Sparse Banded Matrix Filter for Image Denoising

Transcription

1 Inin Journl of Science n Technology, Vol 8(24), DOI: /ijst/2015/v8i24/80153, September 2015 ISSN (Print) : ISSN (Online) : Sprse Bne Mtrix Filter for Imge Denoising V. Sowmy *, Neethu Mohn n K. P. Somn Centre for Excellence in Computtionl Engineering n Networking, Amrit Vishw Viypeethm, Amrit Ngr, Coimbtore , Tmil Nu, Ini; v_sowmy@cb.mrit.eu, neethumohn.nkm@gmil.com, kp_somn@mrit.eu Abstrct Noise is one of the prime fctors which egre the qulity of n imge. Hence, imge enoising is n essentil imge enhncement technique in the imge processing omin. In this pper, we use low-pss sprse bne filter mtrices for imge enoising. Sprsity is the key concept in this filter esign. We pplie the esigne low-pss filter both row-wise n column-wise to enoise the imge. The propose metho is experimente on stnr test imges corrupte with ifferent types of noises nmely Gussin, White Gussin, Slt & Pepper n Speckle with noise level equls to 0.01, 0.05 n 0.1. The effectiveness of the propose metho of enoising is evlute by the computtion of stnr qulity metric known s Pek Signl-to-Noise Rtio (PSNR). The experimentl result nlysis shows tht the propose imge enoising technique bse on sprse bne filter mtrices results in significnt improvement in PSNR roun 2B to 8B for ifferent type of noises with noise level equl to 0.1 n is lso ie by the visul nlysis. Keywors: Imge Denoising, Low-pss Filter, Noise, Sprse Bne Filter 1. Introuction The igitl imges re usully corrupte with noises ue to vrious sources such s, imge cquisition, bckgroun illumintions, sensors, processors n trnsmission chnnels. All these kin of noises will egre the qulity of the imges. Imge enoising is the process of removing noisy content from the imges in orer to improve the qulity of the imges for further processing. Imge enoising is n essentil requirement in meicl ignosis 1. It is wiely exploite for processing stellite imges, since those imges re usully corrupte with high egree of noises 2. The noise level in ech bns re ifferent in hyperspectrl imges n hence the enoising is complicte tsk in hyperspectrl imgery 3. The ocument imges hve complex bckgroun non uniform illumintion n noises. Hence imge enoising techniques re pplie in Opticl Chrcter Recognition (OCR) 4. Vieo nlysis, object recognition, imge restortion, imge segmenttion n pttern nlysis re some of the omins which require efficient noise removl. Imge enoising is wie re of reserch n severl lgorithmic pproches hve been propose for enoising the imges. A moifie non-locl mens metho for ultrsoun imge enoising is propose 1. An imge enoising lgorithm bse on non-locl thresholing n wvelet omin shrinkge is use for Synthetic Aperture Rr (SAR) imge enoising 2. A noise juste itertive low rnk mtrix pproximtion for hyperspectrl imge enoising is propose 3. An itertive regulrize frmework is opte in this pproch for noise removl. A iscrete curvelet trnsform bse imge enoising is propose for OCR pplictions 4. The sprse representtion n ege preservtion cpbility of curvelet trnsform is use for bckgroun noise removl from OCR imges. The concept of wvelet trnsforms long with wvelet shrinkge n thresholing techniques re wiely utilize for imge enoising purpose 5,6. The sprsity bse ictionry pproch is gretly employe in imge enoising frmework 7,8. Three imensionl over complete wvelet ictionry bse hyper spectrl imge enoising is propose in 9. Multi scle sprse representtion metho with non-seprble wvelet is use for imge enoising 10. *Author for corresponence

2 Sprse Bne Mtrix Filter for Imge Denoising An over complete ictionry bse imge enoising lgorithm combine with K-SVD n OMP is use for imge enoising 11. An imge enoising metho bse on Mrkov Rnom Fiel (MRF) n Mximum Posteriori (MAP) is propose 12. MRF is two imensionl rnom process efine on iscrete lttice. In 13, n impulsemowing nisotropic iffusion filter is use for noise removl. This filter pproch hs been efficiently pplie for removing combine Gussin noise n rnom vlue impulses. A Filtering-Direction-Controlle Digitl Totl-Vrition Filter (FDC-DTVF) pproch for rel time enoising is propose 14. Qing Guo et l 15. propose Singulr Vlue Decomposition (SVD) bse metho for efficient imge enoising. Non-locl self similrity n low-rnk pproximtion re use here for enoising tsk. In 16, Jussi Mtt et l. evelope n iterte mein filter pproch with utomtic winow selection for imge noise removl. In 17, bi-imensionl empiricl moe ecomposition is exploite for the enoising purpose of Groun Penetrting Rr (GPR) imges. An imge enoising techniques for uner wter imges bse on ptive wvelet trnsform n ptive thresholing is propose 18. In this pper, we pplie low-pss sprse bne filter mtrices esigne by Selesnick et l. 19 for imge enoising. We pplie the esigne low-pss filter both row-wise n column-wise to enoise the imge. The propose metho is experimente on stnr test imges corrupte with ifferent types of noises with vrying noise level. The effectiveness of the propose metho of enoising is evlute by visul effect n by the computtion of stnr qulity metric known s Pek Signl-to-Noise Rtio (PSNR). 2. Propose Metho for Imge Denoising The propose metho uses the sprse bne filter mtrices esigne by Selesnick et l. 19 to remove the noise from the imges. In this section, the sprse bne low pss filter esign is iscusse followe by the propose imge enoising technique. 2.1 Bne Filter Mtrices The esign n implementtion of zero-phse non-cusl recursive high-pss n low-pss filters in terms of bne mtrices re well expline in 19. Let us consier the ifference eqution of the first-orer Butterworth high-pss filter s, yn ( ) + yn ( 1) = xn ( ) xn ( 1) (1) 0 1 where x(n), y(n) re the sequence of input signl n the filter output respectively. This cn be written in mtrix form s, A= Ay = Bx (2) (3) 1 1 B= 1 (4) where A n B re the bne mtrices of size (N 1) (N 1) n (N 1) (N) respectively, is given in (3) n (4) respectively. The length of the input signl is represente by N. The filter output y of size ((N 1) 1) cn be obtine for the input signl x by, -1 y = A Bx (5) The trnsfer function of the zero-phse non-cusl higher-orer () high-pss Buttterworth filter is, Bz () ( z+ 2 z ) Hz () = = (6) 1 1 Az () ( z + 2 z ) + ( z z ) The bove eqution cn lso be written s, α ( z+ 2 z ) Hz = (7) + +α + + () 1 ( 2 ) ( 2 ) z z z z The frequency response of this filter is unity gin t ω = π, since the secon term of the numertor becomes zero when z = 1, n its first 2-1 erivtives re zero there. Therefore, the frequency response is mximlly flt t ω = 0, hence this is zero-phse igitl filter. The filter is efine by the positive integer n by α. The prmeter α cn be set so tht the frequency response hs specifie cut-off frequency ω c. 2 Vol 8 (24) September Inin Journl of Science n Technology

3 V. Sowmy, Neethu Mohn n K. P. Somn Solving for α gives, (1 cos wc ) α= (1 + cos w ) c (8) Bse on the high-pss filter given in (7), the low pss filter L(z) =1 H(z) hs the trnsfer function, α ( z+ 2 z ) Lz = (9) + +α + + () 1 ( 2 ) ( 2 ) z z z z with 2-orer zero t z = 1. The low-pss filter eqution is given by, y xˆ A Bx -1 = (10) The zero-phse low-pss Butterworth filter given in (9) cn be implemente using (10). B is bne sprse mtrix of size (N 2) (N); A is squre symmetric bne sprse mtrix of size (N 2) (N 2). Both the sprse bne mtrices hve igonls bove n below the min igonl. The imension of x is (N 2) 1. x is obtine by removing first smples n lst smples from x. 2.2 Imge Denoising using Sprse Bne Filter Mtrices In the propose metho, the sprse bne low-pss filter is pplie row-wise n column-wise to remove the noise in the imge. The block igrm of the propose methoology of imge enoising is shown in Figure 1. The propose metho consists of the following steps: Let us consier n input imge x R M N, whose row n column is represente s x r R N n x c R M respectively. The input imge is subjecte to borer repetition, which is represente by x R (M+2) (N+2), where refers to the orer of the filter. Therefore, the size of sprse bne mtrices A n B is (N N) n (N (N+2)) respectively. Figure 1. Block igrm of the propose metho of imge enoising. Ech row of the imge represente s X r R(N+2), is psse s n input to the (10) to obtin the filter output, y r R N. r r r y = x A BX (11) The bove step is repete for ll the rows in the input imge n is represente s, Y r R M N. The sme proceure (steps (3)-(4)) is repete for ech column of the imge, X c R (M+2). The filter output sequence for ech column is mthemticlly expresse s y r R N, where -1 c c c y = x A BX (12) All the columns operte in the imge re represente s Y c R M N. The enoise output imge is obtine by, ( Yr + Yc) Y = (13) 2 3. Experimentl Results n Anlysis In our propose metho, the low-pss sprse bne mtrix filter is use for imge enoising. The filter is esigne with the following input prmeters: egree = 2, cut-off frequency = 0.9 n length of sequence = 262. The experiment is performe on vrious stnr imges nmely, cmermn, Len, peppers, Brbr, bot n house. The ifferent noise type consiere re Gussin, White Gussin, Speckle n Slt & Pepper with ifferent noise level equl to n 0.1. The specifie noise levels inictes the men vlues in the cse of Gussin noise with vrince equl to In cse of White Gussin n Speckle noise, the noise level refers to locl vrince with zero men. The noise ensity of the Slt & Pepper noise is efine by the noise level. All the input noisy imges re resize to To mtch the input length sequence to the filter, the input imge is converte to by borer repetition. The enoise output obtine by our propose technique for ifferent noises on vrious stnr imges with noise level 0.1 is shown in Figure 2 Figure 7. The visul effect of the propose metho for imge enoising is ie by the qulity metric mesurement. The Pek-Signl-to- Noise Rtio (PSNR) compute for ifferent noises with noise level 0.01,0.05 n 0.1 for vrious stnr imges re tbulte in Tble 1 Tble 3. Vol 8 (24) September Inin Journl of Science n Technology 3

4 Sprse Bne Mtrix Filter for Imge Denoising Figure 4. Denoise output of peppers imge for ifferent noises with noise level = 0.1. Figure 5. Denoise output of Brbr imge for ifferent noises with noise level = 0.1. Figure 2. Denoise output of cmermn imge for Figure 5. Denoise output of Brbr imge for ifferent ifferent noises with noise level = 0.1. Figure 2. Denoise output of cmermn cmermn imge imgefor forifferent ifferentnoises noiseswith withnoise noiselevel level== noises with noise level = 0.1. Figure 3. Denoise output output of of Len Len imge imgefor forifferent ifferentnoises noiseswith withnoise noiselevel level== Figure 3. Denoise output of Len imge for ifferent noises with noise level = 0.1. FigureFigure Denoise offorbot Denoise output output of bot imge ifferentimge noises withfor noiseifferent level = 0.1. noises with noise level = Imge Denoising using Sprse Bne Filter Mtrices In the propose metho, the sprse bne low-pss filter is pplie row-wise n column-wise to remove the noise in the imge. The block igrm of the propose methoology of imge enoising is shown in Figure 1. The propose metho consists of the following steps: x Let us consier n input imge x R M u N, whose row n column is represente s xr R N n xc R M respectively. x The input imge is subjecte to borer repetition, which is represente by X R( M 2 )u( N 2 ), where refers to the orer of the filter. Therefore, the size of sprse bne mtrices A n B is ( N u N ) n ( N u ( N 2 )) respectively. Figure 4. Denoise output of peppers imge for ifferent noisesfigure with4.noise 0.1. imge for ifferent noises with noise level = 0.1. Denoiselevel output = of peppers 4 Figure Figure 7. Denoise output of house imge fornoise ifferent 7. Denoise output of house imge for ifferent noises with level = 0.1. noises with noise level = 0.1. x Vol 8 (24) September Ech row of the imge represente s X r R ( N 2 ), is psse s n input to the (10) to obtin the filter output, yr R N. Journl of Science n Technology yrinin xr A-1 BX r x The bove step is repete for ll the rows in the input imge n is represente s, Yr R M u N. ( M 2 )

5 V. Sowmy, Neethu Mohn n K. P. Somn Tble 1. Noise Type Pek Signl-to-Noise Rtio (PSNR) for ifferent noises with noise level = 0.01 on stnr imges Cmermn Len Peppers Brbr Bot House Noise Denoise Noise Denoise Noise Denoise Noise Denoise Noise Denoise Noise Denoise Gussin White Gussin Speckle Slt & Pepper Tble 2. Noise Type Pek Signl-to-Noise Rtio (PSNR) for ifferent noises with noise level = 0.05 on stnr imges Cmermn Len Peppers Brbr Bot House Noise Denoise Noise Denoise Noise Denoise Noise Denoise Noise Denoise Noise Denoise Gussin White Gussin Speckle Slt & Pepper Tble 3. Noise Type Pek Signl-To-Noise Rtio (PSNR) for ifferent noises with noise level = 0.1 on stnr imges Cmermn Len Peppers Brbr Bot House Noise Denoise Noise Denoise Noise Denoise Noise Denoise Noise Denoise Noise Denoise Gussin White Gussin Speckle Slt & Pepper From the experimentl result nlysis, it is evient tht the propose enoising technique removes the vrious types of noise with noise level less thn or equl to 0.1. From Tble 1, it is evient tht the propose enoising methoology results in the significnt improvement in PSNR for ifferent noises on vrious stnr imges with noise level equl to The PSNR improvement is roun 5b for Gussin n White Gussin n 3B for Speckle n Slt n Pepper noise. The propose metho is experimente for ifferent noises on vrious stnr imges with noise level equl to The PSNR vlue is increse roun 2 B for Gussin noise, 6B for White Gussin noise, 7B for Speckle n 8B for Slt n Pepper noise with noise level equl to 0.05 for vrious stnr imges, which is tbulte in Tble 2. Similrly, Tble 3 shows tht for noise level equl to 0.1, the PSNR vlue is improve roun 2B, 8B n 7B for Gussin, White Gussin, Speckle n Slt & Pepper noise respectively. Figure 2 Figure 7 shows the visul emphsis of the qulity metric compute for the propose metho experimente for ifferent noises on vrious stnr imges with noise level equl to 0.1 tbulte in Tble Conclusion Imge enoising bse on sprse bne filter mtrices is propose in this pper. The esigne filter is pplie row-wise n column-wise to enoise the imge. The propose technique is experimente on stnr test imges Vol 8 (24) September Inin Journl of Science n Technology 5

6 Sprse Bne Mtrix Filter for Imge Denoising subjecte to ifferent noises with vrying noise level. The effectiveness of enoising by our propose technique is prove by the significnt improvement in stnr qulity metric known s PSNR ie by the visul nlysis. 5. References 1. De Fontes FPX, Brroso GA, Coupe P, Hellier P.Rel time ultrsoun imge enoising. Journl of Rel-Time Imge Processing. 2011; 6(1): Sr P, Poerico M, Angelino CV, Veroliv L. A nonlocl SAR imge enoising lgorithm bse on LLMMSE wvelet shrinkge. IEEE Trnsctions on Geoscience n Remote Sensing. 2012; 50(2): He W, Zhng H, Zhng L, Shen H. Hyperspectrl imge enoising vi noise-juste itertive low-rnk mtrix pproximtion. IEEE Journl on Selecte Topics in Applie Erth Observtions n Remote Sensing p Ptvrhn C, Verm AK, Vsnth Lkshmi C. Document imge enoising n binriztion using Curvelet trnsform for OCR pplictions. IEEE Nirm University Interntionl Conference on Engineering (NUiCONE); p Zho S, Yunpeng L. A novel imge enosing scheme vi combining ul-tree complex wvelet trnsform n bnelets. 3r Interntionl Symposium on Intelligent Informtion Technology Appliction (IITA); p Yin S, Co L, Ling Y, Jin G. Imge enoising with nisotropic bivrite shrinkge. Signl Processing. 2011; 91(8): Yng R, Ren M. Lerning overcomplete ictionries with ppliction to imge Denoising. Symposium on Photonics n Optoelectronic (SOPO); p Hung D-E, Kng L-W, Wng Y-CF, Lin C-W. Self-lerning bse imge ecomposition with pplictions to single imge enoising. IEEE Trnsctions on Multimei. 2014; 16(1): Rsti B, Sveinsson JR, Ulfrsson MO, Beneiktsson JA. Hyperspectrl imge enoising using 3D wvelets. IEEE Interntionl Geoscience n Remote Sensing Symposium (IGARSS); p Zeng W, Zhou L, Xu R, Li B. Multi-scle sprse enoising moel bse on non-seprble wvelet. IEEE Interntionl Conference on Security, Pttern Anlysis n Cybernetics (SPAC); p Chen Y, Zhn Y. A fst imge enoising lgorithm vi over-complete ictionry. IEEE Interntionl Conference on Progress in Informtics n Computing (PIC); p Suresh KV. Imge enoising: A DAMRF moel. IEEE 5th Interntionl Conference on Signl n Imge Processing (ICSIP); p Kim H, Kim S. Impulse-mowing nisotropic iffusion filter for imge enoising. IEEE Interntionl Conference on Imge Processing (ICIP); p Kent S, To M, Tsuk M. Efficient implementtion of filtering-irection-controlle igitl TV filter for imge enoising. IEEE Interntionl Conference on Consumer Electronics (ICCE); p Guo Q, Zhng C, Zhng Y, Liu H. An Efficient SVD- Bse Metho for Imge Denoising. IEEE Trnsctions on Circuits n Systems for Vieo Technology. 2015; p Mtt J, Siltnen S, Roos T. A fixe-point imge enoising lgorithm with utomtic winow selection. Proceeings of the 5th Europen Workshop on Visul Informtion Processing (EUVIP); Gn L, Zhou L, You X. A new GPR imge e-nosing metho bse on BEMD. IEEE Interntionl Conference on Security, Pttern Anlysis n Cybernetics (SPAC); p Gn L, Zhou L, You X. The reserch of unerwter imge e-noising metho bse on ptive wvelet trnsform. IEEE 26th Chinese Control n Decision Conference (CCDC); p Selesnick IW, Grber HL, Pfeil DS, Brbour RL. Simultneous low-pss filtering n totl vrition enoising. IEEE Trnsctions on Signl Processing p Vol 8 (24) September Inin Journl of Science n Technology