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Volumn 34, Issue 1, 2009, Pages 32-47

Semi-explicit solution and fast minimization scheme for an energy with ℓ 1-Fitting and Tikhonov-Like regularization

Author keywords

1 data fitting; Image denoising; Impulsive noise; Non smooth analysis; Nonsmooth optimization; Numerical methods; Random matrices; Signal denoising; Tikhonov regularization

Indexed keywords

IMAGE DENOISING; IMPULSIVE NOISE; NON-SMOOTH ANALYSIS; NONSMOOTH OPTIMIZATION; RANDOM MATRICES; SIGNAL DENOISING; TIKHONOV REGULARIZATION;

EID: 67349203307     PISSN: 09249907     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10851-008-0125-y     Document Type: Article
Times cited : (1)

References (27)
  • 1
    • 0026883172 scopus 로고
    • Digital filters as absolute norm regularizers
    • S. Alliney 1992 Digital filters as absolute norm regularizers IEEE Trans. Signal Process. SP-40 1548 1562
    • (1992) IEEE Trans. Signal Process. , vol.SP-40 , pp. 1548-1562
    • Alliney, S.1
  • 2
    • 0031124308 scopus 로고    scopus 로고
    • A property of the minimum vectors of a regularizing functional defined by means of absolute norm
    • S. Alliney 1997 A property of the minimum vectors of a regularizing functional defined by means of absolute norm IEEE Trans. Signal Process. 45 913 917
    • (1997) IEEE Trans. Signal Process. , vol.45 , pp. 913-917
    • Alliney, S.1
  • 4
    • 24644481115 scopus 로고    scopus 로고
    • Image deblurring in the presence of salt-and-pepper noise
    • Proceeding of 5th International Conference on Scale Space and PDE methods in Computer Vision Springer Berlin
    • Bar, L., Sochen, N., Kiryati, N.: Image deblurring in the presence of salt-and-pepper noise. In: Proceeding of 5th International Conference on Scale Space and PDE methods in Computer Vision. LNCS, vol. 3439, pp. 107-118. Springer, Berlin (2005)
    • (2005) LNCS , vol.3439 , pp. 107-118
    • Bar, L.1    Sochen, N.2    Kiryati, N.3
  • 5
    • 31144459533 scopus 로고    scopus 로고
    • Semi-blind image restoration via Mumford-Shah regularization
    • L. Bar N. Sochen N. Kiryati 2006 Semi-blind image restoration via Mumford-Shah regularization IEEE Trans. Image Process. 15 483 493
    • (2006) IEEE Trans. Image Process. , vol.15 , pp. 483-493
    • Bar, L.1    Sochen, N.2    Kiryati, N.3
  • 7
    • 10244230862 scopus 로고    scopus 로고
    • An iterative procedure for removing random-valued impulse noise
    • R. Chan C. Hu M. Nikolova 2004 An iterative procedure for removing random-valued impulse noise IEEE Signal Process. Lett. 11 921 924
    • (2004) IEEE Signal Process. Lett. , vol.11 , pp. 921-924
    • Chan, R.1    Hu, C.2    Nikolova, M.3
  • 8
    • 34250213234 scopus 로고    scopus 로고
    • An optimization-based multilevel algorithm for total variation image denoising
    • T. Chan K. Chen 2006 An optimization-based multilevel algorithm for total variation image denoising SIAM J. Multiscale Model. Simul. 5 615 645
    • (2006) SIAM J. Multiscale Model. Simul. , vol.5 , pp. 615-645
    • Chan, T.1    Chen, K.2
  • 10
    • 33750153530 scopus 로고    scopus 로고
    • Algorithms for finding global minimizers of image segmentation and denoising models
    • T. Chan S. Esedoglu M. Nikolova 2006 Algorithms for finding global minimizers of image segmentation and denoising models SIAM J. Appl. Math. 66 1632 1648
    • (2006) SIAM J. Appl. Math. , vol.66 , pp. 1632-1648
    • Chan, T.1    Esedoglu, S.2    Nikolova, M.3
  • 11
    • 0003972915 scopus 로고    scopus 로고
    • Introduction à l'analyse numérique matricielle et à l'optimisation, 5th edn.
    • Dunod Paris
    • Ciarlet, P.G.: Introduction à l'analyse numérique matricielle et à l'optimisation, 5th edn. Collection mathématiques appliquées pour la maîtrise. Dunod, Paris (2000)
    • (2000) Collection Mathématiques Appliquées Pour la Maîtrise
    • Ciarlet, P.G.1
  • 12
    • 0036871107 scopus 로고    scopus 로고
    • An adaptive level set method for nondifferentiable constrained image recovery
    • P. Combettes J. Luo 2002 An adaptive level set method for nondifferentiable constrained image recovery IEEE Trans. Image Process. 11 1295 1304
    • (2002) IEEE Trans. Image Process. , vol.11 , pp. 1295-1304
    • Combettes, P.1    Luo, J.2
  • 13
    • 33845482689 scopus 로고    scopus 로고
    • Image restoration with discrete constrained total variation part I: Fast and exact optimization
    • J. Darbon M. Sigelle 2006 Image restoration with discrete constrained total variation part I: Fast and exact optimization J. Math. Imaging Vis. 26 261 276
    • (2006) J. Math. Imaging Vis. , vol.26 , pp. 261-276
    • Darbon, J.1    Sigelle, M.2
  • 14
    • 33845478943 scopus 로고    scopus 로고
    • Image restoration with discrete constrained total variation part II: Levelable functions, convex and non-convex cases
    • J. Darbon M. Sigelle 2006 Image restoration with discrete constrained total variation part II: Levelable functions, convex and non-convex cases J. Math. Imaging Vis. 26 277 291
    • (2006) J. Math. Imaging Vis. , vol.26 , pp. 277-291
    • Darbon, J.1    Sigelle, M.2
  • 15
    • 45849138905 scopus 로고    scopus 로고
    • Denoising of frame coefficients using l1 data-fidelity term and edge-preserving regularization
    • S. Durand M. Nikolova 2007 Denoising of frame coefficients using l1 data-fidelity term and edge-preserving regularization SIAM J. Multiscale Model. Simul. 6 547 576
    • (2007) SIAM J. Multiscale Model. Simul. , vol.6 , pp. 547-576
    • Durand, S.1    Nikolova, M.2
  • 19
    • 21444455206 scopus 로고    scopus 로고
    • Denoising of smooth images using l1-fitting
    • T. Kärkkäinen K. Kunisch K. Majava 2005 Denoising of smooth images using l1-fitting Computing 74 353 376
    • (2005) Computing , vol.74 , pp. 353-376
    • Kärkkäinen, T.1    Kunisch, K.2    Majava, K.3
  • 20
    • 0013212015 scopus 로고    scopus 로고
    • Markovian reconstruction using a GNC approach
    • M. Nikolova 1999 Markovian reconstruction using a GNC approach IEEE Trans. Image Process. 8 1204 1220
    • (1999) IEEE Trans. Image Process. , vol.8 , pp. 1204-1220
    • Nikolova, M.1
  • 21
    • 0038042413 scopus 로고    scopus 로고
    • Minimizers of cost-functions involving nonsmooth data-fidelity terms. Application to the processing of outliers
    • M. Nikolova 2002 Minimizers of cost-functions involving nonsmooth data-fidelity terms. Application to the processing of outliers SIAM J. Numer. Anal. 40 965 994
    • (2002) SIAM J. Numer. Anal. , vol.40 , pp. 965-994
    • Nikolova, M.1
  • 22
    • 1242284980 scopus 로고    scopus 로고
    • A variational approach to remove outliers and impulse noise
    • Nikolova, M.: A variational approach to remove outliers and impulse noise, J. Math. Imaging Vis. 20 (2004)
    • (2004) J. Math. Imaging Vis. , vol.20
    • Nikolova, M.1
  • 23
    • 3142712959 scopus 로고    scopus 로고
    • Weakly constrained minimization. Application to the estimation of images and signals involving constant regions
    • M. Nikolova 2004 Weakly constrained minimization. Application to the estimation of images and signals involving constant regions J. Math. Imaging Vis. 21 155 175
    • (2004) J. Math. Imaging Vis. , vol.21 , pp. 155-175
    • Nikolova, M.1
  • 24
    • 0004267646 scopus 로고
    • Princeton University Press Princeton
    • Rockafellar, R.T.: Convex Analysis. Princeton University Press, Princeton (1970)
    • (1970) Convex Analysis
    • Rockafellar, R.T.1
  • 25
    • 44049111982 scopus 로고
    • Nonlinear total variation based noise removal algorithm
    • L. Rudin S. Osher C. Fatemi 1992 Nonlinear total variation based noise removal algorithm Physica D 60 259 268
    • (1992) Physica D , vol.60 , pp. 259-268
    • Rudin, L.1    Osher, S.2    Fatemi, C.3
  • 27
    • 0032096686 scopus 로고    scopus 로고
    • Fast, robust total variation-based reconstruction of noisy, blurred images
    • C.R. Vogel M.E. Oman 1998 Fast, robust total variation-based reconstruction of noisy, blurred images IEEE Trans. Image Process. 7 813 824
    • (1998) IEEE Trans. Image Process. , vol.7 , pp. 813-824
    • Vogel, C.R.1    Oman, M.E.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.