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Hindawi Publishing Corporati<strong>on</strong>EURASIP Journal <strong>on</strong> Applied Signal ProcessingVolume 2006, Article ID 69042, Pages 1–11DOI 10.1155/ASP/2006/69042<str<strong>on</strong>g>Facial</str<strong>on</strong>g> <str<strong>on</strong>g>Image</str<strong>on</strong>g> <str<strong>on</strong>g>Compressi<strong>on</strong></str<strong>on</strong>g> <str<strong>on</strong>g>Based</str<strong>on</strong>g> <strong>on</strong> <strong>Structured</strong><strong>Codebooks</strong> in Overcomplete DomainJ. E. Vila-Forcén, S. Voloshynovskiy, O. Koval, and T. PunStochastic <str<strong>on</strong>g>Image</str<strong>on</strong>g> Processing Group, CUI, University of Geneva, 24 rue du Général-Dufour, Geneva 1211, SwitzerlandReceived 31 July 2004; Revised 16 June 2005; Accepted 27 June 2005We advocate facial image compressi<strong>on</strong> technique in the scope of distributed source coding framework. The novelty of the proposedapproach is twofold: image compressi<strong>on</strong> is c<strong>on</strong>sidered from the positi<strong>on</strong> of source coding with side informati<strong>on</strong> and, c<strong>on</strong>trarilyto the existing scenarios where the side informati<strong>on</strong> is given explicitly; the side informati<strong>on</strong> is created based <strong>on</strong> a deterministicapproximati<strong>on</strong> of the local image features. We c<strong>on</strong>sider an image in the overcomplete transform domain as a realizati<strong>on</strong> of arandom source with a structured codebook of symbols where each symbol represents a particular edge shape. Due to the partialavailability of the side informati<strong>on</strong> at both encoder and decoder, we treat our problem as a modificati<strong>on</strong> of the Berger-Flynn-Grayproblem and investigate a possible gain over the soluti<strong>on</strong>s when side informati<strong>on</strong> is either unavailable or available at the decoder.Finally, the paper presents a practical image compressi<strong>on</strong> algorithm for facial images based <strong>on</strong> our c<strong>on</strong>cept that dem<strong>on</strong>strates thesuperior performance in the very-low-bit-rate regime.Copyright © 2006 Hindawi Publishing Corporati<strong>on</strong>. All rights reserved.1. INTRODUCTIONThe urgent demand of efficient image representati<strong>on</strong> is recognizedby the industry and research community. Its necessityis highly increased due to the novel requirements of manyauthenticati<strong>on</strong> documents such as passports, ID cards, andvisas as well as recent extended functi<strong>on</strong>alities of wirelesscommunicati<strong>on</strong> devices. The document, ticket, or even entrypass pers<strong>on</strong>alizati<strong>on</strong> are often requested in many authenticati<strong>on</strong>or identificati<strong>on</strong> protocols. In most cases, classicalcompressi<strong>on</strong> techniques developed for generic applicati<strong>on</strong>sare not suitable for these purposes.Wavelet-based [1, 2] lossy image compressi<strong>on</strong> techniques[3–6] have proved to be the most efficient from the ratedistorti<strong>on</strong>point of view for the rate range of 0.2–1 bits perpixel (bpp). The superior performance of this class of algorithmsis justified by both decorrelati<strong>on</strong> and energy compacti<strong>on</strong>properties of the wavelet transform and by the efficientadaptive both interband (zero trees [5]) and intraband(estimati<strong>on</strong> quantizati<strong>on</strong> (EQ) [7, 8]) models that describethe data in the wavelet subbands. Recent results in waveletbasedimage compressi<strong>on</strong> show that some modest performanceimprovement (in terms of peak signal-to-noise ratio(PSNR) up to 0.3 dB) could be achieved either taking intoaccount the n<strong>on</strong>orthog<strong>on</strong>ality of the transform [9] or usingmore complex higher-order c<strong>on</strong>text models of wavelet coefficients[10].During years, a standard benchmark database of imagesfor wavelet-based compressi<strong>on</strong> algorithm evaluati<strong>on</strong>was used. It includes several 512 × 512 grayscale test images(like Lena, Barbara, Goldhill) and the verificati<strong>on</strong> was performedfor the rates 0.2–1 bpp. In some applicati<strong>on</strong>s, whichinclude pers<strong>on</strong> authenticati<strong>on</strong> data like photo images or fingerprintimages, the operati<strong>on</strong>al c<strong>on</strong>diti<strong>on</strong>s might be different.In this case, especially for str<strong>on</strong>g compressi<strong>on</strong> (below0.15 bpp), the resulting image quality of the state-of-the-artalgorithms is not satisfactory enough (Figure 1). Therefore,for this kind of applicati<strong>on</strong>s more advanced techniques areneeded to satisfy the fidelity c<strong>on</strong>strains.In this paper, we address the problem of classical waveletbasedimage compressi<strong>on</strong> enhancement by using side informati<strong>on</strong>within a framework of distributed coding of correlatedsources. Recently, it was practically shown that it ispossible to achieve a significant performance gain when theside informati<strong>on</strong> is available at the decoder, while the encoderhas no access to the side informati<strong>on</strong> [11]. Using the side informati<strong>on</strong>from an auxiliary analog additive white Gaussiannoise (AWGN) channel in the form of a noisy copy of theinput image at the decoder, it was reported a PSNR enhancementin the range of 1–2 dB depending <strong>on</strong> the test imageand the compressi<strong>on</strong> rate. It could be noted that the performanceof this scheme str<strong>on</strong>gly depends <strong>on</strong> the state of theauxiliary channel, which should be known in advance at theencoding stage. Moreover, it is assumed that the noisy copy
2 EURASIP Journal <strong>on</strong> Applied Signal ProcessingXEncoderi ∈{1, 2,...,2 NRX }Decoder̂XFigure 3: Lossy source coding system without side informati<strong>on</strong>.(a) (b) (c)Figure 1: (a) 256 × 256 8-bit test image Slava. Results of compressi<strong>on</strong>with rate 0.071 bits per pixel (bpp) using (b) JPEG2000 standardsoftware (PSNR is 25.09 dB) and (c) state-of-the-art EQ coder(PSNR is 26.36 dB).{X, Y}p{x, y}XYEncoder XEncoder YNR XNR YFigure 2: Slepian-Wolf coding.Jointdecoderof the original image should be directly available at the decoder.This situati<strong>on</strong> is typical for the distributed coding inthe remote sensing applicati<strong>on</strong>s or can be simulated as inthe case of analog and digital televisi<strong>on</strong> simulcast [11]. Inthe case of single-source compressi<strong>on</strong>, the side informati<strong>on</strong>is not directly available at the decoder.The main goal of this paper c<strong>on</strong>sists in the developmentof a c<strong>on</strong>cept of single-source compressi<strong>on</strong> within adistributed coding framework using virtually created side informati<strong>on</strong>.This c<strong>on</strong>cept is based <strong>on</strong> the accurate approximati<strong>on</strong>of a source data using a structured codebook, whichis shared by the encoder and decoder, and the communicati<strong>on</strong>of the residual approximati<strong>on</strong> term within the classicalwavelet-based compressi<strong>on</strong> paradigm.The paper is organized as follows. In Secti<strong>on</strong> 2, fundamentalsof source coding with side informati<strong>on</strong> are presented.In Secti<strong>on</strong> 3, an approach for single-source distributedlossy coding is introduced. A practical algorithm fora very-low-bit-rate compressi<strong>on</strong> of passport photo images isdeveloped in Secti<strong>on</strong> 4. Secti<strong>on</strong> 5 c<strong>on</strong>tains the experimentalresults and Secti<strong>on</strong> 6 c<strong>on</strong>cludes the paper.Notati<strong>on</strong> 1. Scalar random variables are denoted by capitalletters X, bold capital letters X denote vector random variables,letters x and x are reserved to denote the realizati<strong>on</strong> of scalarand vector random variables, respectively. The superscript N isused to denote N-length vectors x N = x = {x 1 , x 2 , ..., x N },where the ith element is denoted as x i . X ∼ p X (x) or X ∼ p(x)indicates that a random variable X is distributed according top X (x). The mathematical expectati<strong>on</strong> of a random variableX ∼ p X (x) is denoted by E pX [X] or E[X]. H(X), H(X, Y),H(X | Y) denotetheentropyoftherandomvariableX, thejoint entropy of the random variables X and Y,andthec<strong>on</strong>diti<strong>on</strong>alentropy of the random variable X given Y, respectively.By I(X; Y) and I(X; Y | Z),wedenotethemutualinformati<strong>on</strong>between the random variables X and Y, and the c<strong>on</strong>diti<strong>on</strong>almutual informati<strong>on</strong> between the random variables X and Ygiven the random variable Z,respectively.R X denotes the rate ofcommunicati<strong>on</strong>s for the random variable X. Calligraphic f<strong>on</strong>tX is used to indicate sets X ∈ X, and|X| indicates the cardinalityof a set. R + is used to represent the set of positive realnumbers.2. DISTRIBUTED CODING OF CORRELATED SOURCES2.1. Slepian-Wolf encodingAssume that it is necessary to encode two discrete-alphabetpair wisely independent and identically distributed (i.i.d.)random variables X and Y with joint distributi<strong>on</strong> p XY (x, y) =∏ Nk=1p XkY k(x k , y k ). A Slepian-Wolf [12, 13] codeallowsperforminglossless encoding of X and Y individually using twoseparate encoders, and the decoding is performed jointly aspresented in Figure 2. Using a random binning argument, itwas shown that the efficiency of such a code is the same as inthe case when joint encoding is used. It means that the encoderbit rates pair (R X , R Y ) is achievable when the followingrelati<strong>on</strong>ships hold:R X ≥ H(X | Y),R Y ≥ H(Y | X),R X + R Y ≥ H(X, Y).2.2. Lossy compressi<strong>on</strong> with side informati<strong>on</strong>In the lossy compressi<strong>on</strong> setup, it is necessary to achieve theminimal possible distorti<strong>on</strong>s for a given target coding rate.Depending <strong>on</strong> the availability of side informati<strong>on</strong>, severalpossible scenarios exist [14].No side informati<strong>on</strong> is availableImagine that it is needed to represent an i.i.d. source sequenceX ∼ p X (x), X ∈ X N using the encoding mappingf E : X N →{1, 2, ...,2 NRX } and the decoding mapping f D :{1, 2, ...,2 NRX }→X N with the minimum average bit rate Rbits per element. The fidelity of representati<strong>on</strong> is evaluatedusing the average distorti<strong>on</strong> D = (1/N) ∑ Nk=1 E[d(x k , ̂x k )],where the distorti<strong>on</strong> measure d(x, ̂x) is determined in generalas a mapping X N × ̂X N → R + . Due to Shann<strong>on</strong> [12, 15], itis well known that the optimal performance of such a compressi<strong>on</strong>system (Figure 3) (the minimal achievable rate forcertain distorti<strong>on</strong> level) is determined by the rate-distorti<strong>on</strong>functi<strong>on</strong>,R X (D) =(1)min I( X; ̂X ) . (2)p(̂x|x): ∑̂x,x p(̂x|x)d(̂x,x)≤D
J. E. Vila-Forcén et al. 3{X, Y}XEncoder XNR XXEncoder XNR X{X, Y}JointJointlem, that is, R X (0) WZX|Y = H(X | Y). rate regime.p{x, y}decoderp{x, y}decoderYYFigure 4: Wyner-Ziv coding.Side informati<strong>on</strong> is available <strong>on</strong>ly at the encoderIn this case, the performance limits coincide with the previouscase and the rate-distorti<strong>on</strong> functi<strong>on</strong> could be determinedusing (2)[16].Figure 5: Berger-Flynn-Gray coding.Lossy compressi<strong>on</strong> of correlated sources(Berger-Flynn-Gray coding)This problem was investigated by Berger [18] and Flynn andGray [19], and the general scheme is presented in Figure 5.As in the previous case, Berger-Flynn-Gray coding refersSide informati<strong>on</strong> is available <strong>on</strong>ly at the decoderto the sequence of pairs {X, Y} ∼p(x, y), (X, Y) ∈ X N ×Y N ,(Wyner-Ziv coding)where now Y is available at both encoder and decoder, whilein the Wyner-Ziv problem it was available <strong>on</strong>ly at the decoder.Fundamental performance limits of source coding systemswith side informati<strong>on</strong> available <strong>on</strong>ly at the decoder (Figure 4)were established by Wyner and Ziv [12, 17]. The Wyner-Zivproblem could be formulated in the following way: given theIt is necessary to c<strong>on</strong>struct an R X -bits-per-elementjoint coder f E : X N × Y N →{1, 2, ...,2 NRX } and a joint decoderf D : {1, 2, ...,2 NRX }×Y N → ̂X N such that the averagedistorti<strong>on</strong> satisfies E[d(X, f D (Y, f E (X, Y)))] ≤ D. In thisside informati<strong>on</strong> <strong>on</strong>ly at the decoder, what will be the minimumrate R X necessary to rec<strong>on</strong>struct the source X with avti<strong>on</strong>alrate-distorti<strong>on</strong> functi<strong>on</strong>,case, the performance limits are determined by the c<strong>on</strong>dieragedistorti<strong>on</strong> less than or equal to a given distorti<strong>on</strong> valueD? By other words, assume that we have a sequence of independentdrawings of pairs {X k , Y k } of dependent randomR X (D) BFGX|Y = min ̂X; X | Y ) ,p(̂x|x,y)(6)variables, {X, Y} ∼p(x, y), (X, Y) ∈ X N × Y N .Ourgoalis to c<strong>on</strong>struct an R X -bits-per-element encoder f E : X N →{1, 2, ...,2 NRX } and joint decoder f D : {1, 2, ...,2where the minimizati<strong>on</strong> is performed over all p(̂x | x, y)subjectto the fidelity c<strong>on</strong>straint (3). The Berger-Flynn-Gray rateNRX }×Y N → ̂X N such that the average distorti<strong>on</strong> satisfies the fidelityc<strong>on</strong>straint:in (6) is, in general, smaller than the Wyner-Ziv rate (5) sincethe availability of the correlated source Y at both encoder andE [ d ( (X, f D Y, fE (X) ))] = ∑ p(x, y)p (̂x | x, y ) ≤ D.x,̂x(3)decoder makes possible to reduce the ambiguity about X.Comparing the rate-distorti<strong>on</strong> performance of differentcoding scenarios with the side informati<strong>on</strong>, it should beUsing the asymptotic properties of random codes, it wasnoted that, in general, the following inequalities hold [20]:shown [17] that the set of achievable rate-distorti<strong>on</strong> pairs ofsuch a coding system will be bounded by the Wyner-Ziv ratedistorti<strong>on</strong>R X (D) ≥ R X (D) WZX|Y ≥ R X(D) BFGX|Y . (7)functi<strong>on</strong>:R X (D) WZX|Y = min [ ( ] The last inequality becomes equality, that is, R X (D) WZX|Y =I U; X) − I(U; Y) , (4)p(u|x)p(̂x|x,y)R X (D) BFGX|Y , <strong>on</strong>ly for the case of Gaussian distributi<strong>on</strong> of thesource X and mean square error (MSE) distorti<strong>on</strong> measure.where the minimizati<strong>on</strong> is performed over all p(u | x)p(̂x |x, y) and all decoder functi<strong>on</strong>s f D satisfying the fidelity c<strong>on</strong>straint(3). U is an auxiliary random variable such that |U| ≤For any other pdf, performance loss exists in the Wyner-Zivcoding. It was shown in [20] that this loss is upper boundedby 0.5 bit,|X| +1andY → X → U forms a Markov chain. Hence, (4)could be rewritten as follows:R X (D) WZX|Y − R X(D) BFGX|Y ≥ 0.5. (8)R X (D) WZX|Y = min I(U; X | Y),p(u|x)p(̂x|x,y)(5)Therefore, due to the fact that natural images have highlyn<strong>on</strong>-Gaussian statistics [8, 21, 22], compressi<strong>on</strong> of this datawhere the minimizati<strong>on</strong> is performed over all p(u | x)p(̂x |x, y) subject to the fidelity c<strong>on</strong>straint (3).It is worth to note that for the case of zero distorti<strong>on</strong>s, theWyner-Ziv problem corresp<strong>on</strong>ds to the Slepian-Wolf prob-using the Wyner-Ziv strategy will always lead to the performanceloss. The main goal of subsequent secti<strong>on</strong>s c<strong>on</strong>sists inthe extensi<strong>on</strong> of the classical distributed coding setup to thecase of a single-source coding scenario in the very-low-bit-
4 EURASIP Journal <strong>on</strong> Applied Signal ProcessingXiMain encoderTransiti<strong>on</strong> detecti<strong>on</strong> Y Index encoderShape codebookjDecoderFigure 6: Block diagram of single-source distributed coding withside informati<strong>on</strong>.̂XShape index j··· ··· ··· ··· ···y 1 (1) y 2 (1) ... y J (1) y 1 (i) y 2 (i) ... y J (i) y 1 (M) y 2 (M) ... y J (M)Shape coset 1 Shape coset i Shape coset MFigure 8: Shape cosets from the shape codebook Y.(a)Figure 7: (a) Test image Slava and its fragment (marked by square):two-regi<strong>on</strong> modeling of the fragment, (b) in the coordinate domain,and (c) in the n<strong>on</strong>decimated wavelet transform domain.3. PRACTICAL APPROACH: DISTRIBUTED SOURCECODING OF A SINGLE SOURCE3.1. Coding block diagramThe block diagram of a practical single-source distributedcoding system with side informati<strong>on</strong> is presented in Figure 6.The system c<strong>on</strong>sists of two main functi<strong>on</strong>al parts. The firstpart includes the main encoder that is working as a classicalquantizati<strong>on</strong>-based lossy coder with varying rates. The sec<strong>on</strong>dpart includes the block of transiti<strong>on</strong> detecti<strong>on</strong> that approximatesthe image edges and creates some auxiliary imageY, as a close approximati<strong>on</strong> to X. The index encoder communicatesthe parameters of approximati<strong>on</strong> model to the decoder.The shape codebook is shared by both transiti<strong>on</strong> detecti<strong>on</strong>block and decoder.The intuiti<strong>on</strong> behind our approach is based <strong>on</strong> the assumpti<strong>on</strong>that natural images in the coordinate domain canbe represented as a uni<strong>on</strong> of several stati<strong>on</strong>ary regi<strong>on</strong>s of differentintensity levels or in the n<strong>on</strong>decimated wavelet transformdomain [23] using edge process (EP) model. This assumpti<strong>on</strong>and the EP model have been used in our previouswork in image denoising where promising results have beenreported [24].Under the EP model, an image in the coordinate domain(Figure 7(a)) is composed of a number of n<strong>on</strong>overlappingsmooth regi<strong>on</strong>s (Figure 7(b)). Accordingly, in the criticallysampled or n<strong>on</strong>decimated wavelet transform domain, it isrepresented as a uni<strong>on</strong> of two types of subsets: the first <strong>on</strong>ec<strong>on</strong>tains all samples from flat image areas, while the sec<strong>on</strong>d(b)(c)<strong>on</strong>e represents edges and textures. It is supposed that thesamples from the latter subset propagate al<strong>on</strong>g the transiti<strong>on</strong>directi<strong>on</strong> (Figure 7(c)). Accurate tracking of the regi<strong>on</strong> separati<strong>on</strong>boundary in the coordinate domain setup or transiti<strong>on</strong>profile propagati<strong>on</strong> in the transform domain setup allowedto achieve image denoising results that are am<strong>on</strong>g thestate-of-the-art for the case of AWGN [24].3.2. Codebook c<strong>on</strong>structi<strong>on</strong>C<strong>on</strong>trarily to the image denoising setup, in the case of lossywavelet-based image compressi<strong>on</strong> we are interested in c<strong>on</strong>sideringnot the behavior of edge profile al<strong>on</strong>g the directi<strong>on</strong>of edge propagati<strong>on</strong>, but the different edge profiles. Due tothe high variability of edge shapes in real images and thecorresp<strong>on</strong>ding complexity of the approximati<strong>on</strong> problem, wewill exploit a structured codebook for shape representati<strong>on</strong>.It means that several types of shapes will be used to c<strong>on</strong>structa codebook where each codeword represents <strong>on</strong>e edgeof some magnitude. A schematic example of such a codebookis given in Figure 8, where several different edge profilesare exploited for image approximati<strong>on</strong>. This structured codebookhas a coset-based structure, where each coset c<strong>on</strong>tainsthe selected triple of edge profiles of a certain amplitude.More formally, the structured codebook Y = {y(i)},where i = 1, 2, ..., M, andacoset(9) canberepresentedasin Figure 9:⎧y1(i) 1 y2(i) 1 ··· y 1 ⎫N(i)⎪⎨ y1(i) 2 y2(i) 2 ··· yN(i)2 ⎪⎬y(i) =... ... ... (9)⎪⎩y1(i) J y2(i) J ··· yN(i)J ⎪⎭Here, y j (i) represents the shape j from the shape coset i. Allshape cosets i c<strong>on</strong>sist of the same shape profiles, that is, j ∈{1, 2, ..., J},andi ∈{1, 2, ..., M} for the example presentedin Figure 8.Important points about the codebook are as follows: (a)it is image independent, (b) the c<strong>on</strong>sidered shapes are unidimensi<strong>on</strong>al,(c) the codewords shape could be expressed analytically,for instance, using apparatus of splines, and (d) thecodebook dimensi<strong>on</strong>ality is determined by the type of transformused and the compressi<strong>on</strong> regime. Therefore, a c<strong>on</strong>ceptof successive c<strong>on</strong>structi<strong>on</strong> refinement [25] of the codebook
J. E. Vila-Forcén et al. 5⎡ ⎡y1(1) 1 y2(1) 1 ··· y 1 ⎤ ⎤N(1)y 1(1) 2 y2(1) 2 ··· y 2 N(1)⎢⎣ ... ... ..⎥⎦y 1(1) J y2(1) J ··· y J N(1).⎡y 1(i) 1 y2(i) 1 ··· y 1 ⎤N(i)y 1(i) 2 y2(i) 2 ··· y 2 N(i)⎢⎣ ... ... ..⎥⎦y J 1(i) y2(i) J ··· yN(i)J .⎡y 1(M) 1 y2(M) 1 ··· yN(M)1 ⎤y 2 1(M) y2(M) 2 ··· yN(M)2 ⎢⎣⎢⎣ ... ... ..⎥⎥⎦⎦y1(M) J y2(M) J ··· yN(M)JShape coset 1Shape coset iShape coset MFigure 9: <strong>Structured</strong> codebook: shape coset index i (or magnitude)is communicated explicitly by the main encoder as transiti<strong>on</strong> locati<strong>on</strong>and magnitude of quantized coefficients, and shape index j(j ∈{1, 2, ..., J}) is encoded by index encoder.might be used. The intuiti<strong>on</strong> behind this approach could beexplained using the coarse-fine quantizati<strong>on</strong> framework presentedin Figure 10.It means that for the case of high compressi<strong>on</strong> ratios,when there is not much rate to code the shape index, a singleshape profile will be used (like a coarse quantizer). In otherregimes (at medium or at high rates), it is possible to improvethe fidelity of approximati<strong>on</strong> adding more edge shapes to thecodebook. In this case, we could assume that the high-ratequantizati<strong>on</strong> assumpti<strong>on</strong> becomes valid.The task of real edge approximati<strong>on</strong> according to theshape codebook can be formulated, for instance, like a classicall 2 norm approximati<strong>on</strong> problem,ỹ j (i) =argmin{y j (i)},1≤i≤M,1≤j≤J∥ x − y j (i) ∥ ∥ 2 , (10)where the minimizati<strong>on</strong> is performed over the whole codebookin each image point.3.3. Practical implementati<strong>on</strong>: high-, medium-,and low-bit-rate regimesIt is clear that in the presented setup, the computati<strong>on</strong>al complexityof image approximati<strong>on</strong> in each point will be significant,and can be unacceptable in some realtime applicati<strong>on</strong>scenarios. To simplify the situati<strong>on</strong>, searching space dimensi<strong>on</strong>alitymight be significantly reduced using techniques thatsimplify the edge localizati<strong>on</strong>. Canny edge detector [26] canbe used for this purpose.The edge of a real image could be c<strong>on</strong>sidered as anoisy or distorted versi<strong>on</strong> of the corresp<strong>on</strong>ding codeword{y j 1(i), y j 2(i), ..., y j N(i)} (edge shape) with respect to thecodebook Y, that is, some correlati<strong>on</strong> between an originalCompr. ratioShape coset iCoarsecodebookFinecodebookFigure 10: Successive refinement codebook c<strong>on</strong>structi<strong>on</strong>.edge and a codeword can be assumed. Therefore, the structureof the codebook is similar to the structure of a channelcoset code [27], meaning that the distance between codewordsofequalmagnitude(Figure8) in the transform domainshould be large enough to perform correct shape approximati<strong>on</strong>.The coding strategy can be performed in a distributedmanner. In general, the main encoder performs the quantizati<strong>on</strong>of the edge and communicates the corresp<strong>on</strong>ding indicesof rec<strong>on</strong>structi<strong>on</strong> levels to the decoder. This informati<strong>on</strong>is sufficient to determine the shape coset index i at thedecoder for different compressi<strong>on</strong> regimes, including evenvery-low-bit-rate regime (besides the case when quantizati<strong>on</strong>to zero is performed). The index j of edge shape withina coset is communicated by the index encoder to the decoder.Having the coset index and the shape index, the decoderlooks in the coset bin i for y j (i) and generates the reproducti<strong>on</strong>sequence ̂x = f D (̂x ′ (i), ỹ j (i)), where ̂x ′ (i) is thedata reproduced at the decoder based <strong>on</strong>ly <strong>on</strong> the index i.In the case of high rates, the main encoder performs ahigh-rate (high-accuracy) approximati<strong>on</strong> of the image edges.It means that the index encoder does not produce any output,that is, both edge magnitude and edge shape could be rec<strong>on</strong>structeddirectly from the informati<strong>on</strong> c<strong>on</strong>tained in the maindecoder bit stream. Therefore, the role of side informati<strong>on</strong>represented by the fine codebook c<strong>on</strong>sists in the compensati<strong>on</strong>of quantizati<strong>on</strong> noise influence.For middle rates, the edge magnitude predicti<strong>on</strong> is stillpossible using the main encoder bitstream. However, theedge shape approximati<strong>on</strong> accuracy for this regime is nothigh enough to estimate the edge shape and its index shouldbe communicated to the decoder by the index encoder. Onecan note that in such a way we end up with vector-like edgequantizati<strong>on</strong> using the off-line designed edge codebook. Therole of the side informati<strong>on</strong> remains similar to the previouscase and targets the compensati<strong>on</strong> of quantizati<strong>on</strong> error.At low rates, a single codeword (optimal in the meansquare error sense) should be chosen to represent all shapeswithin the given image (coarse codebook in Figure 10). Inmore general case, <strong>on</strong>e can choose a single shape codewordthat is the same for all images. This is a valid assumpti<strong>on</strong> forthe compressi<strong>on</strong> of image databases with the same type ofimages. C<strong>on</strong>trarily to the above case of middle rates, the decoderoperates with a single edge codeword that can be appliedto all cases where the edge coefficients are partially preservedin the corresp<strong>on</strong>ding subbands. Moreover, the edge
6 EURASIP Journal <strong>on</strong> Applied Signal Processingrec<strong>on</strong>structi<strong>on</strong> is possible even when the edge coefficientsin some subbands are completely discarded by the deadz<strong>on</strong>equantizati<strong>on</strong>.The practical aspects of implementati<strong>on</strong> of the presentedsingle source coding system with side informati<strong>on</strong> are outof the scope of the paper. In the following secti<strong>on</strong>, we willpresent an applicati<strong>on</strong> of the proposed framework to thevery-low-bit-rate compressi<strong>on</strong> of passport photo images.4. DISTRIBUTED CODING OF IMAGES WITHSYMMETRIC SIDE INFORMATION:COMPRESSION OF PASSPORT PHOTOSAT VERY LOW BIT RATES141062−2−6−10−14Zero-crossing pointIn this secti<strong>on</strong>, the case of single source distributed codingsystem with side informati<strong>on</strong> is discussed for the case ofvery-low-bit-rate (less than 0.1 bpp) compressi<strong>on</strong> of passportphoto images. The importance of this task is justified by theurgent necessity to store pers<strong>on</strong>al informati<strong>on</strong> <strong>on</strong> the capacityrestricted media authenticati<strong>on</strong> documents that includepassports, visas, ID cards, driver licenses, and credit cards usingdigital watermarks, barcodes, or magnetic strips. In thispaper, we assume that the images of interest are 8-bit grayscale images of 256 × 256 size. As it was shown in Figure 1,existing compressi<strong>on</strong> tools are unable to provide the satisfactoryquality soluti<strong>on</strong> to this task.The scheme presented in Figure 6 is used as a basic setupfor this applicati<strong>on</strong>. As it was discussed earlier, for the caseof very-low-bit-rate regime, <strong>on</strong>ly <strong>on</strong>e shape profile (simplestep edge) is exploited. Therefore, index encoder is not usedin this particular case since <strong>on</strong>ly <strong>on</strong>e index is possible as itsoutput and, therefore, it is known a priory by the decoder.Certainly, better performance can be expected if <strong>on</strong>e approximatestransiti<strong>on</strong>s using complete image codeword (Figure 6).The price to pay for that is additi<strong>on</strong>al log 2 J bits of side informati<strong>on</strong>per shape, where J is the number of edge shapeswithin each coset.In the next subsecti<strong>on</strong>s, we discuss in details the particularitiesof encoding and decoding at the very-low-bit rates.4.1. Transiti<strong>on</strong> detecti<strong>on</strong>EncodingDue to the fact that high-c<strong>on</strong>trast edges c<strong>on</strong>sume a significantamount of the allocated bit budget for the complete imagestorage, it would be beneficial from the rec<strong>on</strong>structed imagequality perspective to reduce the ambiguity about theseimage features.On the first step, the positi<strong>on</strong> of the principal edges (theedges with the highest c<strong>on</strong>trast) is detected using the Cannyedge detector. Due to the fact that the detecti<strong>on</strong> result isnot always precise (some positi<strong>on</strong> deviati<strong>on</strong> is possible), actualtransiti<strong>on</strong> locati<strong>on</strong> is detected using the zero-crossingc<strong>on</strong>cept.Zero-crossing c<strong>on</strong>cept is based <strong>on</strong> the fact that in the n<strong>on</strong>decimatedwavelet transform domain (algorithm atrois[23]1st subband2nd subband3rd subband4th subbandFigure 11: Zero-crossing c<strong>on</strong>cept: 4-level decompositi<strong>on</strong> of the stepedge in the n<strong>on</strong>decimated domain.is used for its implementati<strong>on</strong>) all the representati<strong>on</strong>s of anideal step edge from different decompositi<strong>on</strong> levels in thesame spatial orientati<strong>on</strong> cross the horiz<strong>on</strong>tal axis in the samepoint referred to as the zero-crossing point (Figure 11). Thispoint coincides with a spatial positi<strong>on</strong> of the transiti<strong>on</strong> inthe coordinate domain. Besides, the magnitudes of principlepeaks (maximum and minimum values of the data inthe vicinity of transiti<strong>on</strong> in the n<strong>on</strong>decimated domain) ofthe comp<strong>on</strong>ents are related pairwise from high to low frequencieswith certain fixed ratios which are known in advance.Therefore, when the positi<strong>on</strong> of the zero-crossing pointis given and, at least, <strong>on</strong>e of the comp<strong>on</strong>ent peak magnitudesis known from original step edge, it is possible to predict andto rec<strong>on</strong>struct the missing data comp<strong>on</strong>ents with no error.C<strong>on</strong>sequently, if it is known at the decoder that an idealstep edge with a given amplitude is presented in a given imagelocati<strong>on</strong>, it is possible to assign zero rate to the predictablecoefficients at the encoder, allowing higher quality rec<strong>on</strong>structi<strong>on</strong>of unpredictable informati<strong>on</strong>.DecodingFor this mode, it is assumed that the low-resoluti<strong>on</strong> versi<strong>on</strong>of the original data obtained using main encoder bitstreamis already available. Detecti<strong>on</strong> of the coarse positi<strong>on</strong>s of mainedges is performed <strong>on</strong> the interpolated image analogically tothe encoder case. To adjust detecti<strong>on</strong> results, a new c<strong>on</strong>ceptof zero-crossing detecti<strong>on</strong> is used.In the targeted very-low-bit-rate compressi<strong>on</strong> scenario,the data are severely degraded by quantizati<strong>on</strong>. To make zerocrossingdetecti<strong>on</strong> more reliable in this case, more levels ofthe n<strong>on</strong>decimated wavelet transform can be used. The additi<strong>on</strong>alreliability is coming from the fact that the data atthe very low-frequency subbands almost do not suffer fromquantizati<strong>on</strong>. The gain in this case is limited by the informati<strong>on</strong>that is still presented at these low frequencies: <strong>on</strong>ly the
J. E. Vila-Forcén et al. 7210−1−2Maximum (3rd)Maximum (4th)Zero-crossing point3rd subband4th subbandFigure 12: Zero-crossing c<strong>on</strong>cept: decoding stage.edges propagating in all the subbands could be detected insuch a way.In order to rec<strong>on</strong>struct high-frequency subbands, bothedge positi<strong>on</strong> and edge magnitude are predicted usinglow-frequency subbands. In Figure 12, the positi<strong>on</strong> of thezero-crossing point is estimated based <strong>on</strong> the data from the3rd and 4th subbands. Having their maximum magnitudevalues, the rec<strong>on</strong>structi<strong>on</strong> of high frequency subbands canbe performed accurately based <strong>on</strong> the fixed magnitude relati<strong>on</strong>ships(Figure 11).4.2. Main encoderTo justify the main encoder structure, we would like to pointout that the main gain achieved recently in wavelet-basedlossy transform image coding is due to the accuracy of theunderlying stochastic image model.One of the most efficient and accurate stochastic imagemodels that represent images in the wavelet transformdomain is based <strong>on</strong> the parallel splitting of the Laplaciansource firstly introduced by Hjorungnes et al. [28]. The mainunderlying assumpti<strong>on</strong> here is that global i.i.d. zero-meanLaplacian data can be represented, without loss according tothe Kullback-Leibler divergence, using an infinite mixture ofGaussian pdfs with zero-mean and exp<strong>on</strong>entially distributedvariances,λ2 e(−λ|x|) =∫ ∞01√ 2πσ 2 e(x2 /2σ 2) λe (−λσ2) dσ 2 , (11)where λ is the parameter of the Laplacian distributi<strong>on</strong>. TheLaplacian distributi<strong>on</strong> is often used to model the globalstatistics of the high-frequency wavelet coefficients [8, 21,22].Hjorungnes et al. [28] were the first who dem<strong>on</strong>stratedthat, if the side informati<strong>on</strong> (the local variances) are availableat both encoder and decoder, the gain in the rate-distorti<strong>on</strong>sense of coding the Gaussian mixture instead of the globalLaplacian source is given byR L (D) − R MG (D) ≈ 0.312 bit/sample, (12)where R L (D) andR MG (D) denote the rate-distorti<strong>on</strong> functi<strong>on</strong>sfor the global i.i.d. Laplacian source and the Gaussianmixture, respectively.The practical problem of the side informati<strong>on</strong> communicati<strong>on</strong>to the decoder was elegantly solved in [7, 8]. Thedeveloped EQ coder is based <strong>on</strong> the assumpti<strong>on</strong> of the slowvarying nature of the local variances of the high-frequencysubband image samples. As a c<strong>on</strong>sequence, this variance canbe accurately estimated (predicted) given its quantized causalneighborhood.According to the EQ coding strategy, the local variancesof the samples in the high-frequency wavelet subbands are estimatedbased <strong>on</strong> the causal neighborhood using maximumlikelihood strategy. When it is available, the data from theparent subband are also included to enhance the estimati<strong>on</strong>accuracy.At the end of the estimati<strong>on</strong> step, the coefficients arequantized using a uniform threshold quantizer selected accordinglyto the results of the rate-distorti<strong>on</strong> optimizati<strong>on</strong>.In particular, the Lagrange functi<strong>on</strong>al should be minimized,that <strong>on</strong> the sample level is given byy i = r i + λd i , (13)where r i is the rate corresp<strong>on</strong>ding to the entropy of the quantizeroutput applied to the ith sample, d i is the corresp<strong>on</strong>dingdistorti<strong>on</strong>, and λ is the Lagrange multiplier. The encoding ofthe quantized data is performed using the bin probabilitiesof the quantizers, where the samples fall, by an arithmeticcoder.While at the high-rate regime the approximati<strong>on</strong> of thelocal variance field by its quantized versi<strong>on</strong> is valid, in thecase of low rates it fails. The reas<strong>on</strong> for that is the quantizati<strong>on</strong>to zero most of the data samples that makes local varianceestimati<strong>on</strong> extremely inaccurate.The simple soluti<strong>on</strong> proposed in [7, 8] c<strong>on</strong>sists in theplacement of all the coefficients that fall into the quantizerdeadz<strong>on</strong>e in the so-called unpredictable class, and the rest inthe so-called predictable class. The samples of the first <strong>on</strong>eare c<strong>on</strong>sidered to be distributed globally as an i.i.d. generalizedGaussian distributi<strong>on</strong>, while the infinite Gaussian mixturemodel is used to capture the statistics of the samples inthe sec<strong>on</strong>d <strong>on</strong>e. This separati<strong>on</strong> is performed using a simplerate-dependent thresholding operati<strong>on</strong>. The parametersof the unpredictable class are exploited in the rate-distorti<strong>on</strong>optimizati<strong>on</strong> and are sent to the decoder as side informati<strong>on</strong>.The experimental results presented in [7, 8]allowtoc<strong>on</strong>cludeabout the state-of-the-art performance of this techniquein the image compressi<strong>on</strong> applicati<strong>on</strong>.
8 EURASIP Journal <strong>on</strong> Applied Signal ProcessingTable 1: Benchmarking of the developed compressi<strong>on</strong> method versus existing lossy encoding techniques.Bytes(bpp)300(0.037)400(0.049)500(0.061)600(0.073)700(0.085)800(0.099)Slava (PSNR, dB) Julien (PSNR, dB) Jose (PSNR, dB)ROIROIROIROIROIROIJPEG EQ DSSCEQ DSSCSPIHTJPEG EQSPIHTJPEGSPIHT2000 2000 200021.04 25.27 10.33 25.93 19.87 22.82 9.76 23.35 20.76 26.11 10.39 27.2922.77 26.08 18.56 26.81 21.47 23.43 17.94 23.89 23.21 27.30 19.86 28.2724.92 26.85 22.36 27.41 23.07 23.81 21.86 24.15 25.50 28.20 25.09 28.8125.78 27.41 25.96 27.85 23.78 24.17 22.81 24.28 26.39 28.74 27.09 29.1026.66 27.96 27.12 28.09 24.53 24.44 23.61 24.50 28.08 29.31 28.37 29.3527.39 28.56 27.71 28.16 25.04 24.68 24.24 24.56 28.72 29.89 29.31 29.46DSSCpositi<strong>on</strong> of the rectangular regi<strong>on</strong>-of-interest, and four bytescharacterizing the background brightness.(a)Figure 13: Test image Slava: (a) regi<strong>on</strong> of interest and (b) backgroundfour-quadrant splitting.Motivated by the EQ coder performance, we designedour main encoder using the same principles with severalmodificati<strong>on</strong>s as follows:(i) at the very-low-bit-rate regime, most of the informati<strong>on</strong>at the first and the sec<strong>on</strong>d wavelet decompositi<strong>on</strong>levels is quantized to zero. We assume that all the dataabout str<strong>on</strong>g edges could be rec<strong>on</strong>structed with someprecisi<strong>on</strong> using the side informati<strong>on</strong> and do not allocateany rate to these subbands;(ii) high-frequency subbands of the third decompositi<strong>on</strong>level are compressed using a regi<strong>on</strong> of interest strategy(Figure 13(a)), where the regi<strong>on</strong> of interest is indicatedusing three extra bytes. The image regi<strong>on</strong>s outside ofthe regi<strong>on</strong> of interest will be rec<strong>on</strong>structed using lowfrequencyinformati<strong>on</strong>, and four extra bytes for themean brightness of the background of the photo imagein four quadrants (Figure 13(b));(iii) a 3 × 3 causal window is applied for local variance estimati<strong>on</strong>;(iv) no parent dependencies are taken into account <strong>on</strong> thestochastic image model, and <strong>on</strong>ly samples from thegiven subband are used [29].The actual bitstream from the encoder is c<strong>on</strong>stituted bythe data from the EQ encoder, three bytes determining the(b)4.3. Index encoderAs it was menti<strong>on</strong>ed in the previous subsecti<strong>on</strong>, <strong>on</strong>ly <strong>on</strong>eedge profile (the step edge) is used at the very-low-rateregime. Thus, index encoder does not produce any output.4.4. DecoderThe decoder performs the rec<strong>on</strong>structi<strong>on</strong> of the compresseddata using the main encoder output and the available sideinformati<strong>on</strong>. The bitstream of the main encoder is decompressedby the EQ decoder. The fourth wavelet transform decompositi<strong>on</strong>level is decompressed using classical algorithmversi<strong>on</strong>, and the third level is rec<strong>on</strong>structed using regi<strong>on</strong> ofinterest EQ decoding.Having two lowpass levels of decompositi<strong>on</strong>, the lowresoluti<strong>on</strong>rec<strong>on</strong>structi<strong>on</strong> (with two high-frequency decompositi<strong>on</strong>levels equal to zero) of the original photo usingwavelet transform is obtained. Final rec<strong>on</strong>structi<strong>on</strong> of highqualitydata is performed based <strong>on</strong> the interpolated image,and the transiti<strong>on</strong> detecti<strong>on</strong> block informati<strong>on</strong> in the n<strong>on</strong>decimatedwavelet transform domain.5. EXPERIMENTAL RESULTSIn this secti<strong>on</strong>, we present the experimental results of verylow-bit-ratepassport photo compressi<strong>on</strong> based <strong>on</strong> the proposedframework of distributed single source coding withsymmetrical side informati<strong>on</strong> (DSSC). A set of 11 imageswere used in our experiments. The results for three of themare presented in Table 1, Figures 14 and 15 versus those providedby the standard EQ algorithm as well as JPEG2000 withregi<strong>on</strong> of interest coding (ROI-JPEG2000) [30] and set partiti<strong>on</strong>ingin hierarchical trees algorithm with regi<strong>on</strong> of interestcoding (ROI-SPIHT) [31].
J. E. Vila-Forcén et al. 9292530272428PSNR (dB)2523PSNR (dB)2322PSNR (dB)2621300 400 500 600 700 800BytesROI-JPEG 2000ROI-SPIHTEQDSSC21300 400 500 600 700 800BytesROI-JPEG 2000ROI-SPIHTEQDSSC24300 400 500 600 700 800BytesROI-JPEG 2000ROI-SPIHTEQDSSC(a)(b)(c)Figure 14: Benchmarking of the developed compressi<strong>on</strong> method versus existing lossy encoding techniques: (a) Slava,(b)Julien, and (c) Josetest images.(1a) (1b) (1c) (1d) (1e) (1f) (1g) (1h) (1i)(2a) (2b) (2c) (2d) (2e) (2f) (2g) (2h) (2i)(3a) (3b) (3c) (3d) (3e) (3f) (3g) (3h) (3i)Figure 15: Experimental results. The first column: the original test images; the sec<strong>on</strong>d column: ROI-JPEG2000 compressi<strong>on</strong> results for therate 400 bytes; the third column: ROI-SPIHT compressi<strong>on</strong> results for the rate 400 bytes; the fourth column: EQ compressi<strong>on</strong> results for therate 400 bytes; the fifth column: DSSC compressi<strong>on</strong> results for the rate 400 bytes; the sixth column: ROI-JPEG2000 compressi<strong>on</strong> results forthe rate 700 bytes; the seventh column: ROI-SPIHT compressi<strong>on</strong> results for the rate 700 bytes; the eighth column: EQ compressi<strong>on</strong> resultsfor the rate 700 bytes; and the ninth column: DSSC compressi<strong>on</strong> results for the rate 700 bytes.The performance is evaluated in terms of the peak signalto-noiseratio PSNR = 10 log 10 (255 2 /‖x − ̂x‖ 2 ).The obtained results allow to c<strong>on</strong>clude about the proposedmethod advantages over the selected competitors forcompressi<strong>on</strong> rates below 0.09 bpp in terms of both visualquality and PSNR. Performance loss at higher rate in our casein comparis<strong>on</strong> with ROI-SPIHT and ROI-JPEG2000 is explainedby the necessity of algorithm performance optimizati<strong>on</strong>for this rate regime that includes a modificati<strong>on</strong> of theunpredictable class definiti<strong>on</strong>.6. CONCLUSIONSIn this paper, the problem of distributed source coding of asingle source with side informati<strong>on</strong> was c<strong>on</strong>sidered. It wasshown that the compressi<strong>on</strong> system optimal performancefor n<strong>on</strong>-Gaussian sources can be achieved using the Berger-Flynn-Gray coding setup. A practical very-low-bit-rate compressi<strong>on</strong>algorithm based <strong>on</strong> this setup was proposed for codingof passport photo images. Experimental validati<strong>on</strong> of thisalgorithm performed <strong>on</strong> a set of passport photos allows to
10 EURASIP Journal <strong>on</strong> Applied Signal Processingc<strong>on</strong>clude its superiority over a number of existing encodingtechniques at rates below 0.09 bpp in terms of both visualquality and PSNR. The realized performance loss of thedeveloped algorithm at rates higher than 0.09 bpp is justifiedby the necessity of its parameters optimizati<strong>on</strong> for thisrate range. This extensi<strong>on</strong> is a subject of our <strong>on</strong>going research.DISCLAIMERThe informati<strong>on</strong> in this document reflects <strong>on</strong>ly the authors’views, is provided as is and no guarantee or warranty is giventhat the informati<strong>on</strong> is fit for any particular purpose. Theuser thereof uses the informati<strong>on</strong> at its sole risk and liability.ACKNOWLEDGMENTSThis paper was partially supported by SNF ProfessorshipGrant no. 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Moulin,“Low-complexity image denoising based <strong>on</strong> statistical modelingof wavelet coefficients,” IEEE Signal Processing Letters,vol. 6, no. 12, pp. 300–303, 1999.[22] Y. Yoo, A. Ortega, and B. Yu, “<str<strong>on</strong>g>Image</str<strong>on</strong>g> subband coding usingc<strong>on</strong>text based classificati<strong>on</strong> and adaptive quantizati<strong>on</strong>,” IEEETransacti<strong>on</strong>s <strong>on</strong> <str<strong>on</strong>g>Image</str<strong>on</strong>g> Processing, vol. 8, no. 12, pp. 1702–1715,1999.[23] S. G. Mallat, A Wavelet Tour of Signal Processing, AcademicPress, New York, NY, USA, 1997.[24] S. Voloshynovskiy, O. Koval, and T. Pun, “Wavelet-based imagedenoising using n<strong>on</strong>-stati<strong>on</strong>ary stochastic geometrical imagepriors,” in Proceedings of IS&T/SPIE’s 15th Annual Symposium,Electr<strong>on</strong>ic Imaging: <str<strong>on</strong>g>Image</str<strong>on</strong>g> and Video Communicati<strong>on</strong>sand Processing 2003, vol. 5022 of Proceedings of SPIE, pp. 675–687, Santa Clara, Calif, USA, January 2003.[25] I. Kozintsev and K. Ramchandran, “Multiresoluti<strong>on</strong> jointsource-channel coding using embedded c<strong>on</strong>stellati<strong>on</strong>s forpower-c<strong>on</strong>strained time-varying channels,” in Proceedings of
J. E. Vila-Forcén et al. 11IEEE Internati<strong>on</strong>al C<strong>on</strong>ference <strong>on</strong> Acoustics, Speech, and SignalProcessing (ICASSP ’96), vol. 4, pp. 2343–2346, Atlanta, Ga,USA, May 1996.[26] J. Canny, “A computati<strong>on</strong>al approach to edge detecti<strong>on</strong>,”IEEE Transacti<strong>on</strong>s <strong>on</strong> Pattern Analysis and Machine Intelligence,vol. 8, no. 6, pp. 679–698, 1986.[27] J. G. Proakis, Digital Communicati<strong>on</strong>s, McGraw-Hill,NewYork, NY, USA, 3rd editi<strong>on</strong>, 1995.[28] A. Hjorungnes, J. M. Lervik, and T. A. Ramstad, “Entropycoding of composite sources modeled by infinite Gaussianmixture distributi<strong>on</strong>s,” in Proceedings of IEEE Digital SignalProcessing Workshop, pp. 235–238, Loen, Norway, September1996.[29] K. R. Rao and P. C. Yip, Eds., The Transform and Data <str<strong>on</strong>g>Compressi<strong>on</strong></str<strong>on</strong>g>Handbook, CRC Press, Boca Rat<strong>on</strong>, Fla, USA, 2000.[30] C. Christopoulos, J. Askelof, and M. Larss<strong>on</strong>, “Efficient methodsfor encoding regi<strong>on</strong>s of interest in the upcoming JPEG2000 still image coding standard,” IEEE Signal Processing Letters,vol. 7, no. 9, pp. 247–249, 2000.[31] E. Atsumi and N. Farvardin, “Lossy/lossless regi<strong>on</strong>-of-interestimage coding based <strong>on</strong> set partiti<strong>on</strong>ing in hierarchical trees,”in Proceedings of IEEE Internati<strong>on</strong>al C<strong>on</strong>ference <strong>on</strong> <str<strong>on</strong>g>Image</str<strong>on</strong>g> Processing.(ICIP ’98), vol. 1, pp. 87–91, Chicago, Ill, USA, October1998.J. E. Vila-Forcén received the Telecommunicati<strong>on</strong>sEngineer degree from the CarlosIII University of Madrid, Spain, in 2001. In2001–2002, he joined the Signal Theory andCommunicati<strong>on</strong>s Department of the CarlosIII University, working in the developmentof the MPEG4 standard. Since 2002,he has been an Assistant Professor and aPh.D. student at the Stochastic <str<strong>on</strong>g>Image</str<strong>on</strong>g> ProcessingGroup, Computer Visi<strong>on</strong> and MultimediaLab, Department of Computer Science of the Universityof Geneva, Geneva, Switzerland. His current research interests arethe informati<strong>on</strong>-theoretic aspects of digital data hiding, communicati<strong>on</strong>swith side informati<strong>on</strong>, and stochastic image modeling forcompressi<strong>on</strong>.O. Koval received his M.S. Degree in electricalengineering from the Nati<strong>on</strong>al UniversityLvivska Politechnika, Lviv, Ukraine,in 1996. In 1996–2001, he was with theDepartment of Synthesis, Processing, andIdentificati<strong>on</strong> of <str<strong>on</strong>g>Image</str<strong>on</strong>g>s, Institute of Physicsand Mechanics (Lviv, Ukraine) as a researcherand Ph.D. student. He receivedhis Ph.D. degree in electrical engineeringfrom the Nati<strong>on</strong>al University Lvivska Politechnika,in 2002. Since 2002, he has been with Stochastic <str<strong>on</strong>g>Image</str<strong>on</strong>g>Processing Group, Computer Visi<strong>on</strong> and Multimedia Lab, Universityof Geneva, from which he received his Ph.D. degree in stochasticimage modeling in 2004, where he is currently a PostdoctoralFellow. His research interests cover stochastic image modeling fordifferent image processing applicati<strong>on</strong>s, digital watermarking, informati<strong>on</strong>theory, and communicati<strong>on</strong>s with side informati<strong>on</strong>.T. Pun received his Ph.D. degree in imageprocessing in 1982, at the Swiss FederalInstitute of Technology in Lausanne(EPFL). He joined the University of Geneva,Switzerland, in 1986, where he is currently aFull Professor at the Computer Science Departmentand Head of the Computer Visi<strong>on</strong>and Multimedia Lab. Since 1979, hehas been active in various domains of imageprocessing, image analysis, and computervisi<strong>on</strong>. He has authored or coauthored over 200 journal andc<strong>on</strong>ference papers in these areas as well as seven patents, and ledor participated to a number of nati<strong>on</strong>al and European researchprojects. His current research interests, related to the design of multimediainformati<strong>on</strong> systems and multimodal interacti<strong>on</strong>, focus<strong>on</strong> data hiding, image and video watermarking, image and videoc<strong>on</strong>tent-based informati<strong>on</strong> retrieval systems, EEG signals analysis,and brain-computer interacti<strong>on</strong>.S. Voloshynovskiy received the Radio Engineerdegree from Lviv Polytechnic Institutein 1993, and the Ph.D. degree inelectrical engineering from State UniversityLvivska Politechnika, Lviv, Ukraine, in 1996.In 1998–1999, he has been with Universityof Illinois at Urbana-Champaign, USA,as a Visiting Scholar. Since 1999, he hasbeen with University of Geneva, Switzerland,where he is currently an Associate Professorwith the Department of Computer Science, and Head of theStochastic <str<strong>on</strong>g>Image</str<strong>on</strong>g> Processing Group. His current research interestsare in informati<strong>on</strong>-theoretic aspects of digital data hiding, visualcommunicati<strong>on</strong>s with side informati<strong>on</strong>, and stochastic image modelingfor denoising, compressi<strong>on</strong>, and restorati<strong>on</strong>. He has coauthoredover 100 journal and c<strong>on</strong>ference papers in these areas as wellas nine patents. He has served as a c<strong>on</strong>sultant to private industry inthe above areas.
EURASIP JOURNAL ON APPLIED SIGNAL PROCESSINGSpecial Issue <strong>on</strong>Transforming Signal Processing Applicati<strong>on</strong>s intoParallel Implementati<strong>on</strong>sCall for PapersThere is an increasing need to develop efficient “systemlevel”models, methods, and tools to support designers toquickly transform signal processing applicati<strong>on</strong> specificati<strong>on</strong>to heterogeneous hardware and software architectures suchas arrays of DSPs, heterogeneous platforms involving microprocessors,DSPs and FPGAs, and other evolving multiprocessorSoC architectures. Typically, the design process involvesaspects of applicati<strong>on</strong> and architecture modeling aswell as transformati<strong>on</strong>s to translate the applicati<strong>on</strong> modelsto architecture models for subsequent performance analysisand design space explorati<strong>on</strong>. Accurate predicti<strong>on</strong>s are indispensablebecause next generati<strong>on</strong> signal processing applicati<strong>on</strong>s,for example, audio, video, and array signal processingimpose high throughput, real-time and energy c<strong>on</strong>straintsthat can no l<strong>on</strong>ger be served by a single DSP.There are a number of key issues in transforming applicati<strong>on</strong>models into parallel implementati<strong>on</strong>s that are not addressedin current approaches. These are engineering theapplicati<strong>on</strong> specificati<strong>on</strong>, transforming applicati<strong>on</strong> specificati<strong>on</strong>,or representati<strong>on</strong> of the architecture specificati<strong>on</strong> aswell as communicati<strong>on</strong> models such as data transfer and synchr<strong>on</strong>izati<strong>on</strong>primitives in both models.The purpose of this call for papers is to address approachesthat include applicati<strong>on</strong> transformati<strong>on</strong>s in the performance,analysis, and design space explorati<strong>on</strong> efforts when takingsignal processing applicati<strong>on</strong>s to c<strong>on</strong>current and parallel implementati<strong>on</strong>s.The Guest Editors are soliciting c<strong>on</strong>tributi<strong>on</strong>sin joint applicati<strong>on</strong> and architecture space explorati<strong>on</strong> thatoutperform the current architecture-<strong>on</strong>ly design space explorati<strong>on</strong>methods and tools.Topics of interest for this special issue include but are notlimited to:• modeling applicati<strong>on</strong>s in terms of (abstract)c<strong>on</strong>trol-dataflow graph, dataflow graph, and processnetwork models of computati<strong>on</strong> (MoC)• transforming applicati<strong>on</strong> models or algorithmicengineering• transforming applicati<strong>on</strong> MoCs to architecture MoCs• joint applicati<strong>on</strong> and architecture space explorati<strong>on</strong>• joint applicati<strong>on</strong> and architecture performanceanalysis• extending the c<strong>on</strong>cept of algorithmic engineering toarchitecture engineering• design cases and applicati<strong>on</strong>s mapped <strong>on</strong>multiprocessor, homogeneous, or heterogeneousSOCs, showing joint optimizati<strong>on</strong> of applicati<strong>on</strong> andarchitectureAuthors should follow the EURASIP JASP manuscriptformat described at http://www.hindawi.com/journals/asp/.Prospective authors should submit an electr<strong>on</strong>ic copy oftheir complete manuscript through the EURASIP JASP manuscripttracking system at http://www.hindawi.com/mts/, accordingto the following timetable:Manuscript Due September 1, 2006Acceptance Notificati<strong>on</strong> January 1, 2007Final Manuscript Due April 1, 2007Publicati<strong>on</strong> Date 3rd Quarter 2007GUEST EDITORS:F. Deprettre, Leiden Embedded Research Center, LeidenUniversity, Niels Bohrweg 1, 2333 CA Leiden, TheNetherlands; edd@liacs.nlRoger Woods, School of Electrical and Electr<strong>on</strong>icEngineering, Queens University of Belfast, Ashby Building,Stranmillis Road, Belfast, BT9 5AH, UK; r.woods@qub.ac.ukIngrid Verbauwhede, Katholieke Universiteit Leuven,ESAT-COSIC, Kasteelpark Arenberg 10, 3001 Leuven,Belgium; Ingrid.verbauwhede@esat.kuleuven.beErwin de Kock, Philips Research, High Tech Campus 31,5656 AE Eindhoven, The Netherlands;erwin.de.kock@philips.comHindawi Publishing Corporati<strong>on</strong>http://www.hindawi.com
EURASIP JOURNAL ON APPLIED SIGNAL PROCESSINGSpecial Issue <strong>on</strong>Video Adaptati<strong>on</strong> for Heterogeneous Envir<strong>on</strong>mentsCall for PapersThe explosive growth of compressed video streams andrepositories accessible worldwide, the recent additi<strong>on</strong> of newvideo-related standards such as H.264/AVC, MPEG-7, andMPEG-21, and the ever-increasing prevalence of heterogeneous,video-enabled terminals such as computer, TV, mobileph<strong>on</strong>es, and pers<strong>on</strong>al digital assistants have escalated theneed for efficient and effective techniques for adapting compressedvideos to better suit the different capabilities, c<strong>on</strong>straints,and requirements of various transmissi<strong>on</strong> networks,applicati<strong>on</strong>s, and end users. For instance, Universal MultimediaAccess (UMA) advocates the provisi<strong>on</strong> and adaptati<strong>on</strong> ofthe same multimedia c<strong>on</strong>tent for different networks, terminals,and user preferences.Video adaptati<strong>on</strong> is an emerging field that offers a richbody of knowledge and techniques for handling the hugevariati<strong>on</strong> of resource c<strong>on</strong>straints (e.g., bandwidth, display capability,processing speed, and power c<strong>on</strong>sumpti<strong>on</strong>) and thelarge diversity of user tasks in pervasive media applicati<strong>on</strong>s.C<strong>on</strong>siderable amounts of research and development activitiesin industry and academia have been devoted to answeringthe many challenges in making better use of video c<strong>on</strong>tentacross systems and applicati<strong>on</strong>s of various kinds.Video adaptati<strong>on</strong> may apply to individual or multiplevideo streams and may call for different means depending <strong>on</strong>the objectives and requirements of adaptati<strong>on</strong>. Transcoding,transmoding (cross-modality transcoding), scalable c<strong>on</strong>tentrepresentati<strong>on</strong>, c<strong>on</strong>tent abstracti<strong>on</strong> and summarizati<strong>on</strong> arepopular means for video adaptati<strong>on</strong>. In additi<strong>on</strong>, video c<strong>on</strong>tentanalysis and understanding, including low-level featureanalysis and high-level semantics understanding, play an importantrole in video adaptati<strong>on</strong> as essential video c<strong>on</strong>tentcan be better preserved.The aim of this special issue is to present state-of-theartdevelopments in this flourishing and important researchfield. C<strong>on</strong>tributi<strong>on</strong>s in theoretical study, architecture design,performance analysis, complexity reducti<strong>on</strong>, and real-worldapplicati<strong>on</strong>s are all welcome.Topics of interest include (but are not limited to):• Heterogeneous video transcoding• Scalable video coding• Dynamic bitstream switching for video adaptati<strong>on</strong>• Signal, structural, and semantic-level videoadaptati<strong>on</strong>• C<strong>on</strong>tent analysis and understanding for videoadaptati<strong>on</strong>• Video summarizati<strong>on</strong> and abstracti<strong>on</strong>• Copyright protecti<strong>on</strong> for video adaptati<strong>on</strong>• Crossmedia techniques for video adaptati<strong>on</strong>• Testing, field trials, and applicati<strong>on</strong>s of videoadaptati<strong>on</strong> services• Internati<strong>on</strong>al standard activities for video adaptati<strong>on</strong>Authors should follow the EURASIP JASP manuscriptformat described at http://www.hindawi.com/journals/asp/.Prospective authors should submit an electr<strong>on</strong>ic copy oftheir complete manuscript through the EURASIP JASP manuscripttracking system at http://www.hindawi.com/mts/, accordingto the following timetable:Manuscript Due September 1, 2006Acceptance Notificati<strong>on</strong> January 1, 2007Final Manuscript Due April 1, 2007Publicati<strong>on</strong> Date 3rd Quarter 2007GUEST EDITORS:Chia-Wen Lin, Department of Computer Science andInformati<strong>on</strong> Engineering, Nati<strong>on</strong>al Chung ChengUniversity, Chiayi 621, Taiwan; cwlin@cs.ccu.edu.twYap-Peng Tan, School of Electrical and Electr<strong>on</strong>icEngineering, Nanyang Technological University, NanyangAvenue, Singapore 639798, Singapore; eyptan@ntu.edu.sgMing-Ting Sun, Department of Electrical Engineering,University of Washingt<strong>on</strong>, Seattle, WA 98195, USA ;sun@ee.washingt<strong>on</strong>.eduAlex Kot, School of Electrical and Electr<strong>on</strong>ic Engineering,Nanyang Technological University, Nanyang Avenue,Singapore 639798, Singapore; eackot@ntu.edu.sg
Anth<strong>on</strong>y Vetro, Mitsubishi Electric Research Laboratories,201 Broadway, 8th Floor, Cambridge, MA 02138, USA;avetro@merl.comHindawi Publishing Corporati<strong>on</strong>http://www.hindawi.com
EURASIP JOURNAL ON APPLIED SIGNAL PROCESSINGSpecial Issue <strong>on</strong>Knowledge-Assisted Media Analysis for InteractiveMultimedia Applicati<strong>on</strong>sCall for PapersIt is broadly acknowledged that the development of enablingtechnologies for new forms of interactive multimedia servicesrequires a targeted c<strong>on</strong>fluence of knowledge, semantics,and low-level media processing. The c<strong>on</strong>vergence of these areasis key to many applicati<strong>on</strong>s including interactive TV, networkedmedical imaging, visi<strong>on</strong>-based surveillance and multimediavisualizati<strong>on</strong>, navigati<strong>on</strong>, search, and retrieval. Thelatter is a crucial applicati<strong>on</strong> since the exp<strong>on</strong>ential growthof audiovisual data, al<strong>on</strong>g with the critical lack of tools torecord the data in a well-structured form, is rendering uselessvast porti<strong>on</strong>s of available c<strong>on</strong>tent. To overcome this problem,there is need for technology that is able to produce accuratelevels of abstracti<strong>on</strong> in order to annotate and retrieve c<strong>on</strong>tentusing queries that are natural to humans. Such technologywill help narrow the gap between low-level features orc<strong>on</strong>tent descriptors that can be computed automatically, andthe richness and subjectivity of semantics in user queries andhigh-level human interpretati<strong>on</strong>s of audiovisual media.This special issue focuses <strong>on</strong> truly integrative research targetingof what can be disparate disciplines including imageprocessing, knowledge engineering, informati<strong>on</strong> retrieval,semantic, analysis, and artificial intelligence. High-qualityand novel c<strong>on</strong>tributi<strong>on</strong>s addressing theoretical and practicalaspects are solicited. Specifically, the following topics are ofinterest:• Semantics-based multimedia analysis• C<strong>on</strong>text-based multimedia mining• Intelligent exploitati<strong>on</strong> of user relevance feedback• Knowledge acquisiti<strong>on</strong> from multimedia c<strong>on</strong>tents• Semantics based interacti<strong>on</strong> with multimedia• Integrati<strong>on</strong> of multimedia processing and SemanticWeb technologies to enable automatic c<strong>on</strong>tent sharing,processing, and interpretati<strong>on</strong>• C<strong>on</strong>tent, user, and network aware media engineering• Multimodal techniques, high-dimensi<strong>on</strong>ality reducti<strong>on</strong>,and low level feature fusi<strong>on</strong>Authors should follow the EURASIP JASP manuscriptformat described at http://www.hindawi.com/journals/asp/.Prospective authors should submit an electr<strong>on</strong>ic copy oftheir complete manuscript through the EURASIP JASP manuscripttracking system at http://www.hindawi.com/mts/ accordingto the following timetable:Manuscript Due September 1, 2006Acceptance Notificati<strong>on</strong> January 15, 2007Final Manuscript Due April 1, 2007Publicati<strong>on</strong> Date 3rd Quarter, 2007GUEST EDITORS:Ebroul Izquierdo, Department of Electr<strong>on</strong>ic Engineering,Queen Mary, University of L<strong>on</strong>d<strong>on</strong>, Mile End Road, L<strong>on</strong>d<strong>on</strong>E1 4NS, United Kingdom; ebroul.izquierdo@elec.qmul.ac.ukHyoung Jo<strong>on</strong>g Kim, Department of C<strong>on</strong>trol and Instrumentati<strong>on</strong>Engineering, Kangw<strong>on</strong> Nati<strong>on</strong>al University, 192 1Hyoja2 D<strong>on</strong>g, Kangw<strong>on</strong> Do 200 701, Korea;khj@kangw<strong>on</strong>.ac.krThomas Sikora, Communicati<strong>on</strong> Systems Group, TechnicalUniversity Berlin, Einstein Ufer 17, 10587 Berlin, Germany;sikora@nue.tu-berlin.deHindawi Publishing Corporati<strong>on</strong>http://www.hindawi.com
EURASIP JOURNAL ON APPLIED SIGNAL PROCESSINGSpecial Issue <strong>on</strong>Advanced Signal Processing and Computati<strong>on</strong>alIntelligence Techniques for Power Line Communicati<strong>on</strong>sCall for PapersIn recent years, increased demand for fast Internet access andnew multimedia services, the development of new and feasiblesignal processing techniques associated with faster andlow-cost digital signal processors, as well as the deregulati<strong>on</strong>of the telecommunicati<strong>on</strong>s market have placed major emphasis<strong>on</strong> the value of investigating hostile media, such aspowerline (PL) channels for high-rate data transmissi<strong>on</strong>s.Nowadays, some companies are offering powerline communicati<strong>on</strong>s(PLC) modems with mean and peak bit-ratesaround 100 Mbps and 200 Mbps, respectively. However,advanced broadband powerline communicati<strong>on</strong>s (BPLC)modems will surpass this performance. For accomplishing it,some special schemes or soluti<strong>on</strong>s for coping with the followingissues should be addressed: (i) c<strong>on</strong>siderable differencesbetween powerline network topologies; (ii) hostile propertiesof PL channels, such as attenuati<strong>on</strong> proporti<strong>on</strong>al to high frequenciesand l<strong>on</strong>g distances, high-power impulse noise occurrences,time-varying behavior, and str<strong>on</strong>g inter-symbolinterference (ISI) effects; (iv) electromagnetic compatibilitywith other well-established communicati<strong>on</strong> systems workingin the same spectrum, (v) climatic c<strong>on</strong>diti<strong>on</strong>s in differentparts of the world; (vii) reliability and QoS guarantee forvideo and voice transmissi<strong>on</strong>s; and (vi) different demandsand needs from developed, developing, and poor countries.These issues can lead to exciting research fr<strong>on</strong>tiers withvery promising results if signal processing, digital communicati<strong>on</strong>,and computati<strong>on</strong>al intelligence techniques are effectivelyand efficiently combined.The goal of this special issue is to introduce signal processing,digital communicati<strong>on</strong>, and computati<strong>on</strong>al intelligencetools either individually or in combined form for advancingreliable and powerful future generati<strong>on</strong>s of powerline communicati<strong>on</strong>soluti<strong>on</strong>s that can be suited with for applicati<strong>on</strong>sin developed, developing, and poor countries.Topics of interest include (but are not limited to)• Multicarrier, spread spectrum, and single carrier techniques• Channel modeling• Channel coding and equalizati<strong>on</strong> techniques• Multiuser detecti<strong>on</strong> and multiple access techniques• Synchr<strong>on</strong>izati<strong>on</strong> techniques• Impulse noise cancellati<strong>on</strong> techniques• FPGA, ASIC, and DSP implementati<strong>on</strong> issues of PLCmodems• Error resilience, error c<strong>on</strong>cealment, and Joint sourcechanneldesign methods for video transmissi<strong>on</strong>through PL channelsAuthors should follow the EURASIP JASP manuscript formatdescribed at the journal site http://asp.hindawi.com/.Prospective authors should submit an electr<strong>on</strong>ic copy of theircomplete manuscripts through the EURASIP JASP manuscripttracking system at http://www.hindawi.com/mts/, accordingto the following timetable:Manuscript Due October 1, 2006Acceptance Notificati<strong>on</strong> January 1, 2007Final Manuscript Due April 1, 2007Publicati<strong>on</strong> Date 3rd Quarter, 2007GUEST EDITORS:Moisés Vidal Ribeiro, Federal University of Juiz de Fora,Brazil; mribeiro@ieee.orgLutz Lampe, University of British Columbia, Canada;lampe@ece.ubc.caSanjit K. Mitra, University of California, Santa Barbara,USA; mitra@ece.ucsb.eduKlaus Dostert, University of Karlsruhe, Germany;klaus.dostert@etec.uni-karlsruhe.deHalid Hrasnica, Dresden University of Technology, Germanyhrasnica@ifn.et.tu-dresden.deHindawi Publishing Corporati<strong>on</strong>http://asp.hindawi.com
EURASIP JOURNAL ON APPLIED SIGNAL PROCESSINGSpecial Issue <strong>on</strong>Numerical Linear Algebra in Signal ProcessingApplicati<strong>on</strong>sCall for PapersThe cross-fertilizati<strong>on</strong> between numerical linear algebra anddigital signal processing has been very fruitful in the lastdecades. The interacti<strong>on</strong> between them has been growing,leading to many new algorithms.Numerical linear algebra tools, such as eigenvalue and singularvalue decompositi<strong>on</strong> and their higher-extensi<strong>on</strong>, leastsquares, total least squares, recursive least squares, regularizati<strong>on</strong>,orthog<strong>on</strong>ality, and projecti<strong>on</strong>s, are the kernels of powerfuland numerically robust algorithms.Thegoalofthisspecialissueistopresentnewefficient andreliable numerical linear algebra tools for signal processingapplicati<strong>on</strong>s. Areas and topics of interest for this special issueinclude (but are not limited to):• Singular value and eigenvalue decompositi<strong>on</strong>s, includingapplicati<strong>on</strong>s.• Fourier, Toeplitz, Cauchy, Vanderm<strong>on</strong>de and semiseparablematrices, including special algorithms andarchitectures.• Recursive least squares in digital signal processing.• Updating and downdating techniques in linear algebraand signal processing.• Stability and sensitivity analysis of special recursiveleast-squares problems.• Numerical linear algebra in:• Biomedical signal processing applicati<strong>on</strong>s.• Adaptive filters.• Remote sensing.• Acoustic echo cancellati<strong>on</strong>.• Blind signal separati<strong>on</strong> and multiuser detecti<strong>on</strong>.• Multidimensi<strong>on</strong>al harm<strong>on</strong>ic retrieval and directi<strong>on</strong>-of-arrivalestimati<strong>on</strong>.• Applicati<strong>on</strong>s in wireless communicati<strong>on</strong>s.• Applicati<strong>on</strong>s in pattern analysis and statisticalmodeling.• Sensor array processing.Authors should follow the EURASIP JASP manuscriptformat described at http://www.hindawi.com/journals/asp/.Prospective authors should submit an electr<strong>on</strong>ic copy oftheir complete manuscript through the EURASIP JASP manuscripttracking system at http://www.hindawi.com/mts/, accordingto the following timetable:Manuscript Due October 1, 2006Acceptance Notificati<strong>on</strong> February 1, 2007Final Manuscript Due May 1, 2007Publicati<strong>on</strong> Date 3rd Quarter, 2007GUEST EDITORS:Shivkumar Chandrasekaran, Department of Electricaland Computer Engineering, University of California, SantaBarbara, USA; shiv@ece.ucsb.eduGene H. Golub, Department of Computer Science, StanfordUniversity, USA; golub@sccm.stanford.eduNicola Mastr<strong>on</strong>ardi, Istituto per le Applicazi<strong>on</strong>i del Calcolo“Mauro Pic<strong>on</strong>e,” C<strong>on</strong>siglio Nazi<strong>on</strong>ale delle Ricerche, Bari,Italy; n.mastr<strong>on</strong>ardi@ba.iac.cnr.itMarc Mo<strong>on</strong>en, Department of Electrical Engineering,Katholieke Universiteit Leuven, Belgium;marc.mo<strong>on</strong>en@esat.kuleuven.bePaul Van Dooren, Department of Mathematical Engineering,Catholic University of Louvain, Belgium;vdooren@csam.ucl.ac.beSabine Van Huffel, Department of Electrical Engineering,Katholieke Universiteit Leuven, Belgium;sabine.vanhuffel@esat.kuleuven.beHindawi Publishing Corporati<strong>on</strong>http://www.hindawi.com