wav

elet c

oeffi

cien

t map

ping

Finalimage

times

times

times =

=

=


Inve

rse t

wo-

dim

ensio

nal w

avele

t tra

nsfo

rm








119895


119908

119895

output (119898 119899)

= 119886 times

1

1 + 1 exp [(119908

119895

input (119898 119899) minus 119888) 119887]

times 119908

119895

input (119898 119899)

(5)

where 119908

119895



119908

119895


1

1 + [1 exp ((119908

119895

input minus 119888) 119887)]

times 119908

119895

input []

(6)




119895


119886 = 2 minus

(119895 minus 1)

119873

(7)


119888 = 119889 + 119887 times log119890(119886 minus 10) (8)










MSR =

120583119889

120590119889

(9)

where 120583119889and 120590



CNR =

10038161003816100381610038161003816

120583119889minus 120583120583

10038161003816100381610038161003816

radic05 (1205902

119889+ 1205902

120583)

(10)

where 120583120583and 120590




CIR =

sum119894sum119895

10038161003816100381610038161003816

119888 (119894 119895) minus 119888

1015840(119894 119895)

210038161003816100381610038161003816

sum119894sum119895119888(119894 119895)

2 (11)

where 119888(119894 119895) and 119888










119888 (119894 119895) =

1003816100381610038161003816119901 (119894 119895) minus 119886 (119894 119895)

1003816100381610038161003816

1003816100381610038161003816119901 (119894 119895) + 119886 (119894 119895)

1003816100381610038161003816

(12)



PSNR = 10 log10

119872 times 119873 times 119879

2

sum119894sum119895[119889 (119894 119895) minus 119889

1015840(119894 119895)]

2 (13)












(a) (b) (c) (d)

(e) (f) (g) (h)


(a) (b) (c)





50

100

150

200Pi

xel v

alue

OriginalProposed

x-axis position

(a)

UDWT

50

100

150

200

Pixe

l val

ue

Original

x-axis position

(b)

Sigmoid

50

100

150

200

Pixe

l val

ue

Original

x-axis position

(c)

135

140

145

150

155

160

165

Pixe

l val

ue

OriginalProposed

x-axis position

(d)

135

140

145

150

155

160

165Pi

xel v

alue

OriginalUDWT

x-axis position

(e)

135

140

145

150

155

160

165

Pixe

l val

ue

OriginalSigmoid

x-axis position

(f)

135

140

145

150

155

160

165

Pixe

l val

ue

UDWTProposed

x-axis position

(g)

135

140

145

150

155

160

165

Pixe

l val

ue

SigmoidProposed

x-axis position

(h)







(a) (b) (c)













2000

2500

3000

3500

4000

4500Pi

xel v

alue

OriginalProposed

x-axis position

(a)

2000

2500

3000

3500

4000

4500

Pixe

l val

ue

OriginalUDWT

x-axis position

(b)

Sigmoid

2000

2500

3000

3500

4000

4500

Pixe

l val

ue

Original

x-axis position

(c)

2200

2400

2600

2800

3000

3200

Pixe

l val

ue

OriginalProposed

x-axis position

(d)

2200

2400

2600

2800

3000

3200Pi

xel v

alue

OriginalUDWT

x-axis position

(e)

Sigmoid

2200

2400

2600

2800

3000

3200

Pixe

l val

ue

Original

x-axis position

(f)

2200

2400

2600

2800

3000

3200

Pixe

l val

ue

UDWTProposed

x-axis position

(g)

Sigmoid

2200

2400

2600

2800

3000

3200

Pixe

l val

ue

Proposed

x-axis position

(h)








mdash




lowast P lt 005




mdash









Acknowledgments



References






































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











119895


119886 = 2 minus

(119895 minus 1)

119873

(7)


119888 = 119889 + 119887 times log119890(119886 minus 10) (8)










MSR =

120583119889

120590119889

(9)

where 120583119889and 120590



CNR =

10038161003816100381610038161003816

120583119889minus 120583120583

10038161003816100381610038161003816

radic05 (1205902

119889+ 1205902

120583)

(10)

where 120583120583and 120590




CIR =

sum119894sum119895

10038161003816100381610038161003816

119888 (119894 119895) minus 119888

1015840(119894 119895)

210038161003816100381610038161003816

sum119894sum119895119888(119894 119895)

2 (11)

where 119888(119894 119895) and 119888










119888 (119894 119895) =

1003816100381610038161003816119901 (119894 119895) minus 119886 (119894 119895)

1003816100381610038161003816

1003816100381610038161003816119901 (119894 119895) + 119886 (119894 119895)

1003816100381610038161003816

(12)



PSNR = 10 log10

119872 times 119873 times 119879

2

sum119894sum119895[119889 (119894 119895) minus 119889

1015840(119894 119895)]

2 (13)












(a) (b) (c) (d)

(e) (f) (g) (h)


(a) (b) (c)





50

100

150

200Pi

xel v

alue

OriginalProposed

x-axis position

(a)

UDWT

50

100

150

200

Pixe

l val

ue

Original

x-axis position

(b)

Sigmoid

50

100

150

200

Pixe

l val

ue

Original

x-axis position

(c)

135

140

145

150

155

160

165

Pixe

l val

ue

OriginalProposed

x-axis position

(d)

135

140

145

150

155

160

165Pi

xel v

alue

OriginalUDWT

x-axis position

(e)

135

140

145

150

155

160

165

Pixe

l val

ue

OriginalSigmoid

x-axis position

(f)

135

140

145

150

155

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(g)

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(h)







(a) (b) (c)













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l val

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x-axis position

(h)








mdash




lowast P lt 005




mdash









Acknowledgments



References






































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation
















119888 (119894 119895) =

1003816100381610038161003816119901 (119894 119895) minus 119886 (119894 119895)

1003816100381610038161003816

1003816100381610038161003816119901 (119894 119895) + 119886 (119894 119895)

1003816100381610038161003816

(12)



PSNR = 10 log10

119872 times 119873 times 119879

2

sum119894sum119895[119889 (119894 119895) minus 119889

1015840(119894 119895)]

2 (13)












(a) (b) (c) (d)

(e) (f) (g) (h)


(a) (b) (c)





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(a) (b) (c)













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l val

ue

Proposed

x-axis position

(h)








mdash




lowast P lt 005




mdash









Acknowledgments



References






































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










(a) (b) (c) (d)

(e) (f) (g) (h)


(a) (b) (c)





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alue

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x-axis position

(e)

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l val

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x-axis position

(f)

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l val

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(g)

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(a) (b) (c)













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x-axis position

(f)

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x-axis position

(g)

Sigmoid

2200

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3000

3200

Pixe

l val

ue

Proposed

x-axis position

(h)








mdash




lowast P lt 005




mdash









Acknowledgments



References






































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










50

100

150

200Pi

xel v

alue

OriginalProposed

x-axis position

(a)

UDWT

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l val

ue

Original

x-axis position

(b)

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l val

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x-axis position

(c)

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l val

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x-axis position

(d)

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x-axis position

(e)

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l val

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x-axis position

(f)

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x-axis position

(g)

135

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l val

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x-axis position

(h)







(a) (b) (c)













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(a)

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l val

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Original

x-axis position

(c)

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OriginalProposed

x-axis position

(d)

2200

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xel v

alue

OriginalUDWT

x-axis position

(e)

Sigmoid

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l val

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Original

x-axis position

(f)

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l val

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UDWTProposed

x-axis position

(g)

Sigmoid

2200

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2800

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3200

Pixe

l val

ue

Proposed

x-axis position

(h)








mdash




lowast P lt 005




mdash









Acknowledgments



References






































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










(a) (b) (c)













2000

2500

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4500Pi

xel v

alue

OriginalProposed

x-axis position

(a)

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l val

ue

OriginalUDWT

x-axis position

(b)

Sigmoid

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l val

ue

Original

x-axis position

(c)

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OriginalProposed

x-axis position

(d)

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x-axis position

(e)

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l val

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Original

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(f)

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UDWTProposed

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(g)

Sigmoid

2200

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Pixe

l val

ue

Proposed

x-axis position

(h)








mdash




lowast P lt 005




mdash









Acknowledgments



References






































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










2000

2500

3000

3500

4000

4500Pi

xel v

alue

OriginalProposed

x-axis position

(a)

2000

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l val

ue

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x-axis position

(b)

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l val

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x-axis position

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l val

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OriginalProposed

x-axis position

(d)

2200

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xel v

alue

OriginalUDWT

x-axis position

(e)

Sigmoid

2200

2400

2600

2800

3000

3200

Pixe

l val

ue

Original

x-axis position

(f)

2200

2400

2600

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3000

3200

Pixe

l val

ue

UDWTProposed

x-axis position

(g)

Sigmoid

2200

2400

2600

2800

3000

3200

Pixe

l val

ue

Proposed

x-axis position

(h)








mdash




lowast P lt 005




mdash









Acknowledgments



References






































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











mdash




lowast P lt 005




mdash









Acknowledgments



References






































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









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