Separation of Image Sources Using AMMCA Algorithm

Transcription

1 Separaton of Image Sources Usng AMMCA Algorthm Nmmy Nce.A 1, V.Vno Ruban Sngh PG student, Appled Electroncs, Loyola Insttute of echnology and Scence,Nagercol, Inda 1 nce4.nmmy@gmal.com 1 Assstant professor, Dept of ECE, Loyola Insttute of echnology and Scence,Nagercol, Inda Abstract-Sparsty has been shown to be very useful n source separaton of multchannel observatons. However, n most cases, the sources of nterest are not sparse n ther current doman and one need to sparsfy them usng a known transform or dctonary. If such a pror about the underlyng sparse doman of the sources s not avalable, then the current algorthms wll fal to successfully recover the sources. In ths paper, we address ths problem and attempt to gve a soluton va fusng the dctonary learnng nto the source separaton. We frst defne a cost functon based on ths dea and propose an extenson of the denosng method n the work of Elad and Aharon to mnmze t. Due to mpractcalty of such drect extenson, we then propose a feasble approach. In the proposed herarchcal method, a local dctonary s adaptvely learned for each source along wth separaton. Image compresson s done by usng Block runcaton Codng(BC). Keywords- Blnd Source Separaton(BSS),Adaptve Multchannel Component Analyss (AMMCA), Block runcatoncodng(bc). I. INRODUCION Input mage From deosng to source seperaton In sgnal and mage processng, there are many nstances where a set of observatons s avalable and we wsh to recover the sources generatng these observatons. hs problem, whch s known as blnd source separaton (BSS). Blnd source separaton by Independent Component Analyss (ICA) has receved attenton because of ts potental applcatons n sgnal processng such as n speech recognton systems, telecommuncatons and medcal sgnal processng. he goal of ICA Independent Component Analyss s to recover ndependent sources gven only sensor observatons that are unknown lnear mxtures of the unobserved ndependent source sgnals. In contrast to correlaton-based transformatons such as Prncpal Component Analyss(PCA), Independent Component Analyss ICA not only decorrelates the sgnals (ndorder statstcs) but also reduces hgher order statstcal dependences, attemptng to make the sgnals as ndependent as possble. here have been two dfferent felds of research consderng the analyss of ndependent components. On one hand, the study of separatng mxed sources observed n an array of sensors has been a classcal and dffcult sgnal processng problem. II. IMAGE DENOISING AMMCA algorthm Global dct. Vs dct. Result Local Consder a nosy mage corrupted by addtve nose. Elad and Aharon showed that f the knowledge about the nose power s avalable, t s possble to denose t by learnng a local dctonary from the nosy mage tself. In order to deal wth large mages, they used small (overlapped) patches to learn such dctonary. he obtaned dctonary s consdered local snce t descrbes the features extracted from small patches. Let us represent the nosy N x N mage y by vector y of length N. he unknown denosed mage x s also vectorzed and represented as x. he th patch from x s shown by vector R x of r<< N pxels. For notatonal smplcty, the th patch s expressed as explct multplcaton of operator R (a bnary r x N matrx) by x. he overall denosng problem s expressed as 115

2 mn λ y x µ S 0 D s R x D, { S },x Where scalars λ and µ control the nose power and sparsty degree, respectvely. In addton, rxk D R s the sparsfyng dctonary that contans normalzed columns (also called atoms), and { s } are sparse coeffcents of length. In the proposed algorthm by Elad and Aharon x and D, and are respectvely ntalzed wth y and overcomplete (r < k) dscrete cosne transform (DC) dctonary. he mnmzaton of starts wth extractng and rearrangng all the patches of x. he patches are then processed by K- SVD, whch updates D and estmates sparse coeffcents { } and x s estmated by computng s. Afterward, D and are assumed fxed 1 xˆ = λi R R λy R Ds Where I s the dentty matrx and xˆ s the refned s are updated by K- verson of x. Agan, D and { } SVD but ths tme usng the patches from xˆ that are less nosy. Such cononed denosng and dctonary adaptaton s repeated to mnmze. In practce, s obtaned computatonally easer snce R R s dagonal and the above expresson can be calculated n a pxel wse fashon. It s shown that s a knd of averagng usng both nosy and denosed patches, whch, f repeated along wth updatng of other parameters, wll denose the entre mage. However, n the sequel, we wll try to fnd out f ths strategy s extendable for the cases where the nose s added to the mxtures of more than one mage. Image Separaton Image separaton s a more complcated case of mage denosng where more than one mage are to be recovered from a sngle observaton. Consder a sngle lnear mxture of two textures wth addtve nose: =χ χ v(or x x v) y 1 1 he authors of attempt to recover and usng the pror knowledge about two sparsfyng dctonares D 1 and D. hey use a mnmum meansquared-error (MSE) estmator for ths purpose. In contrast, the recent work n does not assume any pror knowledge about the dctonares. It rather attempts to learn a sngle dctonary from the mxture and then apples a decson crteron to the dctonary atoms to separate the mages. In another recent work, Peyre et al. presented an adaptve MCA scheme by learnng the morphologes of mage layers. hey proposed to use both adaptve local dctonares and fxed global transforms (e.g., wavelet and curvelet) for mage separaton from a sngle mxture. her smulaton results show the effects of adaptve dctonares on separaton of complex texture patterns from natural mages. All the related studes have demonstrated the advantages that adaptve dctonary learnng can have on the separaton task. However, there s stll one mssng pece and that s consderng such adaptvty for the multchannel mxtures. Performng the dea of learnng local dctonares wthn the source separaton of multchannel observatons obvously has many benefts n dfferent applcatons. Next, we extend the denosng method n for ths purpose. Global Dctonares Versus Local Dctonares he proposed method takes the advantages of fully local dctonares that are learned wthn the separaton task. We call these dctonares local snce they capture the structure of small mage patches to generate dctonary atoms. In contrast, the global dctonares are generally appled to the entre mage or sgnal and capture the global features. Incorporatng the global fxed dctonares nto the proposed method can be advantageous where a pror knowledge about the structure of sources s avalable. Such combned local and global dctonares have been used n for sngle mxture separaton. Here, we consder the multchannel case and extend our proposed. Consder a known global untary N x N bass Φ for each source. he mnmzaton problem can be modfed as follows to capture both global and local structures of the sources: Note that term x Φ s exactly smlar to what was : 1 used n the orgnal MMCA. All varables n the above expresson can be smlarly estmated usng x sources. In order Algorthm 1, except the actual { } : 116

3 to fnd x, the gradent of wth respect to : zero, leadng to x s set to : λ I R R x : x : = λ E a: R D s β Φ sgn( Φ x : ) Where sgn(.) s a component wse sgnum functon. he above expresson amounts to soft thresholdng due to the sgnum functon, and hence, the estmaton of can be obtaned by the followng steps: Φ ~ x Soft thresholdng of α wth threshold β and attanng ˆα ; Reconstructng by xˆ : = λ I 1 R R Φ αˆ III. Note that, snce Φ s a untary and known matrx, t s not explctly stored but mplctly appled as a forward or nverse transform where applcable. Smlar to the prevous secton, the above expresson can be executed pxel wse and s not computatonally expensve. AMMCA ALGORIHM Morphologcal Component Analyss Morphologcal component analyss s a popular mage processng algorthm that extracts degradng patterns or textures from mages and smultaneously performs n pantng. he Morphologcal Component Analyss (MCA) s a new method whch allows us to separate features contaned n an mage when these features present dfferent morphologcal aspects. o extend MCA to a multchannel MCA (MMCA) for analyzng multspectral data and present a range of examples whch llustrates the results. FUURE ENHANCEMEN BC Algorthm Block runcaton Codng s used for future enhancement. After get the resultant mage to apply the encrypton standard. Step1: he gven mage s dvded nto non overlappng rectangular regons. For the sake of smplcty the blocks were let to be square regons of sze m x m. Step : For a two level (1 bt) quantzer, the dea s to select two lumnance values to represent each pxel n the block. hese values are the mean x and standard devaton (1) () Where x represents the th pxel value of the mage block and n s the total number of pxels n that block. Step3: he two values x and σ are termed as quantzers of BC.. We can use 1 to represent a pxel whose gray level s greater than or equal to x and 0 to represent a pxel whose gray level s less than 117

4 (3) Step 4: In the decoder an mage block s reconstructed by replacng 1 s n the bt plane wth H and the 0 s wth L, whch are gven by: (4) (5) Where p and q are the number of 0 s and 1 s n the compressed bt plane respectvely. IV. SIMULAED RESULS (d)separated by ammca [] (a)nosy mxture for two mages [1](a) Input Image (b)clear mage by dctonary (b)mxture mage (e)clear mage by dctonary (c)dctonary for mxture V. CONCLUSION In ths paper, the BSS problem has been addressed. he am has been to take advantage of sparsfyng dctonares for ths purpose. Unlke the exstng sparsty-based methods, assumed no pror knowledge about the underlyng sparsty doman of the sources. Instead, have proposed to fuse the learnng of adaptve sparsfyng dctonares for each ndvdual source nto the separaton process. Motvated by the dea of mage denosng va a learned dctonary from 118

5 the patches of the corrupted mage n, proposed a herarchcal approach for ths purpose. REFERENCES [1] A. onazzn, L. Bedn, E. E. Kuruoglu, and E. Salerno, Blnd separaton of autocorrelated mages from nosy mxtures usng MRF models, n Proc. Int. Symp. ICA, Nara, Japan, Apr. 003, pp [] onazzn, L. Bedn, and E. Salerno, A Markov model for blnd mage separaton by a mean-feld EM algorthm, IEEE rans. Image Process., vol. 15, no., pp , Feb [3] H.Snouss and A. Mohammad-Dafar, Fast ont separaton and segmentaton of mxed mages, J. Electron. Imagng, vol. 13, no., pp , Apr [4] E. Kuruoglu, A. onazzn, and L. Banch, Source separaton n nosy astrophyscal mages modelled by Markov random felds, n Proc. ICIP, Oct. 004, vol. 4, pp [5] M.M. Ichr and A. Mohammad-Dafar, Hdden Markov models for wavelet-based blnd source separaton, IEEE rans. Image Process., vol. 15, no. 7, pp , Jul [6] W. Addson and S. Roberts, Blnd source separaton wth non-statonary mxng usng wavelets, n Proc. Int. Conf. ICA, Charleston, SC, 006 [7] A.M. Bronsten, M. M. Bronsten, M. Zbulevsky, and Y. Y. Zeev, Sparse ICA for blnd separaton of transmtted and reflected mages, Int. J. Imagng Syst. echnol., vol. 15, no. 1, pp , 005. [8] M. G. Jafar and M. D. Plumbley, Separaton of stereo speech sgnals based on a sparse dctonary algorthm, n Proc. 16th EUSIPCO, Lausanne, Swtzerland, Aug. 008, pp [9] M. G. Jafar, M. D. Plumbley, and M. E. Daves, Speech separaton usng an adaptve sparse dctonary algorthm, n Proc. Jont Workshop HSCMA, rento, Italy, May 008, pp [10] J. Bobn, Y. Moudden, J. Starck, and M. Elad, Morphologcal dversty and source separaton, IEEE Sgnal Process. Lett., vol. 13, no. 7, pp , Jul. 006 [11] J. Bobn, J. Starck, J. Fadl, and Y. Moudden, Sparsty and morphologcal dversty n blnd source separaton, IEEE rans. Image Process., vol. 16, no. 11, pp , Nov [1] J. Starck, M. Elad, and D. Donoho, Redundant multscale transforms and ther applcaton for morphologcal component separaton, Adv. Imagng Electron Phys., vol. 13, pp , 004. [13] J.-L. Starck, M. Elad, and D. Donoho, Image decomposton va the combnaton of sparse representatons and a varatonal approach, IEEE rans. Image Process., vol. 14, no. 10, pp , Oct [14] M. Elad, J. Starck, P. Querre, and D. Donoho, Smultaneous cartoon and texture mage npantng usng morphologcal component analyss (MCA), Appl. Comput. Harmonc Anal., vol. 19, no. 3, pp , Nov [15] J. Bobn, J.-L. Starck, J. M. Fadl, Y. Moudden, and D. L. Donoho, Morphologcal component analyss: An adaptve thresholdng strategy, IEEE rans. Image Process., vol. 16, no. 11, pp , Nov Author Profle A.Nmmy Nce,P.G student n Loyola Insttute Of echnology & Scence.She has completed her U.G(B.E-ECE)degree n Noorul Islam College of Engneerng under Anna Unversty.Her Current research s Dgtal Image Processng. 119