SPECKLE NOISE REDUCTION IN SAR IMAGING USING 2-D LATTICE FILTERS BASED SUBBAND DECOMPOSITION

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1 7th Europan Signal Procssing Confrnc EUSIPCO 9 Glasgow Scotland August SPECKLE REDUCTION IN SAR IMAGING USING -D LATTICE FILTERS ASED SUAND DECOMPOSITION Göhan Karasaal N.. Kaplan I. Err Informatics Institut Advancd Tchnologis in Enginring Satllit Communications and Rmot Snsing Istanbul Tchnical Univrsity Masla Istanbul 4469 TURKEY Faculty of Elctrical and Elctronic Enginring Elctronics and Communication Dpartmnt Istanbul Tchnical Univrsity Masla Istanbul 4469 TURKEY mail: irr@itu.du.tr ASTRACT A nw spcl rduction algorithm basd on -D lattic filtrs for SAR imaging is prsntd. In th nw mthod th subband dcomposition of th spcld imag is prformd using -D lattic filtrs. Th noisy imag is dcomposd into subband imags using high-pass and low-pass filtrs having lattic structur thn a thrshold valu is stimatd according to nois varianc in ach subband and soft-thrsholding is applid on th subband imags. Th dspcld imag is obtaind from th thrsholdd subband imags using th invrs lattic filtrs. Th proposd spcl rduction mthod is applid to RADARSAT/SAR imags. Th prformanc of th proposd mthod has also bn compard with mdian filtring and stationary wavlt transform basd spcl rduction mthods. Rsults show that th proposd mthod may b usd fficintly for spcl nois rduction in SAR imags.. INTRODUCTION Synthtic Aprtur Radar SAR systms which ar abl to oprat undr all wathr conditions hav a significant rol in th obsrvation and collction of th ground information. owvr du to cohrnt microwav illumination SAR imags ar oftn corruptd by multiplicativ spcl nois. Thus rmoval of nois without blurring th dgs is an important problm in SAR imaging. Classical approachs to spcl nois rduction problm in SAR imaging may b citd as mdian filtring [] local statistical mthods [] homomorphic filtring [] and wavlt basd mthods [4 5]. In wavlt basd dnoising mthods th spcld imag is dcomposd into subband imags using discrt or stationary wavlt transforms thn hard or soft thrsholding mthods ar applid on th ths subband imags which corrspond to wavlt approximation or dtail cofficints. Th dnoisd imag is obtaind by applying th invrs transform on ths thrsholdd subband imags. sids th wavlt basd dnoising tchniqus a nw spcl rduction algorithm using a novl multidcomposition approach basd on ral discrt Fourir transform RDFT digital filtr ban rprsntation has bn prsntd rcntly [6]. In this tchniqu th low-pass and high-pass subband componnts ar obtaind in a tr structur using ro-phas filtrs implmntd by RDFT. Th input imag is dcomposd in multipl lvls and thn a thrshold valu is stimatd according to th nois varianc in ach subband and usd for soft-thrsholding of th subband cofficints. Th dnoisd imag is obtaind from th subband imags by a nw prfct rconstruction algorithm. In this papr w prsnt a nw spcl rduction algorithm basd on -D lattic filtrs for SAR imaging. In th nw mthod th subband dcomposition of th spcld imag is prformd using -D nonsparabl lattic filtrs. Lattic filtrs ar usd in digital filtr implmntations bcaus thy hav a numbr of intrsting and important proprtis including modularity low snsitivity to paramtr quantiation ffcts and a simpl stability tst [7]. Two channl QMF quadratur mirror filtr ban with lattic structur has prfct rconstruction proprty whil it guarants good stop band attnuation for ach of th analysis filtrs. Du to th us of lattic structur a highr ordr prfct rconstruction QMF ban can b obtaind from a lowr ordr prfct rconstruction QMF ban simply by adding mor lattic sctions [8]. Th analysis sction of th complt filtr ban is rprsntd by a lattic filtr whil th synthsis part is rprsntd by th invrs lattic filtr. Th noisy imag is dcomposd into subimags using high pass and low-pass filtrs having lattic structur also appropriat lattic paramtrs and lattic stags ar chosn thn a thrshold valu is stimatd according to nois varianc in ach subband and soft-thrsholding is applid on th subband imags. Th dspcld imag is obtaind from th thrsholdd subband imags using th invrs lattic filtr. This papr is organid as follows: brif information about th subband dcomposition basd on lattic filtrs is givn in Sction. Th proposd spcl rduction mthod which uss lattic filtrs basd subband dcomposition is prsntd in Sction. In Sction 4 rsults of -D lattic filtrs basd spcl nois rduction and traditional spcl rduction tchniqus such as mdian filtring and stationary wavlt transform SWT ar givn. Sction 5 prsnts gnral conclusions.. REVIEW OF LATTICE FILTERS -D lattic filtr of [9] has rflction cofficints in vry stag and xpands by assuming that input data has 4 quadrant symmtry. Th filtr has 4 prdiction rror filds can b dfind as rcursiv input-output quation blow. EURASIP 9 598

2 n n n n = n n n n x m m m m n n n n n n n n whr m = mm = and n = N n = N m =... M j ar lattic rflction cofficints of th stag. M is th lngth of filtr. Th initial conditions ar: n n = n n = n n = n n = x n n m n n m n n m n n m and n n ar th prdiction rror filds of st nd rd and 4 th quadratur plan prdiction rror filds of th mth lattic stag. xn n dfins D input data. D transfr functions of quadratur plain filtrs can b dfind in th trms of lattic cofficints. th stag cofficint matrix for D transfr function is: ^ = ^ ^ ^ whr is cofficint matrix rlatd with forward prdiction rror filtr and and ar cofficint matrixs rlatd with bacward prdiction rror filtrs []. Transfr functions of forward and bacward prdiction rror filtrs ar blow: m + m + m + m + = b j l j= l = = = = 4.a 4.b 4.c 4.d Additional and mor dtaild information about 4 channl filtr ban dsign can b found in [].. LATTICE FILTERS ASED SPECKLE REDUCTION. Wavlt asd Spcl Nois Rduction Thr ar lots of approachs in spcl nois rduction sinc spcl nois rduction in SAR imaging without blurring th dgs is an important problm. Espcially wavlt basd tchniqus ar widly usd in spcl nois rduction. In wavlt basd dnoising mthods th spcld imag is dcomposd into subband imags using discrt or stationary wavlt transforms thn hard or soft thrsholding mthods ar applid on th ths subband imags which corrspond to wavlt approximation or dtail cofficints. low is th most widly usd soft thrsholding quation []: T S s g n Y Y δ Y δ Y δ = Y < δ Thrshold δ is stimatd by using Y wavlt cofficints. Thr is a simpl quatition in ordr to stimat δ thrshold: h I δ = ƒ σ = ƒ C m 6 h I Z h I a N h I whr N is imag data numbr m is th man of th C wavlt cofficints and I is dcomposition lvl and ƒ a a is sistmatically I dtrmind thrshold factor []. Aftr applying thrsholding on th subband imags th dnoisd imag is obtaind by applying th invrs wavlt transforms on ths thrsholdd subband imags.. Lattic Filtr asd Spcl Nois Rduction Evry rror fild of th -D lattic filtr is arrangd as to b qual to a subband of 4 channl filtr ban by maing appropriat changs on ths rror filds. LL L and L subband imags ar qual to subbands in th Figur rspctivly. -D lattic filtrs whos transfr functions ar arrangd to crat ths 4 subbands can b sparat to 4 filtrs. Simply whn on of ths filtrs is dfind in trms of lattic paramtrs th othr filtrs can b obtaind from this filtr with appropriat latncis []. w Figur 4 ands of -D Spctrum = 7.a = 7.b = 7.c π π/ L LL w L π/ π 5 599

3 Th rror filds ar obtaind starting from th stag filtr as blow: X = X = X = X = X 8 can b dfind in trms of lattic paramtrs as: = 9 Input-output quation of analysis lattic filtr is givn as []: X X X X = m X. m X x m X m X whr m=..m- and X X X and X ar th lvl lattic filtr outputs and thy corrspond to LL L L and subband imags. Using th optimiation algorithm dvlopd in [] th lattic cofficints ar dtrmind so as to minimi th stop band nrgy in th frquncy domain. Although analysis lattic filtr has 4 filtrs for vry stag it is nough to considr only on sinc thy ar shiftd vrsions of ach othr. If w choos as LL filtr targt will b to minimi th nrgy out of th th ara shown in th Figur. jw jw = dwdw ' w w R ' R w w w w R Φ = π. whr { } Transfr function of th stag filtr abov can b writtn in trms of m-th stag filtr. For st stag; jw jw jw jw jw jw = δ [ ] with initial conditions: jw jw jw jw jw jw jw jw = = = = Lattic cofficints can b calculatd by qualiing gradint of targt function du to lattic cofficints to ro. Th us of lattic structur yilds th combination of 4 analysis subband filtrs into a singl structur in th typ of lattic and on can obtain high lvl filtr bans using hirarchical fatur of lattic structurs asily. Th proposd spcl rduction algorithm may b summarid as follows: Stp : Th spcld imag is dcomposd into subbands using -D lattic filtr. Lattic paramtrs and lattic stags ar chosn suitabl according to th situation. Stp : As similar to wavlt basd spcl nois rduction mthod a thrshold valu is stimatd according to nois varianc in ach dtail subband and soft-thrsholding is applid by using th quations 5 and 6. Stp : Th dspcld imag is obtaind from th thrsholdd subband imags using th invrs lattic filtr. Figur Flow-chart for th proposd spcl rduction mthod 4. RESULTS Th proposd spcl rduction mthod is applid to svral tst imags corruptd by spcl nois as wll as xprimntal RADARSAT/SAR imags. Th prformanc of th proposd mthod has also bn compard with mdian filtring and stationary wavlt transform basd spcl rduction mthods by calculating PSNR Pa Signal to Nois Ratio. Rsults can b sn in Tabl Tabl and Tabl for diffrnt tst imags. PSNR and MSE ar givn as: P S N R 5 5 d M S E = lo g M S E = X P Spcld imag Dcomposition into subimags using Lattic Filtrs Soft thrsholding in dtail subband imags Rconstruction using th invrs Lattic Filtrs 4 K 5 K i = whr X is original imag P is noisy imag and K is th dimnsion of th imag. Figur a b c d and Figur 4 a b c d shows th spcld imag and dspcld imags using mdian filtring stationary wavlt transform and proposd mthods rspctivly. Figurs show that -D lattic filtr basd spcl nois rduction tchniqu is vry succssful in spcl nois rduction. And also whn it is compard with th othr succssful mthods it may b usd fficintly for spcl nois rductions in SAR imags and may b an altrnativ to th othr widly usd mthods. 5. CONCLUSIONS In this wor a nw spcl rduction mthod which uss - D lattic filtrs basd subband dcomposition is prsntd. Th prformanc of th proposd mthod has also bn compard 6

4 with mdian filtring and stationary wavlt transform basd spcl rduction mthods. Although wavlt transform spcially Wavlt has an important plac in succssful spcl nois rduction mthods th proposd lattic filtrs basd mthod is an important altrnativ bcaus of its simplicity and rduc complxity compard to th widly usd wavlt transform basd mthods. In addition th proposd lattic filtrs basd mthod wors fastr than wavlt transform basd spcl rduction mthods and has a structur which is applicabl to vry typ of imags. Rsults also show that th proposd mthod may b an altrnativ to th widly usd wavlt transform basd mthods for spcl nois rduction in SAR imags. REFERENCES [] J.S.Lim99. Two Dimnsional Signal and Imag procssing Prntic-all Englwood Cliffs NJ [] J.S. L 986. Spcl supprssion and analysis for synthtic aprtur radar imags Opt. Eng [].. Arsnault M. Lvsqu984. Combind homomorhic and local-statistics procssing for rstoration of imags dgradd by signal dpndnt nois. APPL. OPT [4] D.L. Donoho995. Dnoising by soft thrsholding. IEEE Trans. Inform. Thory [5] J. Zhang X. Chng J. Liu 998. A spcl rduction algorithm by softthrsholding basd on wavlt filtrs for SAR imags Procdings of th 4th Int. Conf. on Signal Procssing [6] M. Sgin I. Err v O. K. Ersoy DFT/RDFT Filtr an Approach to Spcl Rduction in SAR Imags th IEEE Goscinc and Rmot Snsing Symposium IGARSS5 5-9 July 5 Soul Kora [7] P.P. Vaidyanathan P.Q. oang Lattic Structurs for Optimal Dsign and Robust Implmntation of Two- Channl Prfct Rconstruction QMF ans IEEE Trans. ASSP Vol. 6 pp [8] N. J. Flig Multirat Digital Signal Procssing John Wily&Sons 994 [9] Parr S. R. and Kayran A Lattic Paramtr Autorgrssiv Modlling of Two Dimnsional Filds Part I: Th Quartr Plan Cas IEEE Transactions on Acoustics Spch and Signal Procssing ASSP- 4. [] Smith M. J. T. and arnwll T. P Exact Rconstruction for Tr-Structurd Subband Codrs IEEE Transactions on ASSP 4. [] Sn S. And Ertüün A. 6 D Four Channl Prfct Rconstruction Filtr an Ralid with th D Lattic Filtr Structur S. Sn and A. Ertüün EURASIP Journal on Applid Signal Procssing [] Dachasilaru S. Rangsansr Y. v Thitimahshima P Application of Multiscal Edg Dtction to Spcl Rduction of SAR Imags 55pf.htm a Original b Spcld tst imag c Mdian Filtr d SWT 6

5 a Original Proposd Mthod Fıgur a Original b spcld tst imag dspcld imags using c mdian filtring d SWT-basd mthod Lattic filtrs basd mthod. Mdian Filtr Wavlt SWT Proposd Mthod -D Lattic Filtr b Mdian Filtr Tabl PSNR rsults in d for dspcld Camraman tst imags with diffrnt mthods Mdian Filtr Wavlt SWT Proposd Mthod -D Lattic Filtr c SWT Tabl PSNR rsults in d for dspcld Ppprs tst imags with diffrnt mthods Mdian Filtr Wavlt SWT Proposd Mthod -D Lattic Filtr Tabl PSNR rsults in d for dspcld Lna tst imags with diffrnt mthods d Proposd Mthod Fıgur 4 a original dspcld imags using b mdian filtring c SWT-basd mthod d Lattic filtrs basd mthod. 6