A smoothness constraint set based on local statistics

of BDCT coefficients for image postprocessing

Xiangchao Gana,*, Alan Wee-Chung Liewb, Hong Yana,c

aDepartment of Computer Engineering and Information Technology, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong, ChinabDepartment of Computer Science and Engineering, The Chinese University of Hong Kong, Shatin, Hong Kong, China

cSchool of Electrical and Information Engineering, University of Sydney, Sydney, NSW 2006, Australia

Received 11 February 2004; received in revised form 4 April 2005; accepted 5 May 2005

Abstract

In blocking artifacts reduction based on the projection onto convex sets (POCS) technique, good constraint sets are very important. Until

recently, smoothness constraint sets (SCS) are often formulated in the image domain, whereas quantization constraint set is defined in the

block-based discrete cosine transform (BDCT) domain. Thus, frequent BDCT transform is inevitable in alternative projections. In this paper,

based on signal and quantization noise statistics, we proposed a novel smoothness constraint set in the BDCT transform domain via the

Wiener filtering concept. Experiments show that POCS using this smoothness constraint set not only has good convergence but also has

better objective and subjective performance. Moreover, this set can be used as extra constraint set to improve most existing POCS-based

image postprocessing methods.

q 2005 Elsevier B.V. All rights reserved.

Keywords: Projection onto convex sets; Postprocessing methods; BDCT

1. Introduction

The block-based discrete cosine transform (BDCT) [1]

has been used widely in image and video compression. To

reduce the bit-rate, the coefficients of BDCT are often

quantized. At low bit rate, this causes annoying blocking

artifacts in the decoded image. Recently, several post-

processing methods have been proposed to alleviate

blocking artifacts. Postprocessing techniques are attractive

because they are independent of coding schemes and can be

applied to commonly used JPEG [1], H.263, and MPEG

compression standards.

The approach based on the theory of POCS has a major

advantage in that it can exploit the a priori knowledge about

the image. If the convex constraints sets associated with the

image information can be found, the POCS algorithm with

corresponding projectors will converge to the intersection of

0262-8856/$ - see front matter q 2005 Elsevier B.V. All rights reserved.

doi:10.1016/j.imavis.2005.05.001

* Corresponding author. Tel.: C852 2788 9895; fax: C852 2784 4262.

E-mail address: gan.xiangchao@student.cityu.edu.hk (X. Gan).

all the constraint sets. In the past, various constraint sets

have been proposed. Generally, these constraint sets can be

classified into two categories. One is the quantization

constraint set (QCS) [2,3], and the other is the smoothness

constraint set (SCS) [4,5]. However, most SCS are

implemented in the image domain, whereas QCS are

defined in the BDCT domain. Therefore, a BDCT transform

of the whole image is needed in each iteration. This incurs

high computational cost. Although there are some filtering

methods available that work in BDCT domain [6], they are

not POCS-based and it is difficult to incorporate new a priori

knowledge.

In this paper, we proposed a new SCS, which is

defined in the BDCT domain. The new SCS is derived

from signal and quantization noise statistics and uses

a least mean square formulation based on the Wiener

filter. Experiments show that POCS using this SCS

not only has faster convergence but also has better

objective and subjective performance. Moreover, this new

SCS can be used as a new constraint set to improve most

of the available POCS-based image postprocessing

algorithms.

Image and Vision Computing 23 (2005) 731–737

www.elsevier.com/locate/imavis

X. Gan et al. / Image and Vision Computing 23 (2005) 731–737732

2. Mathematical background

2.1. POC-based image reconstruction

In POCS-based image post-processing [7], every known

a priori property about the original image can be formulated

as a corresponding convex set in a Hilbert space H. Given n

closed convex set Ci, iZ1,2,.,n, and C0 ZhmiZ1Ci none-

mpty, the iteration

xkC1 Z PmPmK1.P1xk; k Z 0; 1; 2;. (1)

where Pi is the projector onto Ci defined by

jjx KPixjj Z ming2Ci

jjx Kgjj (2)

and g is the projection of x onto Ci, will converge to a point

in C0 for any initial x0.

2.2. The mathematical model of image deblocking problem

Throughout this paper we use the following conventions:

a real N!N image x can be treated as an N2!1 vector in the

space RN2

by lexicographic ordering by either rows or

columns. Then, the 2D DCT transform can be expressed as:

X Z Tx; and x Z TK1X (3)

where X is the BDCT coefficients of x and T is the BDCT

transform matrix.

In order to lower the bit-rate, X is quantized. Let Q

denote the quantization process. The BDCT coefficients

suffering lossy quantization can be denoted by

Y Z QTx (4)

The decoded image with blocking artifacts is given by

yZTK1QTx. If a uniform scalar quantizer is used, then Y

can be expressed as

Y Z X Cn (5)

where n is the additive zero mean noise introduced by the

quantizer and contributes to the blocking artifacts in the

encoded image. The POCS deblocking problem thus

involves the estimation of X from Y using the available

information about the quantizer and the image, formulated

as convex constraint sets.

3. Proposed postprocessing technique

It is well known that the least mean square error solution

for Eq. (5) is Wiener filtering. Specifically, the locally

adaptive Wiener filter [8], which is capable of tracking the

signal and noise characteristics over different image regions,

can be used to estimate the true BDCT coefficients by

X̂i Z �Xi Cs2

Xi

s2Xi

Cs2ni

ðYi K �XiÞ (6)

where �X is the a prior mean of X, X, �Xand Y are treated as an

N2!1 vector in the space RN2

by lexicographic ordering by

either rows or columns of their 2D versions. By defining two

matrix M and R,

R Z

1

s2n1

0 0 / 0

01

s2n2

0 / «

0 0 1 0 «

« « 0 1 0

0 / / /1

s2nN$N

26666666666664

37777777777775

M

Z

1

s2X1

0 0 / 0

01

s2X2

0 / «

0 0 1 0 «

« « 0 1 0

0 / / /1

s2XN$N

26666666666664

37777777777775

(7)

Eq. (6) can be written in the matrix form

X̂ Z �X CRðM CRÞK1ðY K �XÞ (8)

Although adaptive Wiener filtering is effective in image

deblocking, it has an apparent shortcoming. If we transform

and quantize the output image, what we obtain does not

equal to the original quantized coefficients. This violates our

information about the original image apparently. In [9], a

method combining low-pass filtering and QCS is provided

to limit the output of low-pass filter to conform to the

quantized information. However, in [10], this method is

approved to be non-convergent unless an ideal low pass

filter is used. As is well known, ideal low pass filter is

impossible to realize.

To solve this problem, we proposed a new SCS to replace

the filtering. It is derived from least mean square

formulation based on the Wiener filter and thus retains its

effectiveness in image deblocking.

In fact, Eq. (8) is the solution to the following

regularization problem [6]:

J Z ðX K �XÞtMðX K �XÞC ðY KXÞtRðY KXÞ (9)

The first term in Eq. (9) accounts for image smoothness,

whereas the second term ensures image fidelity. According

to the POCS theory, we do not need to obtain the solution

minimizing Eq. (9), which clearly depends on our estimate

of �X, M and R. Instead, we only need to find a set that

includes the original image. A reasonable choice is to limit J

with a threshhold value Ea, that is jJj%Ea, where Ea is a

value larger than but close enough to the minimum of J so

that all the images satisfying the condition are smooth and

X. Gan et al. / Image and Vision Computing 23 (2005) 731–737 733

faithful to the original image. Unfortunately, jJj%Ea is not

convex. Instead, we approximate it by imposing constraints

on each term in (9),

Cw Z fX : ðX K �XÞtMðX K �XÞ%Ewg (10)

Cr Z fX : ðX KYÞtRðX KYÞ%Erg (11)

3.1. The constraint set Cw

For a 512!512 image and 8!8 blocks, X is a

512$512!1 vector. M is a (512$512)!(512$512) diagonal

matrix. If we define a new (512$512)!(512$512) diagonal

matrix W with elements

ui Z m1=2i ; i Z 1; 2;.; 512!512 (12)

then Eq. (10) can be rewritten as

Cw Z fX : jjWðX K �XÞjj%Ewg (13)

It is straightforward to show that CW is both convex and

closed. Before describing how ui and �X are obtained, we

examine the projection of Cw in detail. Using the Lagrange

multiplier method, we can obtain the projection

X̂i ZXi Clw2

i�Xi

1 Clw2i

(14)

where l is the only positive root of the equation

X512!512

iZ1

w2i ðXi K �XiÞ

2

1 Clw2i

Z E2w (15)

The parameter l can be computed as follows [4]. Let

jðlÞ ZX512!512

iZ1

w2i ðXi K �XiÞ

2

1 Clw2i

KE2w (16)

be such that j(0)O0. Then, with l0Z0 the iterates

generated by Newton’s method

lkC1 Z lk KjðlÞ

j0ðlÞk Z 0; 1; 2;. (17)

will converge increasingly to lC, the unique positive root of

j(l)Z0. In other words, we have lk!lkC1!lC for every

k.

3.2. The computation of �X, W and Ew

Both the mean and variance of Xi can be estimated from

Yi. Since ni is assumed zero mean and uncorrelated with X,

we can deduce the following from Eq. (5)

�X Z �Y (18)

s2Xi

Z s2Yi

Ks2ni

(19)

By assuming a uniform scalar quantizer, the quantization

error ni has a uniform pdf with s2ni

Z ð1=12Þq2i , where qi is the

known stepsize of the corresponding quantizer applied to Xi.

Taking advantage of the local image smoothness, we can

use the ‘local’ mean and variance of Y as approximation in

practical implementation [6]. Let y!m,nO denote y that is

shifted in the image domain by (m,n) and Ty!m,nOZY!

m,nO,then

�Yi Z1

ð2L C1Þ2

XL

mZKL

XL

nZKL

Y!m;nOi (20)

s2Yi

Z1

ð2L C1Þ2

XL

mZKL

XL

nZKL

ðY KY!m;nOi Þ2 (21)

where L is the window size. Since s2Xi

R0, s2Xi

is determined

as maxf0;s2Yi

Ks2nig.

Now that �X and s2Xi

are available, we get W according to

Eqs. (7) and (12) as follows,

wi Z1

sXi

(22)

To avoid mathematical difficulties associated with

sXiZ0, a reasonable compressed form of this function is

given by [11,12]

wi Z ln 1 C1

1 CsXi

� (23)

To implement the projector of (14), Ew is also an

important parameter. Since �X is unknown and we get it from�XZ �Y , based on Eqs. (10) and (18), Ew is actually a

threshold value of Mahalanobis distance between the

original image and local mean of the blocky image. It is

obvious that the bigger the quantization stepsize, the larger

the distance. So we calculate Ew using the quantization error

variance as,

S Z1

64

X64

iZ1

s2ni

Z1

64

X64

iZ1

q2i

12(24)

Ew Z kffiffis

p(25)

where k is a weighting scale. We find that kZ0.5 is a good

choice in many cases and used it in all our simulation

experiments.

3.3. The constraint set Cr and the image recovery algorithm

Since ni is assumed zero mean, we obtain EfðXi KYiÞ2gZ

s2ni

based on Eq. (5). Then (YKX)tR(YKX) can be viewed as

the Mahalanobis distance between the recovered image and

the blocky image in statistical theory. So the constraint set

Cr guarantees the fidelity of the recovered image. In the

POCS theory, this is realized by the QCS. Hence, Cr is

X. Gan et al. / Image and Vision Computing 23 (2005) 731–737734

replaced by QCS as follows:

CQ Z fx : F0i KDi% ðTxÞi%F0

i CDig; i Z 1; 2;.N2

(26)

where Di is half of the corresponding quantization table

coefficient. The projector for QCS is

X̂i Z

F0i KDi if ðTxÞi!F0

i KDi

F0i CDi if ðTxÞi!F0

i KDi

ðTxÞi otherwise

8>><>>: (27)

Besides the sets defined previously, another set Cp is also

used to capture the information about the range of the pixel

intensity of the image. This set is defined by

Cp Z fx : 0%xi;j%255; 1% i; j%Ng (28)

Using all the convex sets defined above, the POCS theory

yields the following recovery algorithm:

1. Set x0Zy

2. For kZ1,2,., compute xk from

xk Z PQPwPpxkK1

where PQ, Pw, Pp denote the projectors onto the

constraint sets CQ, Cw, Cp, respectively.

3. If xkZxkK1, exit the iteration, else go to step 2.

It should be pointed out that we require PQPwPpxkZxkK

1 to be satisfied, not just kfkKfkK1k%d as in [4], as the

converge measure. It is a stricter measure.

(a) (b)

4. Spatially-adaptive algorithm based on human

visual system

By far, our constraint set is only based on least square

error measure, without considering the visual characteristic.

In order to improve the visual quality of this method, we

modified Eqs. (20) and (21) to incorporate the property of

human visual system (HVS) [13]. Due to the masking effect

in the HVS, artifacts are more visible in smooth areas than

in non-regular areas. In order to account for the masking

effect, a block based classification method is necessary.

Since our algorithm is implemented entirely in the BDCT

domain, we require that the classification method be

realized in the BDCT domain. Fortunately, the method in

[14] can be adopted.

Fig. 1. Block classification using HVS: (a) JPEG-coded image (0.24bpp).

(b) The result of block classification.

4.1. Block-region classification based on HVS

In [15], Ngan et al. proposed an HVS sensitivity function

to measure the relative sensitivity of the eyes at different

frequencies as follows:

HðuÞ Z jAðuÞjHðuÞ (29)

In this equation, the modulation transfer function (MTF)

H(u) is given by

HðuÞ Z ð0:31 C0:69uÞexpðK0:29uÞ (30)

It has a peak at uZ3 cycles per degree (cpd), and the

multiplicative function A(u) is defined as

AðuÞ Z1

4C

1

p2ln

2pu

sC

ffiffiffiffiffiffiffiffiffiffiffiffiffiffi4p2u2

s2

r !" #2( )1=2

(31)

where sZ11.636 degreeK1.

We can relate the DCT coefficients to the radial

frequency u to improve the computation efficiency. In

[16], the conversion was proposed

u Z ud !us (32)

where ud Zffiffiffiffiffiffiffiffiffiffiffiffiffiffiu2Cv2

p=2N for u,vZ0,.NK1 and Ws in

pixels/degree is the sampling density which is dependent on

the viewing distance. For 512!512 images, WsZ64 pixels/

degree is suggested in [16].

Now, we used the HVS sensitivity function to weight the

ac BDCT coefficients to approximate the amount of

masking effect as follows,

~Bm;nðu; vÞ Z HK1ðwÞBðu; vÞ (33)

In BDCT domain, the smoothness of a block can be

estimated from its ac energy. We define the smoothness of a

block bm,n(i,j) as

Am;n Z1

Bm;nð0; 0Þ

XNK1

uZ0

XNK1

vZ0

~Bm;nðu; vÞ2 K ~Bm;nð0; 0Þ

2

" #(34)

With the assistance of Am,n, blocks in the image can be

classified into either smooth or non-regular class, where

different classes of blocks are processed in different ways.

Fig. 1(b) shows the block classification result for ‘Lena’.

4.2. Adaptive windows

The postprocessing can be made adaptive to the block

smoothness. In our algorithm, this can be easily

implemented by using different window size for Eqs. (20)

and (21). For a smooth block, where the blocking artifacts

appear to be visually more discernable, a 7!7 window (i.e.

Table 1

Objective quality evaluation of the image reconstructed with various algorithms

Test Image PSNR(dB)

JPEG Rosenholtz [9] Yang [4] Paek [5] Kim [17] Proposed (no HVS) Proposed (with HVS)

Bridge 29.805 29.308 30.484 30.568 30.621 31.024 30.998

Peppers 30.672 30.244 31.187 31.363 31.412 31.523 31.587

Goldhill 28.883 28.523 29.296 29.280 29.353 29.537 29.522

Lena 30.700 30.130 31.310 31.472 31.552 31.662 31.705

Man 28.435 28.056 28.884 28.916 28.922 29.173 29.145

Tank 27.998 27.891 28.366 28.334 28.406 28.618 28.608

Zelda 31.142 31.869 32.850 33.119 33.102 33.246 33.415

Boat 29.171 28.464 29.676 29.667 29.685 29.861 29.817

X. Gan et al. / Image and Vision Computing 23 (2005) 731–737 735

LZ3) is used. On the other hand, for non-regular blocks, we

use a 3!3 window (i.e. LZ1). A small window for non-

regular blocks is to avoid blurring image details.

5. Perfoemance evaluation

We present some experimental results to evaluate the

performance of the proposed recovery algorithm. A number

of de facto standard 256 gray-level test images of size 512!512 are used. The decoded images, with visible blocking

artifacts are obtained by JPEG compression with the

quantization tables shown in Appendix.

Fig. 2. Deblocking results of the ‘Lena’ image. (a) Original image, (b) JPEG-cod

Paek’s algorithm, (f) Kim’s algorithm and (g) Proposed algorithm.

For comparative studies, several popular deblocking

algorithms reported in the literature, namely, (a) Rosen-

holtz’s algorithm [9], (b) Yang’s algorithm [4], (c) Paek’s

algorithm [5] and (d) Kim’s algorithm [17] are implemented

and compared. As a measure of reconstructed image quality,

the peak signal-to-noise ratio (PSNR) in dB is used, defined

as follows:

PSNR Z 10!log10 2552

� XMs

iZ1

ðxi KyiÞ2

�Ms

( )" #(35)

where xi and yi denote the original and reconstructed pixels,

respectively, and Ms is the number of pixels in a coded

ed image (0.24bpp), (c) Rosenholtz’s algorithm, (d) Yang’s algorihm, (e)

Fig. 3. Deblocking results of the ‘Peppers’ image. (a) Paek’s algorithm and

(b) Proposed algorithm.

0 5 10 1530.6

30.8

31

31.2

31.4

31.6

31.8

Fig. 5. PSNR performance variations on ‘Lena’ image (0.24bpp). Dashed

line: Yang’s algorithm. Dotted line: Paek’s algorithm. Dashdot line: Kim’s

algorithm. Solid line: the proposed algorithm.

X. Gan et al. / Image and Vision Computing 23 (2005) 731–737736

image. The objective results based on PSNR are shown in

Table 1. The proposed SCS without considering HVS model

is also provide. Since Rosenholtz’s algorithm is non-

convergent, we only list results of the four methods after

10 iterations. It can be seen from Table 1 that the proposed

method is superior in objective quality measure.

In Fig. 2, an enlarged portion of ‘Lena’ is shown for

subjective comparison. It can be seen that Rosenholtz’s

algorithm generally produces a blurred image due to the low-

pass filtering operation and Yang’s algorithm still contain

significant blockiness in smooth region. Around the shoulder

region, our method is considerably freer from artifacts. Since

Paek’s algorithm is a very typical deblocking algorithm and

usually gives good visual effect, we also compare it with our

method using ‘Peppers’ and ‘Zelda’ in Figs. 3 and 4. It is

obvious that the proposed algorithm can provide better

visual performance especially in smooth areas.

We also tested the convergence characteristic of our

algorithm. The PSNR variation with the iteration number is

provided using ‘Lena’ image in Fig. 5. It is observed that the

proposed method converges with 2 iterations. Note that the

condition of convergence is xkZxkK1. Under this measure,

Paek’s, Yang’s and Kim’s algorithms all need a few

iterations. In our experiment, all images listed in Table 1

only need 2–3 iterations to converge.

Another major advantage of the proposed algorithm is

that it operates solely in the transform domain, unlike the

POCS-based algorithms we compared, which alternate

between the image domain and the transform domain. So,

it has much lower computation cost. This is particularly

important for real-time video processing.

Fig. 4. Deblocking results of the ‘Zelda’ image. (a) Paek’s algorithm and (b)

Proposed algorithm.

The new SCS can also be used as a new constraint set to

improve most of the available POCS-based deblocking

methods. Fig. 6 has shown the improvement of our SCS on

Rosenholtz’s algorithm. The initial image Lena is coded at

0.24 b/pixel with the above quantization table. For Yang’s

and Paek’s algorithm, the PSNR improvements are 0.324

and 0.102 dB, respectively. This is almost impossible for

BDCT domain filtering algorithm [6].

6. Conclusions

In this paper, a POCS-based deblocking algorithm

utilizing a new smoothness constraint set is proposed. The

new smoothness constraint set is constructed based on

the local statistics of the BDCT transform coefficients and

the probability density function (pdf) of the quantizer.

The proposed method has been shown to give superior

performance in comparison to several well-known POCS-

based deblocking algorithms. Since no BDCT transform is

needed in each POCS iteration, it has a low computational

Fig. 6. Improvement of Rosenholtz’s algorithm with the addition of the new

SCS. Dotted line: Rosenholtz’s algorithm. Solid line: adding the new SCS.

X. Gan et al. / Image and Vision Computing 23 (2005) 731–737 737

cost. Moreover, the new SCS can also be used as an

additional smoothness constraint set to improve most

existing POCS-based deblocking algorithms.

Acknowledgements

This work is supported by a strategic research grant from

City University of Hong Kong (Project 7001556).

Appendix. Quantizatin Table for BDCT

50 60 70 70 90 120 255 255

60 60 70 96 130 255 255 255

70 70 80 120 200 255 255 255

70 96 120 145 255 255 255 255

90 130 200 255 255 255 255 255

120 255 255 255 255 255 255 255

255 255 255 255 255 255 255 255

255 255 255 255 255 255 255 255

References

[1] W.B. Pennebaker, J.L. Mitchell, JPEG Still Image Data Compression

Standard, Van Nostrand Reinhold, New York, 1993.

[2] S.H. Park, D.S. Kim, Theory of projection onto the narrow

quantization constraint set and its application, IEEE Trans. Image

Processing 8 (10) (1999) 1361–1373.

[3] Y. Jeong, I. Kim, H. Kang, A practical projection-based postproces-

sing of block-coded images with fast convergence rate, IEEE Trans.

Circuits Syst. Video Technol. 10 (2000) 617–623.

[4] Y. Yang, N.P. Galatsanos, A.K. Katsaggelos, Regularized reconstruc-

tion to reduce blocking artifacts of block discrete cosine transform

compressed images, IEEE Trans. Circuits Syst. Video Technol. 3

(1993) 421–432.

[5] H. Paek, R.C. Kim, S.U. Lee, On the POCS-based postprocessing

techniques to reduce the blocking artifacts in transform coded images,

IEEE Trans. Circuits Syst. Video Technol. 8 (1998) 358–367.

[6] S.S.O. Choy, Y.H. Chan, W.C. Siu, Reduction of block-transform

image coding artifacts by using local statistics of transform

coefficients, IEEE Signal. Processing Lett. 4 (1) (1997) 5–7.

[7] H. Stark, Y. Yang, Vector Space Projections, A Numerical Approach

to Signal and Image Processing, Neural Nets, and Optics, Wiley, New

York, 1998.

[8] J.S. Lim, Two-Dimensional Signal and Image Processing, Prentice

Hall, New Jersey, 1990. pp. 536–540.

[9] R. Rosenholtz, A. Zakhor, Iterative procedures for reduction of

blocking effects in transform image coding, IEEE Trans. Circuits Syst.

Video Technol. 2 (1) (1992) 91–95.

[10] S.J. Reeves, S.L. Eddins, Comments on iterative procedures for

reduction of blocking effects in transform image coding, IEEE Trans.

Circuits Syst. Video Technol. 3 (1993) 439–440.

[11] Y. Yang, N.P. Galatsanos, A.K. Katsaggelos, Projection-based

spatially adaptive reconstruction of block-transform compressed

images, IEEE Trans. Image Processing 4 (7) (1995) 896–908.

[12] R.L. Lagendijk, J. Biemond, D.E. Boekee, Regularized iterative

restoration with ringing reduction, IEEE Trans. Acoust. Speech Signal

Processing 36 (12) (1988) 1874–1888.

[13] N. Jayant, J. Johnston, R. Safranek, Signal compression based on

models of human perception, Proc. IEEE 81 (1993) 1385–1422.

[14] T. Chen, H.R. Wu, B. Qiu, Adaptive postfiltering of transform

coefficients for the reduction of blocking artifacts, IEEE Trans.

Circuits Syst. Video Technol. 10 (2000) 617–623.

[15] K.N. Ngan, K.S. Leong, H. Singh, Adaptive cosine transform coding

of images in perceptual domain, IEEE Trans. Acoust. Speech Signal

Processing 37 (1989) 1743–1750.

[16] B. Chitprasert, K.R. Rao, Human visual weighted progressive image

transmission, IEEE Trans. Commun. 38 (1990) 1040–1044.

[17] Y. Kim, C.S. Paek, S.J. Ko, Frequency domain post-processing

technique based on POCS, Electronics Lett 39 (22) (2003) 1583–1584.

Xiangchao Gan received his MS in Electrical

and Electronic Engineering from Xi’an Jiao-

tong University, China, in 2001. He is

currently studying for his PhD degrees at

City University of HongKong. His research

interests include image reconstruction, image

compression and multimedia communication.

Alan Wee-Chung Liew received his BE with

first class honors in Electrical and Electronic

Engineering from the University of Auckland,

New Zealand, in 1993 and PhD in Electronic

Engineering from the University of Tasmania,

Australia, in 1997. He is currently an Assistant

Professor in the Department of Computer

Science and Engineering, The Chinese Uni-

versity of Hong Kong. His current research

interests include computer vision, medical

imaging, pattern recognition and bioinfor-

matics. He has served as a technical reviewer for a number of international

conferences and journals in IEEE Transactions, IEE proceedings,

bioinformatics and computational biology. Dr Liew is a member of the

Institute of Electrical and Electronic Engineers (IEEE), and his biography is

listed in the 2005 Marquis Who’s Who in the World and Marquis Who’s

Who in Science and Engineering.

Hong Yan received a BE degree from Nanking

Institute of Posts and Telecommunications,

Nanking, China, in 1982, an MSE degree from

the University of Michigan in 1984, and a PhD

degree from Yale University in 1989, all in

electrical engineering. In 1982 and 1983 he

worked on signal detection and estimation as a

graduate student and research assistant at

Tsinghua University, Beijing, China. From

1986 to 1989 he was a research scientist at

General Network Corporation, New Haven,

CT, USA, where he worked on design and optimization of computer and

telecommunications networks. He joined the University of Sydney in 1989

and became Professor of Imaging Science in 1997. He is currently Professor

of Computer Engineering at City University of Hong Kong. His research

interests include image processing, pattern recognition and bioinformatics.

He is author or co-author of one book and over 200-refereed technical

papers in these areas. Professor Yan is a fellow of the International

Association for Pattern Recognition (IAPR), a fellow of the Institution of

Engineers, Australia (IEAust), a senior member of the Institute of Electrical

and Electronic Engineers (IEEE) and a member of the International Society

for Computational Biology (ISCB).