722 IEEE SIGNAL PROCESSING LETTERS, VOL. 21, NO. 6, JUNE 2014

Optimal Viterbi Based Total Variation SequenceDetection (TVSD) For Robust Image/VideoDecoding In Wireless Sensor NetworksAnkit Kudeshia, Student Member, IEEE, and Aditya K. Jagannatham, Member, IEEE

Abstract—In this letter, we propose a novel scheme for robustreconstruction, based on total variation regularization, towardsimage/video communication in multimedia wireless sensor net-works. We derive the optimal joint source channel decoder asthe combination of a maximum likelihood cost function and ananisotropic total variation norm based regularization factor. Theproposed scheme exploits the bounded variation (BV) property ofimages and is thus ideally suited for reconstruction. Subsequently,it is demonstrated that the trellis based Viterbi decoder can beemployed for robust image reconstruction using modified totalvariation state and branch metrics. Simulation results for BTCand JPEG encoded image transmission demonstrate a superiorreconstruction performance for the proposed scheme in compar-ison to conventional methods.

Index Terms—Image/video reconstruction, total variation regu-larization, Viterbi decoder, wireless sensor networks.

I. INTRODUCTION

T HE advent of wireless sensor networks (WSN) has en-abled several new applications such as target tracking, re-

mote environment monitoring etc. A typical WSN [1] consistsof clusters of sensor nodes which communicate with the clusterhead. Further, image and video communication is a key compo-nent of multimedia sensor networks, which have attracted signif-icant attention for surveillance and defense applications. How-ever, in wireless scenarios, transmission of multimedia contentcomprising of images and video frames is challenging due tothe highly error prone nature of communication over the fadingwireless channel. This has necessitated the development of ro-bust error resilient schemes for image and video reconstructionin fading WSNs. In this context, several schemes have been sug-gested in existing literature, which improve the performance ofimage recovery by exploiting the fading channel diversity prop-erties, such as parallel channel coding at the physical layer andmultiple description (MD) source coding at the application layer[2]. MD coding enhances the error resilience of the multimedia

Manuscript received February 05, 2014; revised March 15, 2014; acceptedMarch 24, 2014. Date of publication March 26, 2014; date of current versionApril 04, 2014. This work was supported by the ISRO-IITK Space TechnologyCell (STC /EE /20120039). The associate editor coordinating the review of thismanuscript and approving it for publication was Prof. Michael Wakin.The authors are with the Department of Electrical Engineering, In-

dian Institute of Technology Kanpur, Kanpur UP 208016, India (e-mail:ankitkud@iitk.ac.in; adityaj@iitk.ac.in).Color versions of one or more of the figures in this paper are available online

at http://ieeexplore.ieee.org.Digital Object Identifier 10.1109/LSP.2014.2313887

stream transmitted over the wireless link by using a correlatingblock transformwhich adds controlled redundancy [3]. Althoughthis proceduremitigates the effect of packet erasureswhich occurduring communication, it leads to an overall reduction of thecompression efficiency. The sensor nodes in a typical WSN aresmall battery operated wireless devices. Thus, they are severelylimited in terms of the number of antennas that can be employedto exploit spatial diversity. Further, the stringent bandwidth andenergy constraints, coupled with the lower computational re-sources, discourage the employment of redundancy increasingschemes such as MD codes, which lead to higher processing andtransmission overheads. It is therefore necessary to design lowcomplexity schemes forWSNs, which limit the transmit pre-pro-cessing at the miniature sensor nodes. The work in [1] describesan interesting scheme which employs the temporal correlation ofthe sensor data for error correction at the cluster head, leading torobust data reconstruction. Further, this scheme is implementedat the cluster head, thereby significantly decreasing the com-putational complexity at the sensor nodes. Also, total variationregularization schemes have been demonstrated to yield supe-rior image/video reconstruction performance as shown in workssuch as [4]. The work in [4] demonstrates an application of TVbased image reconstruction in the context of image/video blurremoval. However, none of the schemes above consider imagereconstruction for digitally modulated coded image transmis-sion over a fading wireless channel. Therefore, in this work,we present a novel scheme based on total variation regulariza-tion in multimedia wireless sensor networks. Specifically, wemotivate the robust image decoding problem as the maximumlikelihood symbol decoder in conjunction with an regular-ization component which is based on the principle of boundedtotal variation of the decoded image stream. It is demonstratedthat the optimal total variation sequence decoder can be derivedemploying the Viterbi algorithm with appropriate state and pathmetrics, thereby making it very attractive and efficient for im-plementation in WSNs. To demonstrate the performance of theproposed scheme, we employ BTC, JPEG encoding for wirelessimage transmission. This demonstrates that the presented algo-rithm is general in nature and can be extended to other compres-sion schemes in a relatively straightforward fashion. Simulationresults are presented to demonstrate the reconstruction perfor-mance of the proposed scheme. The organization of the letteris as follows: Section II describes the wireless system modelfor coded image transmission and introduces the notation usedin the rest of the discussion. Section III details the proposedViterbi algorithm based TVSD (Total Variation Sequence Detec-tion) scheme for image reconstruction alongwith the expressions

1070-9908 © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

KUDESHIA AND JAGANNATHAM: OPTIMAL VITERBI BASED TOTAL VARIATION SEQUENCE DETECTION 723

for the regularized trellis state and branch metrics. In Section IV,we demonstrate the performance of the proposed scheme withthe aid of simulations and conclude with Section V.

II. SYSTEM MODEL FOR CODED IMAGE COMMUNICATION

Consider an digital image , with the individual ele-ments of represented by for , . Eachelement gives the gray scale intensity level correspondingto pixel location , also known as the pixel value. Prior tobeing transmitted to theWSN cluster head, the image may be en-coded at the sensor node employing an appropriate image codingscheme such as BTC, JPEG etc to achieve an appropriate levelof compression, which is necessary due to the limited bandwidthavailable for wireless transmission. The various components ofthe system for wireless coded image transmission and recon-struction are discussed in the following subsections. We beginwith a brief outline of the wireless system model next.

A. Wireless System Model

Let the encoded image comprise of and coded blocks ineach column and row respectively. Hence there are a total of

coded blocks where the th block has coded compo-nents and the th coded component of the th block containssymbols. Let the th modulated symbol of the th coded compo-nent in the th block be represented by , wheredenotes an -ary digital modulation constellation such as BPSK( ), QPSK ( ) etc and denotes the set of complexnumbers. Let denote the received signal correspondingto the transmission of symbol over the wireless channel.The model for the input-output system above can be expressedas,

(1)

where is the complex valued Rayleigh fading coeffi-cient characterizing the wireless channel between the transmitterand receiver and is the complex zero mean additive whiteGaussian noise of variance at the receiver.

B. Conventional Maximum Likelihood (ML) Decoder

Let anddenote the transmit

and receive symbol vectors respectively corresponding to theth coded component of the th block. Let denote the set ofvalid symbol vectors of dimension with ,where consists of all possible dimensional symbolvectors , . Conventionally, the transmitteddimensional symbol vector is recovered from the

received dimensional signal vector atthe receiver employing the least squares cost function basedoptimization rule described as given in [5],

(2)

Here is the effective fading channel coefficient ma-trix, where is the number of symbols in the th coded symbolvector of the th block and is defined as,

.......... . .

...

However, in practical image communication scenarios, the sim-plistic ML decoder above does not exploit the spatial (spatio-temporal in context of videos) bounded variation structure of thecoded image. This leads to a significantly high residual error inthe image reconstructed from the received symbols, which arisesdue to the high probability of symbol error corresponding tocommunication over the fading wireless channel. For such sce-narios, specifically related to the context of image reconstruc-tion, Total Variation (TV) cost based regularization approacheshave been demonstrated to yield significantly superior qualityof image recovery. It has been shown that the regulariza-tion factor based TV optimization framework, which enforcessmoothness of the computed solution, is ideally suited for a widevariety of image processing applications such as deblurring, de-noising, turbulence effect reduction etc. Thus, the optimal algo-rithm for image decoding can be formulated as the paradigm ofTVSD, which jointly decodes the entire transmit stream, unlikethe decoupled decoder in (2). In the next section, we describethe regularization based TV likelihood cost function and themodified TV metric based Viterbi algorithm for image recon-struction.

III. VITERBI ALGORITHM BASED TV SEQUENCE DETECTION

The optimal decoding rule corresponds to estimating thetransmit symbol vector sequence given thereceived signal vector time series where

and . It is well known that

the optimal decoded sequence maximizes the a posterioriprobability density, derived using Bayes’ rule as,

where the likelihood is Gaussian, arising from theinput-output wireless channel observation model in (1) whilethe prior probability distribution follows a Gibbs (Boltz-mann) distribution and is given by the Gibbs measure [6]. Thishas been extensively studied in works such as [7], [8], whereit has been demonstrated that the a posteriori probability max-imization problem further simplifies to the TV regularized costfunction optimization,

(3)

The quantity above represents the TV regularization weightfactor, similar to [6], and it has been demonstrated in [4] that theTV norm is equivalent to the norm of the difference vectori.e. , where is the finite difference operator

724 IEEE SIGNAL PROCESSING LETTERS, VOL. 21, NO. 6, JUNE 2014

along the directions of the connected causal neighbors and isdefined as follows,

and see (4)–(5), shown at the bottom of the next page, whereis the decoding function which computes the coefficient

value for the corresponding modulated symbol vector. Hence,substituting the above TV regularization factor in the likelihoodcost function in (3), the optimization problem for image de-coding can be obtained as given in (4), where representsthe set of causal neighbor blocks in the neighborhood of the thblock of the coded image. The above likelihood cost functioncan be minimized through a novel application of the Viterbi al-gorithm, to compute the optimal decoded sequence as follows.Let denotethe causal decoded neighbors of the previous row. Let the setof all valid symbol vectors be defined as whereis the set of symbol vector lengths required to encode the quan-tized components. Consider now a trellis with stateswhere is the cardinality of the set and each state corre-sponds to , as shown in Fig. 1. One cannow define the state metric as given in (5) and the branchmetric between state at stage and state at stageas . At each transmitted symbol stage

, the accumulated metric and the survivor nodefor the surviving path terminating in the th node are given as,

where is initialized as i.e. for weassign the state metric value to the accumulated metric. Theregularization weight factor is determined by the minimumMSE criterion to minimize the decoding error. Subsequently, wefind the minimum accumulated metric at the last symbol stage

as . The decoded symbol vector

sequence is given as, and where. Therefore, similar to

the conventional Viterbi algorithm, after obtaining the minimumaccumulated metric state corresponding to the last symbol in therow, we trace back the minimum distance path through the sur-vivor nodes, which corresponds to the least total variation regu-larized cost achieving decoded image stream. This procedure isrepeated for all the image rows. This scheme can be readilyextended to video sequences and color images as follows. Foroptimal video decoding, one can consider the three dimensional

Fig. 1. Trellis structure for the proposed TVSD based image reconstruction.

spatio-temporal connected causal neighbors for TV regulariza-tion, similar to [4]. In the case of color images, the algorithmcan be alternately applied to the intensity and chroma compo-nents of the coded image. Next we present simulation results toillustrate the performance of the proposed image reconstructionscheme with different image encoding schemes.

IV. SIMULATION RESULTS

To simulate the performance of the robust total variationbased image reconstruction scheme in a WSN, we considerBlock Truncation Coding (BTC) and JPEG coded wirelessimage transmission for the wireless sensor network. The BTCis a simple yet effective image compression scheme [9], [10],which is well suited for WSN image transmission. We computethe mean and standard deviation of all the pixel elementsbelonging to every image block where . The elements

, of the bit plane are given as ,where denotes the indicator function corresponding tothe set . Thus each block of the coded image comprises of

coded components which are , and withand . The mean and standard deviation are subse-quently quantized and encoded using BPSK modulation asdimensional symbol vectors, where the bit-plane componentis encoded as a -length BPSKmodulated symbol vector. Thesesymbol vectors are subsequently transmitted through a wirelesschannel. At the receiver, the proposed scheme is now employedfor decoding the received signal vectors corresponding to ,to obtain their decoded values , and is recovered usingthe decoder given in (2). Finally, the reconstructed valuecorresponding to pixel is computed as,

where is the number of pixels such that . Thespecial case of corresponds to uncoded transmission ofthe dimensional BPSK encoded symbol vector correspondingto the pixel value at . To further validate the performanceof the proposed scheme, we also consider the JPEG image en-coding scheme [11], [12] which achieves a good compression

(4)

(5)

KUDESHIA AND JAGANNATHAM: OPTIMAL VITERBI BASED TOTAL VARIATION SEQUENCE DETECTION 725

Fig. 2. Test image set: Lena, Cameraman, House.

Fig. 3. Optimum value based on MSE criterion for different SNR values.

efficiency along with an improved reconstruction quality andis thus well suited for WSN image transmission, as reported in[13]. The Huffman entropy coded quantized DC and AC com-ponents corresponding to each block are modulated asBPSK symbol vectors followed by transmission over the wire-less channel. At the receiver, the proposed scheme is applied forViterbi based total variation decoding of the coded DC compo-nents, while the remaining coded AC symbol vectors are de-coded employing the conventional decoder in (2). The recon-structed value corresponding to pixel of the th blockis obtained by performing the 2-D IDCT, as given in (6), on theresulting th block of the decoded and dequantized DCand AC components of the transmitted image followed by in-verse level shifting. Both the above compression schemes areapplied on the image set comprising of the standard Lena, Cam-eraman, House images of size i.e.and shown in Fig. 2. The wireless channel is Rayleigh fadingwith channel coefficient , where , are gen-erated as independent zero mean Gaussian random variables ofvariance unity. Therefore, the average gain of the fading wire-less channel is given as . We consider an SNR in therange of dB, with the symbol power normalized to unity.Therefore, the SNR is given as . For the simulation, we cal-culate the optimal value of the regularization parameter usingthe minimum MSE criterion. The approximate bit rates for theJPEG encoded images are in the range of 0.5 to 0.8 bits/pixel. InFig. 3 from the plot, we observe that the optimal values corre-sponding to the lowest MSE are in the range . Fig. 4shows the reconstructed images for the proposed TVSD and con-ventional ML decoding schemes. Table I shows the PSNR en-

Fig. 4. Test image Lena recovered at dB (ML), dB(TVSD), 15 dB (ML), 15 dB (TVSD) (left to right) for the encoding methods:BTC ( ), BTC ( ) and JPEG (top to bottom).

TABLE ICOMPARISON OF PSNR FOR ML AND TVSD SCHEMES APPLIED ON TESTIMAGES FOR BTC ( ), BTC ( ), BTC ( ) AND JPEG

hancement for the proposed total variation based reconstructionscheme in comparison to the conventional ML decoder for var-ious SNR values; see (6), shown at the bottom of the page

V. CONCLUSION

A total variation regularization based scheme has been pre-sented for optimal image/video stream decoding in multimediacommunication based wireless sensor networks. The proposedscheme employs a novel norm regularization factor to ex-ploit the bounded variation property of the image for recon-struction. It has been demonstrated that the Viterbi algorithmcan then be implemented to estimate the optimal transmit imagestream based on appropriately defined total variation regularizedstate and branch metrics. Simulation results demonstrate a supe-rior image reconstruction performance for the proposed TVSDscheme in comparison to the conventional ML scheme in termsof both decoded image quality and PSNR.

(6)

726 IEEE SIGNAL PROCESSING LETTERS, VOL. 21, NO. 6, JUNE 2014

REFERENCES

[1] S. Mukhopadhyay, C. Schurgers, D. Panigrahi, and S. Dey, “Model-based techniques for data reliability in wireless sensor networks,” IEEETrans. Mobile Comput., vol. 8, no. 4, pp. 528–543, 2009.

[2] J. N. Laneman, E. Martinian, G.W.Wornell, and J. G. Apostolopoulos,“Source-channel diversity for parallel channels,” IEEE Trans. Inf.Theory, vol. 51, no. 10, pp. 3518–3539, 2005.

[3] V. K. Goyal, “Multiple description coding: Compression meets the net-work,” IEEE Signal Process. Mag., vol. 18, no. 5, pp. 74–93, 2001.

[4] S. H. Chan, R. Khoshabeh, K. B. Gibson, P. E. Gill, and T. Q. Nguyen,“An augmented lagrangian method for total variation video restora-tion,” IEEE Trans. Image Process., vol. 20, no. 11, pp. 3097–3111,2011.

[5] D. Tse and P. Viswanath, Fundamentals of wireless communication.Cambridge, U.K.: Cambridge Univ. Press, 2005.

[6] V. Panin, G. Zeng, and G. Gullberg, “Total variation regulated EMalgorithm [spect reconstruction],” IEEE Trans. Nucl. Sci., vol. 46, no.6, pp. 2202–2210, 1999.

[7] P. C. Hansen, Rank-Deficient and Discrete Ill-Posed Problems: Nu-merical Aspects of Linear Inversion. Philadelphia, PA, USA: SIAM,1998, vol. 4.

[8] L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation basednoise removal algorithms,” Physica D: Nonlin. Phenomena, vol. 60,no. 1, pp. 259–268, 1992.

[9] E. Delp and O. Mitchell, “Image compression using block truncationcoding,” IEEE Trans. Commun., vol. 27, no. 9, pp. 1335–1342, 1979.

[10] M. M. Almrabet, A. R. Zerek, A. Chaoui, and A. A. Akash, “Imagecompression using block truncation coding,” Int. J. Sci. Techn. Au-tomat. Contr. Comput. Eng., vol. 3, no. 2, pp. 1046–1053, 2009.

[11] International Telegraph and Telephone Consultative Committee(CCITT), International Telecommunication Union, Informationtechnology-Digital compression and coding of continuous-tone stillimages-Requirements and guidelines/Rec. T.81, (09), 1992.

[12] G. K. Wallace, “The JPEG still picture compression standard,” IEEETrans. Consumer Electron., vol. 38, no. 1, pp. xviii–xxxiv, 1992.

[13] L. W. Chew, L. M. Ang, and K. P. Seng, “Survey of image compres-sion algorithms in wireless sensor networks,” in Int. Symp. InformationTechnology ITSim-2008, 2008, vol. 4, pp. 1–9, IEEE.