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Volumn 20, Issue 5, 2011, Pages 1281-1299

An iterative shrinkage approach to total-variation image restoration

Author keywords

Inverse problems; iterative shrinkage; soft thresholding; sparse representations; total variation (TV)

Indexed keywords

DIGITAL IMAGE; FIRST-ORDER ALGORITHMS; ILL-CONDITIONED; IMAGE DEBLURRING; IMAGE RESTORATION; ITERATIVE SHRINKAGE; LARGE SIZES; LINEAR FILTERING; ORIGINAL IMAGES; PIECEWISE SMOOTH FUNCTIONS; PRIORI INFORMATION; RECURSIVE APPLICATIONS; SOFT THRESHOLDING; SPARSE REPRESENTATION; THRESHOLDING; TOTAL VARIATION; TV FUNCTIONAL;

EID: 79955401358     PISSN: 10577149     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIP.2010.2090532     Document Type: Article
Times cited : (72)

References (50)
  • 1
    • 68749119587 scopus 로고    scopus 로고
    • Deconvolution of medical images from microscopic to whole body images
    • P. Campisi and K. Egiazarian, Eds. Boca Raton, FL: CRC Press
    • O. Michailovich and D. Adam, "Deconvolution of medical images from microscopic to whole body images," in Blind Image Deconvolution: Theory and Applications, P. Campisi and K. Egiazarian, Eds. Boca Raton, FL: CRC Press, 2007, pp. 169-238.
    • (2007) Blind Image Deconvolution: Theory and Applications , pp. 169-238
    • Michailovich, O.1    Adam, D.2
  • 7
    • 36949053366 scopus 로고
    • Restoring atmospherically degraded images
    • S. P. Morgan, "Restoring atmospherically degraded images," Nature, vol. 213, no. 5080, pp. 965-969, 1967.
    • (1967) Nature , vol.213 , Issue.5080 , pp. 965-969
    • Morgan, S.P.1
  • 8
    • 0014509837 scopus 로고
    • Bandlimited image restoration by linear mean-square estimation
    • C. L. Rino, "Bandlimited image restoration by linear mean-square estimation," J. Opt. Soc. Amer., vol. 59, no. 5, pp. 547-553, 1969.
    • (1969) J. Opt. Soc. Amer. , vol.59 , Issue.5 , pp. 547-553
    • Rino, C.L.1
  • 10
    • 0001300994 scopus 로고
    • Solution of incorrectly formulated problems and the regularization method
    • A. N. Tikhonov, "Solution of incorrectly formulated problems and the regularization method," Soviet Math. Dokl., vol. 4, pp. 1035-1038, 1963.
    • (1963) Soviet Math. Dokl. , vol.4 , pp. 1035-1038
    • Tikhonov, A.N.1
  • 11
    • 44049111982 scopus 로고
    • Nonlinear total variation based noise removal algorithms
    • L. I. Rudin, S. Osher, and E. Fatemi, "Nonlinear total variation based noise removal algorithms," Phys. D, vol. 60, no. 1-4, pp. 259-268, 1992.
    • (1992) Phys. D , vol.60 , Issue.1-4 , pp. 259-268
    • Rudin, L.I.1    Osher, S.2    Fatemi, E.3
  • 13
    • 8744270279 scopus 로고    scopus 로고
    • Decomposition of images by the anisotropic Rudin-Osher-Fatemi model
    • DOI 10.1002/cpa.20045
    • S. Esedoglu and S. Osher, "Decomposition of images by the anisotropic Rudin-Osher-Fatemi model," Commun. Pure Appl. Math., vol. 57, pp. 1609-1626, 2004. (Pubitemid 39526435)
    • (2004) Communications on Pure and Applied Mathematics , vol.57 , Issue.12 , pp. 1609-1626
    • Esedoglu, S.1    Osher, S.J.2
  • 17
    • 25444480815 scopus 로고    scopus 로고
    • Blind deconvolution using TV regularization and Bregman iteration
    • DOI 10.1002/ima.20040, Blind Source Separation and De-convolution in Imaging and Image Processing
    • L. He, A. Marquina, and S. J. Osher, "Blind deconvolution using TV regularization and Bregman iteration," Int. J. Imag. Syst. Technol., vol. 15, no. 1, pp. 74-83, Jul. 2005. (Pubitemid 41364767)
    • (2005) International Journal of Imaging Systems and Technology , vol.15 , Issue.1 , pp. 74-83
    • He, L.1    Marquina, A.2    Osher, S.J.3
  • 18
    • 59649097565 scopus 로고    scopus 로고
    • Efficient minimization method for a generalized total variation functional
    • Feb.
    • P. Rodriguez and B. Wohlberg, "Efficient minimization method for a generalized total variation functional," IEEE Trans. Image Process., vol. 18, no. 2, pp. 322-332, Feb. 2009.
    • (2009) IEEE Trans. Image Process. , vol.18 , Issue.2 , pp. 322-332
    • Rodriguez, P.1    Wohlberg, B.2
  • 19
    • 0005352194 scopus 로고    scopus 로고
    • A nonlinear primal-dual method for total variation-based image restoration
    • T. F. Chan, G. H. Golub, and P. Mulet, "A nonlinear primal-dual method for total variation-based image restoration," in Lecture Notes in Control and Information Sciences. New York: Springer-Verlag, 1996, vol. 219, pp. 241-252. (Pubitemid 126087819)
    • (1996) Lecture Notes in Control and Information Sciences , Issue.219 , pp. 241-252
    • Chan, T.F.1    Golub, G.H.2    Mulet, P.3
  • 20
    • 33645038355 scopus 로고    scopus 로고
    • Second-order cone programming methods for total variation-based image restoration
    • D. Goldfarb and W. Yin, "Second-order cone programming methods for total variation-based image restoration," SIAM J. Sci. Comput., vol. 27, no. 2, pp. 622-645, 2006.
    • (2006) SIAM J. Sci. Comput. , vol.27 , Issue.2 , pp. 622-645
    • Goldfarb, D.1    Yin, W.2
  • 21
    • 51849127184 scopus 로고    scopus 로고
    • Parametric maximum flow algorithms for fast total variation minimization
    • Rice Univ., Houston, TX
    • D. Goldfarb and W. Yin, "Parametric maximum flow algorithms for fast total variation minimization," Rice Univ., Houston, TX, Rice CAAM Rep. TR07-09, 2009.
    • (2009) Rice CAAM Rep. TR07-09
    • Goldfarb, D.1    Yin, W.2
  • 22
    • 0031492191 scopus 로고    scopus 로고
    • Image recovery via total variation minimization and related problems
    • A. Chambolle and P.-L. Lions, "Image recovery via total variation minimization and related problems," Numer. Math., vol. 76, pp. 167-188, 1997.
    • (1997) Numer. Math. , vol.76 , pp. 167-188
    • Chambolle, A.1    Lions, P.-L.2
  • 23
    • 19844370110 scopus 로고    scopus 로고
    • An iterative regularization method for total variation-based image restoration
    • DOI 10.1137/040605412
    • S. Osher,M. Burger, D. Goldfarb, J. Xu, and W. Yin, "An iterative regularization method for total variation-based image restoration," Multiscale Model. Sim., vol. 4, no. 2, pp. 460-489, 2005. (Pubitemid 43885248)
    • (2005) Multiscale Modeling and Simulation , vol.4 , Issue.2 , pp. 460-489
    • Osher, S.1    Burger, M.2    Goldfarb, D.3    Xu, J.4    Yin, W.5
  • 24
    • 33845482689 scopus 로고    scopus 로고
    • Image restoration with discrete constrained total variation part I: Fast and exact optimization
    • DOI 10.1007/s10851-006-8803-0
    • J. Darbon and M. Sigelle, "Image restoration with discrete constrained total variation part I: Fast and exact optimization," J. Math. Imag., vol. 26, pp. 261-276, 2006. (Pubitemid 44916361)
    • (2006) Journal of Mathematical Imaging and Vision , vol.26 , Issue.3 , pp. 261-276
    • Darbon, J.1    Sigelle, M.2
  • 25
    • 67651033716 scopus 로고    scopus 로고
    • Some first-order algorithms for total variation based image restoration
    • J.-F. Aujol, "Some first-order algorithms for total variation based image restoration," J. Math. Imag. Vis., vol. 34, pp. 307-327, 2009.
    • (2009) J. Math. Imag. Vis. , vol.34 , pp. 307-327
    • Aujol, J.-F.1
  • 26
    • 33947702051 scopus 로고    scopus 로고
    • Total variation-based image deconvolution: A majorization-minimization approach
    • Toulouse, France, May
    • J. M. Bioucas-Dias, M. A. T. Figueiredo, and J. P. Oliveira, "Total variation-based image deconvolution: A majorization-minimization approach," in Proc. ICASSP, Toulouse, France, May 2006, vol. 2, pp. 861-864.
    • (2006) Proc. ICASSP , vol.2 , pp. 861-864
    • Bioucas-Dias, J.M.1    Figueiredo, M.A.T.2    Oliveira, J.P.3
  • 27
    • 1342332031 scopus 로고    scopus 로고
    • A Tutorial on MM Algorithms
    • D. R. Hunter and K. Lange, "A tutorial on MM algorithms," Amer. Statist., vol. 58, no. 1, pp. 30-37, Feb. 2004. (Pubitemid 38260327)
    • (2004) American Statistician , vol.58 , Issue.1 , pp. 30-37
    • Hunter, D.R.1    Lange, K.2
  • 28
    • 0001556589 scopus 로고    scopus 로고
    • Iterative methods for total variation denoising
    • C. Vogel and M. Oman, "Iterative methods for total variation de-noising," SIAM J. Sci. Comput., vol. 17, no. 1-4, pp. 227-238, Jan. 1996. (Pubitemid 126621162)
    • (1996) SIAM Journal of Scientific Computing , vol.17 , Issue.1 , pp. 227-238
    • Vogel, C.R.1    Oman, M.E.2
  • 30
    • 0142200827 scopus 로고    scopus 로고
    • An em algorithm for waveletbased image restoration
    • Aug.
    • M. A. T. Figueiredo and R. D. Nowak, "An EM algorithm for waveletbased image restoration," IEEE Trans. Image Process., vol. 12, no. 8, pp. 906-916, Aug. 2003.
    • (2003) IEEE Trans. Image Process. , vol.12 , Issue.8 , pp. 906-916
    • Figueiredo, M.A.T.1    Nowak, R.D.2
  • 31
    • 42149167847 scopus 로고    scopus 로고
    • A wide-angle view at iterated shrinkage algorithms
    • San Diego, CA
    • M. Elad, B. Matalon, J. Shtok, and M. Zibulevsky, "A wide-angle view at iterated shrinkage algorithms," in Proc. SPIEWavelet XII, San Diego, CA, 2007, vol. 6701.
    • (2007) Proc. SPIEWavelet XII , vol.6701
    • Elad, M.1    Matalon, B.2    Shtok, J.3    Zibulevsky, M.4
  • 32
    • 57349145416 scopus 로고    scopus 로고
    • Iterative thresholding for sparse approximations
    • Dec.
    • T. Blumensath and M. E. Davies, "Iterative thresholding for sparse approximations," J. Fourier Anal. Appl., vol. 14, no. 5-6, pp. 629-654, Dec. 2008.
    • (2008) J. Fourier Anal. Appl. , vol.14 , Issue.5-6 , pp. 629-654
    • Blumensath, T.1    Davies, M.E.2
  • 33
    • 67651195543 scopus 로고    scopus 로고
    • The split Bregman algorithm for L1 regularized problems
    • UCLA, Los Angeles, CA
    • T. Goldstein and S. Osher, The split Bregman algorithm for L1 regularized problems," UCLA, Los Angeles, CA, Tech. Rep. CAM Report 08-29, 2008.
    • (2008) Tech. Rep. CAM Report 08-29
    • Goldstein, T.1    Osher, S.2
  • 34
    • 85012251675 scopus 로고    scopus 로고
    • A new alternating minimization algorithm for total variation image reconstruction
    • Y. Wang, J. Yang, W. Yin, and Y. Zhang, "A new alternating minimization algorithm for total variation image reconstruction," SIAM J. Imag. Sci., vol. 1, no. 3, pp. 248-272, 2008.
    • (2008) SIAM J. Imag. Sci. , vol.1 , Issue.3 , pp. 248-272
    • Wang, Y.1    Yang, J.2    Yin, W.3    Zhang, Y.4
  • 35
    • 0000044932 scopus 로고    scopus 로고
    • The discrete cosine transform
    • PII S0036144598336745
    • G. Strang, "The discrete cosine transform," SIAM Rev., vol. 41, no. 1, pp. 135-147, 1999. (Pubitemid 129723752)
    • (1999) SIAM Review , vol.41 , Issue.1 , pp. 135-147
    • Strang, G.1
  • 39
    • 0030193423 scopus 로고    scopus 로고
    • Iterative image restoration using approximate inverse preconditioning
    • PII S1057714996045435
    • J. G. Nagy, R. J. Plemmons, and T. C. Torgersen, "Iterative image restoration using approximate inverse preconditioning," IEEE Trans. Image Process., vol. 5, no. 7, pp. 1151-1162, Jul. 1996. (Pubitemid 126784902)
    • (1996) IEEE Transactions on Image Processing , vol.5 , Issue.7 , pp. 1151-1162
    • Nagy, J.G.1    Plemmons, R.J.2    Torgersen, T.C.3
  • 41
    • 0028429724 scopus 로고
    • Symmetric convolution and the discrete sine and cosine transforms
    • May
    • S. A. Martucci, "Symmetric convolution and the discrete sine and cosine transforms," IEEE Trans. Signal Process., vol. 42, no. 5, pp. 1038-1051, May 1994.
    • (1994) IEEE Trans. Signal Process. , vol.42 , Issue.5 , pp. 1038-1051
    • Martucci, S.A.1
  • 43
    • 0034345420 scopus 로고    scopus 로고
    • Nonmonotone spectral projected gradient methods on convex sets
    • E. G. Birgin, J. M. Martínez, and M. Raydan, "Nonmonotone spectral projected gradient methods on convex sets," SIAM J. Optim., vol. 10, no. 4, pp. 1196-1211, 2000.
    • (2000) SIAM J. Optim. , vol.10 , Issue.4 , pp. 1196-1211
    • Birgin, E.G.1    Martínez, J.M.2    Raydan, M.3
  • 44
    • 33947361050 scopus 로고    scopus 로고
    • Why simple shrinkage is still relevant for redundant representations?
    • DOI 10.1109/TIT.2006.885522
    • M. Elad, "Why simple shrinkage is still relevant for redundant representations?," IEEE Trans. Inf. Theory, vol. 52, no. 12, pp. 5559-5569, Dec. 2006. (Pubitemid 46445399)
    • (2006) IEEE Transactions on Information Theory , vol.52 , Issue.12 , pp. 5559-5569
    • Elad, M.1
  • 45
    • 36749005582 scopus 로고    scopus 로고
    • A new TwIST: Two-step iterative shrinkage/thresholding algorithms for image restoration
    • DOI 10.1109/TIP.2007.909319
    • J. M. Bioucas-Dias and M. A. T. Figueiredo, "A new TwIST: Twostep iterative shrinkage/thresholding algorithms for image restoration," IEEE Trans. Image Process., vol. 16, no. 12, pp. 2992-3004, Dec. 2007. (Pubitemid 350201232)
    • (2007) IEEE Transactions on Image Processing , vol.16 , Issue.12 , pp. 2992-3004
    • Bioucas-Dias, J.M.1    Figueiredo, M.A.T.2
  • 46
    • 85014561619 scopus 로고    scopus 로고
    • A fast iterative shrinkage-thresholding algorithm for linear inverse problems
    • A. Beck and M. Teboulle, "A fast iterative shrinkage-thresholding algorithm for linear inverse problems," SIAM J. Imag. Sci., vol. 2, no. 1, pp. 183-202, 2008.
    • (2008) SIAM J. Imag. Sci. , vol.2 , Issue.1 , pp. 183-202
    • Beck, A.1    Teboulle, M.2
  • 47
    • 0035273106 scopus 로고    scopus 로고
    • Atomic decomposition by basis pursuit
    • DOI 10.1137/S003614450037906X, PII S003614450037906X
    • S. S. Chen, D. L. Donoho, and M. A. Saunders, "Atomic decomposition by basis pursuit," SIAM Rev., vol. 43, no. 1, pp. 129-159, Mar. 2001. (Pubitemid 32406896)
    • (2001) SIAM Review , vol.43 , Issue.1 , pp. 129-159
    • Chen, S.S.1    Donoho, D.L.2    Saunders, M.A.3
  • 48
    • 1942436689 scopus 로고    scopus 로고
    • Image quality assessment: From error visibility to structural similarity
    • Apr.
    • Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, "Image quality assessment: From error visibility to structural similarity," IEEE Trans. Image Process., vol. 13, no. 4, pp. 600-612, Apr. 2004.
    • (2004) IEEE Trans. Image Process. , vol.13 , Issue.4 , pp. 600-612
    • Wang, Z.1    Bovik, A.C.2    Sheikh, H.R.3    Simoncelli, E.P.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.