Low Complexity DCT-based DSC approach for Hyperspectral Image Compression with Arithmetic Code

Transcription

1 277 Low Complexty DCT-based DSC approach for Hyperspectral Image Compresson wth Arthmetc Code Meena B. Vallakat 1 and Dr. R. R. Sedamkar 2 1 Electroncs & Telecommuncaton Department, Unversty of Mumba, Thakur college of Engneerng and Technology Mumba, Maharashtra , Inda 2 Computer Department, Unversty of Mumba, Thakur college of Engneerng and Technology Mumba, Maharashtra , Inda Abstract Ths paper proposes low complexty codec for lossy compresson on a sample hyperspectral mage. These mages have two knds of redundances: 1) spatal; and 2) spectral. A dscrete cosne transform (DCT)- based Dstrbuted Source Codng(DSC) paradgm wth Arthmetc code for low complexty s ntroduced. Here, Set-parttonng based approach s appled to reorganze DCT coeffcents nto wavelet lke tree structure as Setparttonng works on wavelet transform, and extract the sgn, refnement, and sgnfcance btplanes. The extracted refnement bts are Arthmetc encoded, then by applyng low densty party check based (LDPC-based) Slepan-Wolf coder s mplement to our DSC strategy. Expermental results for SAMSON (Spectroscopc Aeral Mappng System wth Onboard Navgaton) data show that proposed scheme acheve peak sgnal to nose rato and compresson to a very good extent for water cube compared to buldng, land or forest cube. Keywords: Image compresson; hyperspectral mage; dstrbuted source codng (DSC); dscrete cosne transform (DCT); Arthmetc code; low complexty. 1. Introducton Hyperspectral magng s a powerful technque and has been used n large number of applcatons, such as geology,earth-resource management, polluton montorng, meteorology, and mltary survellance. Hyperspectral mages are three-dmensonal data sets, where two of the dmensons are spatal and the thrd s spectral. These mages are acqured by observng the same object (area or target) n multple narrow wavelength slces at the same tme and reveal the reflecton, transmsson, or radaton features of the observed object n multple spectral bands. The 2D- DCT technque was proposed by Z. Xong, O Guleryuz, M T Orchard[1], for transform coeffcents codng. Ownng to hgh correlaton of hyperspectral mage, n partcular the correlaton across frequency bands, DSC s appled nto hyperspectral mage to obtan a lowly complex and hghly effectve lossy compresson. For DSC can shft the complexty between encoder and decoder, compared to tradtonal source codng. Slepan and Wolf have proved the feasblty of DSC scheme and ensure that such encoder can theoretcally gan the same effcency of the jont one as shown f fg 1[2]. In [3], Wyner and Zv provde the lossy extenson of Slepan-Wolf codng. The applcaton of DSC theory to hyperspectral mage has been wdely used recently. Enrco Magl proposed two dfferent lossless compresson DSCbased ways [4][5][6]. N.-M. Cheung puts forth the DSC based lossy method n DWT doman, named setparttonng n herarchcal tree wth Slepan-Wolf codng (SW-SPIHT) [7,8]. It demonstrates that the presented applcaton s very promsng. X Y DSC Jont Decoder Decoder Fgure 1 DSC based compresson scheme. In the above context, the present research work proposes low complexty hyperspectral mage compresson on the bass of DSC n DCT doman, rather than DWT doman. It s found that hyperspectral mage s hghly correlated not only n DWT doman but also n DCT doman. Moreover, the complexty of DWT s nferor to that of DCT. It s well known that DCT-based coder s much easer than DWT-based one. [9,10] show that the calculaton quantty of DCT s much smaller. Janrong Wang, Rongke Lu modfes the Zxang Xong s embedded zerotree dscrete cosne transform (EZDCT) algorthm [11]. The proposed Yˆ Xˆ

2 278 approach the zerotree quantzer n SPIHT and choose the SPIHT coder nstead of EZW coder. It s used to extract btplanes of reordered DCT coeffcents. Arthmetc code s also ntroduced, arthmetc codng depends manly on the estmaton of the probablty model that the coder use and the arthmetc codng approach the entropy of the source[12]. The smaller the entropy of the nput data s, the hgher the compresson rato s. Accordng to DSC theory, the nter-band correlaton of DCT doman can be exploted at the decoder sde to attan the same compresson rato as the jont compresson of the varous bands. The refnement btplanes are Arthmetc encoded. Afterwards, [6] LDPCbased Slepan-Wolf coder s adopted to the Arthmetc codes and sgn bts n order to generate syndromes. These syndromes are conveyed to the decoder, whle the sgnfcance bts are transmtted straghtly. 2. Codec Desgn It has been observed that DCT-based coder has lower complcaton than ts DWT-based one. Ths paper, brng forth low complexty DSC-based hyperspectral mage compresson n DCT doman wth Arthmetc code. For one thng, the mplementaton of DCT s less expensve than that of WT. Besdes, the regrouped DCT coeffcents wth waveletlke tree structure and hgh dependency help us not merely employ wavelet-based coder to obtan better reconstructon qualty than tradtonal DCT-based ones and EZW coder, but also apply DSC technque at lower cost than most wavelet-based ones. 2.1 DCT-Based Subband Representaton Fg.2 states the process of regrouped 8 8 DCT coeffcents [13]. Frst, an mage (N N) s dvded nto n n blocks. Second, each of the blocks s transformed to DCT doman and can be treated as an L (L=log2n) level tree. Thrd, the correspondng coeffcents from all DCT blocks are rearranged together nto a new wavelet lke subband. 2.2 DCT-Doman Correlaton Analyss For close relatonshp between source and sde nformaton s the vtal factor of DSC prncple, therefore ths paper dscuss whether there s dependency n the reorganzed DCT doman. The ntra-band (.e., spatal) and nter-band (.e. spectral) correlaton are analysed, the correlaton coeffcent wth normalzaton and dscretzaton are defned as follows. R M N f ( x, u f f ( x 1, y k) u f x1 Y 1 ( l, k) (1) M N 2 f ( x, u f x1 y1 Where, R(l,k) = ntra-correlaton value; M N = sze, f(x, = pxel grey value labeled wth space coordnate (x,; uf = the mage s average grey value; l and k = the dstance of analyzed pxels. M N f ( x l, y k) g( x, x1 y1 H ( l, k) (2) M N M N 2 2 f ( x, g( x, x1 y1 x1 y1 Where, H(l,k) = nter-correlaton value; f(x, and g(x, = the pxel grey value of two dfferent bands; l and k = the relatve dstance of analyzed pxels between the two bands. The nter band correlaton results are shown n Fg.3. The x-axs represents band number of hyperspectral mage and y-axs represents correlaton coeffcent. Fg.3 llustrates that most bands have a correlaton coeffcent close to one, except those nosy bands. The relatonshp at the correspondng pont s much closer than that of other postons. Ths suggests the feasblty of DSC prncple. Fgure.2 Process of DCT coeffcents regroupng. Fgure 3 Spectral correlaton curve of hyperspectral SAMSON mage

3 279 From the above graph, t s observed that the frst few bands have low spectral correlatons. Whereas, the bands after 11 th band are hghly correlated wth each other. 3. The proposed Archtecture The hardware (or software) mplementaton of DCT transform s less expensve compared to that of DWT. Zxang Xong s EZDCT[14] algorthm s better than most DCT-based coder lke baselne JPEG and mproved JPEG, and even better than Shapro s wavelet-based EZW coder [8]. Moreover, t s avalable of Arthmetc code to explot bt level s correlaton and reduce the correspondng error bt rate. Hence, referrng to EZDCT, DSC-based method n DCT doman wth Arthmetc code s appled to satsfy our compresson requrement. The scheme s composed of transformng, estmaton, btplanes extracton va set parttonng algorthm, Arthmetc encodng, LDPC-based Slepan-Wolf coder and reconstructon. Three crucal procedures are DCT transform nstead of Wavelet transform, mprovement of sde nformaton by estmaton, and btplane technque wth Arthmetc code. The followng descrbes n detal about the proposed paradgm showed n Fg.4. Take nto consderaton two adjacent hghly correlated hyperspectral bands, the current band to be coded and the prevous band coded already, symbolzed as X and X -1 respectvely. partcularly about the modfcaton, zerotree quantzer n SPIHT algorthm s use and substtute SPIHT coder for EZW coder. Fg.4.b shows the model of the encoder, whch s appled to the band X to be coded by DSC approach n DCT doman. Frst, set-parttonng method s adopted to extract btplanes of regrouped DCT coeffcents, generatng sgnfcance, sgn and refnement. Then, Arthmetc code s ntroduced to encode refnement bts. Arthmetc code s then appled drectly to extract all btplanes n conventonal approach. So as to realze the DSC strategy, LDPC-based Slepan- Wolf coder s then employed to encode sgn and refnement bts to yeld syndromes. The compresson rato reles on the value of crossover probabltes. The crossover probabltes are consdered n the correspondng btplane locaton of X and X, representatve of the predcted X obtaned by the lnear flter. So the sgnfcance tree of X s appled to the regrouped DCT coeffcents of X to extract sgn and refnement btplanes. These generated sgn and refnement bts are compared to those of X and calculate the rate. The need to transmt the coeffcents of the one-order lnear flter s requred because t s unknown to the decoder. Along ths way, more precse verson of band X,.e. X ~ can be generated. X 1 DSC+SPIHT SPIHT decoder + Inv DCT a. Sde nformaton codec ˆ 1 X ˆ 1 X coeffcents 1-order Lnear Flter X ~ DSC+SPIHT Arthmetc code Extracton X DSC+SPIHT Arthmetc code Extracton Syndromes LDPC-based Slepan- Wolf decoder Sgnfcance bts Sgnfcance bts X LDPC-based Slepan- Wolf Syndromes Sgnfcance bts SPIHT decoder + Inv DCT Xˆ 1-order Lnear Flter X 1 X DSC+SPIHT Arthmetc code Extracton b. of Proposed scheme Fgure 4 block dagram of proposed scheme coeffcents Fg.4.a dagrammatcally stated that the reference band X -1 s transmtted by modfed EZDCT, and ts reconstructed mage X ˆ s generated and offered at the decoder. More 1 Fgure 5 Decoder block dagram of proposed scheme As s showed n Fg.5, at the decoder sde, the estmated value X ~ s adopted, nstead of drectly usng X ˆ. Ths s 1 useful n DSC method because the qualty of the sde nformaton decdes the compresson rato to a degree. Once the sgnfcance bts produced at the encoder are passed to the decoder, the X ~ s sgn and refnement bts are reconstructed and are avalable as sde nformaton. Then, wth the precse sde nformaton and conveyed syndromes,

4 280 LDPC-based Slepan-Wolf decoder s ntroduced to reconsttute sgn and refnement bts. 4. Technques used n DSC-based coder Hyperspectral mage exhbt a sgnfcant amount of ' dependency, and one-order lner flter,.e. X a X 1 b provdes an approxmate verson of X at the encoder, so that the dfference between X and X -1 can get smaller. By ths means, the Slepan-Wolf coder can obtan better performance due to DSC theory. Pxels between the X and X -1 are appled to calculate the coeffcent a and b that fts the data best n a least squares sense. For our DSC-based strategy, the btplanes are extracted to reorganzed DCT coeffcents nto bnary data because the usng LDPC-based coder performs best for bnary form. Ths process generates sgn and refnement btplanes, and sgnfcance btplanes whch represent the waveletlke tree structure. Besdes the coeffcents correlaton at the correspondng locaton between the two bands s the hghest. Therefore the sgnfcance bts of X are use to ndex the structure of X -1 and generate sgn and refnement bts of X -1.Partcularly X ~,the estmated reconstructed X -1, as substtute of X -1, s appled at the decoder. These produced sgn and refnement bts are provded as sde nformaton of DSC-based framework. Moreover, the Arthmetc encodng s use to enhance the relatonshp of source and sde nformaton. In DSC system, hgher correlaton between source and sde nformaton can acheve better codng effcency. In most cases, natural bnary code s employed. However, ths natural bnary code s napproprate when the values of source and sde nformaton are very close but the bnary representatons are remarkably dverse. Hence natural bnary code potentally degrades the correlaton, and Arthmetc code s obvously used to replace natural bnary code. So as to further fulfll the scheme s requrement for easly mplementaton, Arthmetc encodng s adopted to all DCT coeffcents drectly. It s merely appled to represent the refnement bts rather than all btplanes, whch can not only sgnfcantly reduce the amount of Arthmetc codes, but also make full use of the advancements of Arthmetc code. It s notced that the sgn bts are not Arthmetc encoded. Because sgn btplane s merely one btplane, and the dfference between source and sde nformaton hardly exsts, Arthmetc encodng s not essental. hyperspectral dataset used, s generated by the SAMSON sensor. It covers the spectral range of 400nm-900nm wth a band wdth of 3.2nm. The data was collected by the Florda Envronmental Research Insttute as part of the GOES-R sponsored experment. The nstrument flown durng the collect s the SAMSON, a push-broom, vsble to near IR, hyperspectral sensor. Ths sensor was desgned and developed by FERI [15]. They have 156 contguous bands and 952X952 pxel resoluton. The 256X256 up left corner s extracted for the experments. Each pxel n each band has 8 bts of radometrc nformaton. Four HIC s are shown below. Whle the land mage was utlzed as test data. All the scenes consst of 156 spectral bands coverng the vsble and near-nfrared spectral wndow (wavelengths from 400nm to 700nm). Band 1 of each scene s shown n Fgure 5.4. The scene are of dfferent spatal szes , , , and for water, forest, buldng and land mages, respectvely. Each pxel n each band has 8 bts of radometrc nformaton. (a) Water cube 5. Results and dscusson The software mplementaton of the algorthm s wrtten n a Matlab envronment usng Matlab7.7 software. The (b) Forest cube

5 281 PSNR b log (3) 10 N M 1 2 X Xˆ I NM x1 y1 An average PSNR s obtaned as the qualty measure, where the averagng s performed over B spectral bands: 1 PSNR B B b1 PSNR b (4) (c) Buldng cube (B=156 n our mage). The hgher PSNR would normally ndcate that the reconstructon s of hgher qualty. It s measured n decbels (db). (d) Land cube Fgure 6 Examples of dfferent scenes or cube(band 1). 5.1 Qualty Measurement Defntons There exst dfferent performance measures for verfcaton of codng algorthms. In order to make a far comparson between the technques, the same performance measure must be used, preferably on the same hyperspectral data. It s known that ths type of magery s not necessarly vewed by human vsual system (HVS). Although the reconstructed cubes were examned also by a subjectve qualty crteron (vsual qualty, artfacts lke blockness, smoothness etc.), t s obvous that the true qualty can be measured manly accordng to the specfc applcaton the encodng s used for. In ths paper t was decded to measure the performance wth the followng performance measures: Peak sgnal-to-nose rato (PSNR): Ths s a commonly used quanttatve fdelty crtera (n mage processng applcatons). Let X be the orgnal pxel n spatal poston of the spectral band b (of sze N M) and Xˆ the respectve reconstructed pxel, then for each spectral band 1 b 156, PSNR b s defned by (a) Orgnal land cube band 1 (b)reconstructed band 1(PSNR= dB, at 0.2bpp,CR= 49.45%) Fgure 7 Examples of the algorthm used for performance measurement of land cube. Fg.8 shows the average PSNR for hyperspectral SAMSON mage as 42.66dB. Ths fgure shows PSNR obtaned by the mplemented algorthm on land mage.

6 282 (a) PSNR of hyperspectral land mage at dfferent wavelengths (a) Orgnal water cube band 1 (b) MSE of hyperspectral land mage at dfferent wavelengths Fgure 8 PSNR and MSE at dfferent wavelength(400nm to 900nm) (b)reconstructed band 1(PSNR= dB, at 0.2bpp,CR= 52%) Fgure 10 Examples of the algorthm used for performance measurement of water cube. (a) Orgnal buldng cube band 1 (b)reconstructed band 1(PSNR= dB, at 0.2bpp,CR= 35.09%) Fgure 9 Examples of the algorthm used for performance measurement of buldng cube. Table 1: PSNR of dfferent mage cubes at dfferent wavelengths(bands) PSNR BAND WATER BUILDING LAND

7 283 Table 2: MSE of dfferent mage cubes at dfferent wavelengths(bands) BAND MSE WATER BUILDING LAND (a) PSNR of hyperspectral land mage, water mage and buldng mage at dfferent wavelengths. (b) MSE of hyperspectral land mage, water mage and buldng mage at dfferent wavelengths Fgure 11 PSNR and MSE of dfferent mage cubes at dfferent wavelength(400nm to 900nm) 6. Conclusons Dscrete cosne transform s a versatle tool n hyperspectral remote sensng whch s utlzed for varous applcatons such data compresson. DCT and SPIHT are the most wdely used methods for compresson of hyperspectral mage. In ths paper, DCT based DSC technque usng arthmetc code was conducted n order to estmate ther performance on hyperspectral magery. The DCT based DSC usng arthmetc code were examned usng SAMSON hyperspectal sample data. The performance of these algorthms s evaluated based on PSNR of the compressed mage and compresson rato. PSNR= db, CR = 48% From MSE, t s observed that the dfference between orgnal and reconstructed mage s very small. A hgher PSNR ndcate that the reconstructon s of hgher qualty. It can also be stated from the observaton that PSNR s good for Water cube as compared to buldng cube may be due to spectrometer range. References [1] Z. Xong, O Guleryuz, M T Orchard, A DCT-based embedded mage Coder, IEEE Sgnal Processng Letters,1996,3(11): [2] D. Slepan, and J. K. Wolf. Noseless codng of correlated nformaton sources, IEEE Trans. on Inform. Theory, IT- 19(4): , July [3] D. Wyner, J. Zv. The rate-dstorton functon for source codng wth sde nformaton at the decoder. IEEE Trans. on Informaton Theory, 1976, 22(1): [4] A. Nonns, M. Grangetto, E. Magl. Improved lowcomplexty ntra-band lossless compresson of hyperspectral mages by means of Slepan-Wolf codng. Proc. of IEEE Internatonal Conference on Image Processng, 2005: [5] E. Magl, M. Barn, A. Abrardo. Dstrbuted source codng technques for lossless compresson of hyperspectral mages. EURASIP Journal on Appled Sgnal Processng,2007. [6] A. D. Lvers, Z. Xong, C. N. Georghades. Compresson of bnary sources wth sde nformaton at the decoder usng LDPC codes. IEEE Communcaton Letters, 2002, 6(1): [7] C. Tang, N. M. Cheung, A. Ortega. Effcent nterband predcton and wavelet-based compresson for hyperspectral magery: a dstrbuted source codng approach. Proc. of IEEE Data Compresson Conference, 2005: [8] N. M. Cheung, C. Tang, A. Ortega. Effcent wavelet-based predctve Slepan-Wolf codng for hyperspectral magery. Sgnal Processng, 2006, 86(11): [9] Z. Xong, K. Ramchandran, M. T. Orchard, and Ya-Qn Zhang, A comparatve study of DCT- and wavelet-based mage codng, IEEE Transactons on Crcuts and Systems for Vdeo Technology, VOL. 9, NO. 5, August 1999: [10] J. Chen, C. WU, An effcent embedded subband codng algorthm for DCT mage compresson, Proceedngs of SPIE, Vol (2001):44-48.

8 284 [11] Janrong Wang, & Rongke Lu. Low Complexty DCT- Based Dstrbuted Source Codng for Hyperspectral Image. Natonal Natural Scence Foundaton of Chna (No ) [12] Todd Owen, Scott Hauck. Arthmetc Compresson on SPIHT Encoded Images. Unversty of Washngton, Dept. of EE, UWEETR May 2002 [13] E. Baccagln, M. Barn, L. Capobanco, et al. Lowcomplexty lossless compresson of hyperspectral mages usng scalar coset. [14] J.Lee, Optmzed quadtree for Karhunen-Loeve transform n multspectral mage codng, IEEE Trans. On Imege Processng, Vol.8, No. 4, pp , Aprl [15] Meena B. Vallakat was born n Mumba(Maharashtra), Inda, on December 21, She receved her bachelor s degree n electroncs and telecommuncaton engneerng from North Maharashtra Unversty, Maharashtra, Inda, n May From 2008 to 2011, she was wth Rzv College of engneerng as Lecturer. She s currently pursung master s degree n electroncs and telecommuncaton from Mumba Unversty and currently workng at VIVA nsttute of Technology, Mumba, Inda. Her area of nterest s n the feld of mage compresson for remote sensng applcatons. Dr. R. R. Sedamkar receved hs bachelor s degree n computer scence engneerng n 1991, masters degree n Computer scence engneerng n 1997 and the Ph.D. degree n He s currently Dean-Academcs, Professor and Head of Computer Department at Thakur college of engneerng and technology, Mumba. Hs area of nterests s Networkng and Image compresson.