메뉴 건너뛰기




Volumn 38, Issue , 2011, Pages 44-68

Error estimates for general fidelities

Author keywords

Bregman distance; Discrepancy principle; Error estimation; Image processing; Imaging; Sparsity

Indexed keywords

ERROR ANALYSIS; ERRORS; IMAGE PROCESSING; IMAGING TECHNIQUES;

EID: 84255187707     PISSN: None     EISSN: 10689613     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (42)

References (31)
  • 1
    • 49449100276 scopus 로고    scopus 로고
    • 4 variational approach to remove multiplicative noise
    • G. AUBERT AND J. F. AUJOL, 4 variational approach to remove multiplicative noise, SIAM J. Appl. Math.. 68 (2008), pp. 925-946.
    • (2008) SIAM J. Appl. Math. , vol.68 , pp. 925-946
    • Aubert, G.1    Aujol, J.F.2
  • 2
    • 67349157591 scopus 로고    scopus 로고
    • Total variation-penalized Poisson likelihood estimation for ill-posed prob-lems
    • J. BARDSLEY AND A. LUTTMAN, Total variation-penalized Poisson likelihood estimation for ill-posed prob-lems , Adv. Comput. Math., 31 (2009), pp. 35-59.
    • (2009) Adv. Comput. Math. , vol.31 , pp. 35-59
    • Bardsley, J.1    Luttman, A.2
  • 3
    • 41549168778 scopus 로고    scopus 로고
    • Convergence rates of general regularization methods for statistical inverse problems and applications
    • N. BlSSANTZ, T. HOHAGE, A. MUNK, AND F. RUYMGAART, Convergence rates of general regularization methods for statistical inverse problems and applications, SIAM J. Numer. Anal., 45 (2007), pp. 2610-2636.
    • (2007) SIAM J. Numer. Anal. , vol.45 , pp. 2610-2636
    • Blssantz, N.1    Hohage, T.2    Munk, A.3    Ruymgaart, F.4
  • 4
    • 49949144765 scopus 로고
    • The relaxation method for finding the common point of convex sets and its application to the solution of problems in convex programming
    • L. M. BREGMAN, The relaxation method for finding the common point of convex sets and its application to the solution of problems in convex programming, Comput. Math. Math. Phys., 7 (1967), pp. 200-217.
    • (1967) Comput. Math. Math. Phys. , vol.7 , pp. 200-217
    • Bregman, L.M.1
  • 5
    • 69049109069 scopus 로고    scopus 로고
    • Bregman-EM-TV methods with application to optical nanoscopy
    • X.-C. Tai, K. Merken, M. Lysaker, and K.-A. Lie, eds., Lecture Notes in Comput. Sci. Springer, Berlin
    • C. BRUNE, A. SAWATZKY, AND M. BURGER, Bregman-EM-TV methods with application to optical nanoscopy, Proceedings of the 2nd International Conference on Scale Space and Variational Methods in Computer Vision, X.-C. Tai, K. Merken, M. Lysaker, and K.-A. Lie, eds., Lecture Notes in Comput. Sci., Vol. 5567, Springer, Berlin, 2009, pp. 235-246.
    • (2009) Proceedings of the 2nd International Conference on Scale Space and Variational Methods in Computer Vision , vol.5567 , pp. 235-246
    • Brune, C.1    Sawatzky, A.2    Burger, M.3
  • 7
    • 84904732030 scopus 로고    scopus 로고
    • Cahn-Hilliard inpainting and a generalization to grayvalue images
    • M. BURGER, L. He, AND C. SCHONLIEB, Cahn-Hilliard inpainting and a generalization to grayvalue images, SIAM J. Imaging Sci., 2 (2009), pp. 1129-1167.
    • (2009) SIAM J. Imaging Sci. , vol.2 , pp. 1129-1167
    • Burger, M.1    He, L.2    Schonlieb, C.3
  • 8
    • 6444243748 scopus 로고    scopus 로고
    • Convergence rates of convex variational regularization
    • M. BURGER AND S. OSHER, Convergence rates of convex variational regularization, Inverse Problems, 20 (2004), pp. 1411-1421.
    • (2004) Inverse Problems , vol.20 , pp. 1411-1421
    • Burger, M.1    Osher, S.2
  • 9
    • 36549078210 scopus 로고    scopus 로고
    • Error estimation for Bregman iterations and inverse scale space methods in image restoration
    • DOI 10.1007/s00607-007-0245-z, Special Issue on Industrial Geometry
    • M. BURGER, E. RESMERITA, AND L. He, Error estimation forBregman iterations and inverse scale space methods, Computing, 81 (2007), pp. 109-135. (Pubitemid 350178349)
    • (2007) Computing (Vienna/New York) , vol.81 , Issue.2-3 , pp. 109-135
    • Burger, M.1    Resmerita, E.2    He, L.3
  • 10
    • 27744554422 scopus 로고    scopus 로고
    • Salt-and-pepper noise removal by median-type noise detectors and detail-preserving regularization
    • DOI 10.1109/TIP.2005.852196
    • R. CHAN, C. Ho, AND M. NIKOLOVA, Salt-and-pepper noise removal by median-type noise detector and detail-preserving regularization, IEEE Trans, on Image Process., 14 (2005), pp. 1479-1485. (Pubitemid 41623079)
    • (2005) IEEE Transactions on Image Processing , vol.14 , Issue.10 , pp. 1479-1485
    • Chan, R.H.1    Ho, C.-W.2    Nikolova, M.3
  • 11
    • 27844461945 scopus 로고    scopus 로고
    • 1 function approximation
    • DOI 10.1137/040604297
    • T. F. CHAN AND S. ESEDOGLU, 4 specte of total variation regularized function approximation, SIAM J. Appl. Math., 65 (2005), pp. 1817-1837. (Pubitemid 41639797)
    • (2005) SIAM Journal on Applied Mathematics , vol.65 , Issue.5 , pp. 1817-1837
    • Chan, T.F.1    Esedoglu, S.2
  • 14
    • 13744252042 scopus 로고    scopus 로고
    • Convergence rates in the Prokhorov metric for assessing uncertainty in ill-posed problems
    • DOI 10.1088/0266-5611/21/1/024
    • H. W. ENGL, A. HOFINGER, AND S. KlNDERMANN, Convergence rates in theProkhorov metric for assessing uncertainty in ill-posed problems, Inverse Problems, 21 (2005), pp. 399-412. (Pubitemid 40238434)
    • (2005) Inverse Problems , vol.21 , Issue.1 , pp. 399-412
    • Engl, H.W.1    Hofinger, A.2    Kindermann, S.3
  • 15
    • 36749089116 scopus 로고    scopus 로고
    • Convergence rates for the Bayesian approach to linear inverse problems
    • A. HOFINGER AND H. K. PlKKARAINEN, Convergence rates for the Bayesian approach to linear inverse problems, Inverse Problems, 23 (2006), pp. 2469-2484.
    • (2006) Inverse Problems , vol.23 , pp. 2469-2484
    • Hofinger, A.1    Plkkarainen, H.K.2
  • 16
    • 61349093573 scopus 로고    scopus 로고
    • Convergence rates for linear inverse problems in the presence of an additive normal noise
    • -, Convergence rates for linear inverse problems in the presence of an additive normal noise, Stoch. Anal. Appl., 27 (2009), pp. 240-257.
    • (2009) Stoch. Anal. Appl. , vol.27 , pp. 240-257
  • 17
    • 34249721452 scopus 로고    scopus 로고
    • A convergence rates result for Tikhonov regularization in Banach spaces with non-smooth operators
    • DOI 10.1088/0266-5611/23/3/009, PII S026656110738129X, 009
    • B. HOFMANN, B. KALTENBACHER, C. POSCHL, AND O. SCHERZER, A convergence rates result for Tikhonov regularization in Banach spaces with non-smooth operators, Inverse Problems, 23 (2007), pp. 987-1010. (Pubitemid 46838837)
    • (2007) Inverse Problems , vol.23 , Issue.3 , pp. 987-1010
    • Hofmann, B.1    Kaltenbacher, B.2    Poschl, C.3    Scherzer, O.4
  • 19
    • 84907779428 scopus 로고    scopus 로고
    • A new total variation method for multiplicative noise removal
    • Y. M. HUANG, M. K. Ng, AND Y. W. Wen, A new total variation method for multiplicative noise removal, SIAM J. Imaging Sci., 2 (2009), pp. 20-40.
    • (2009) SIAM J. Imaging Sci. , vol.2 , pp. 20-40
    • Huang, Y.M.1    Ng, M.K.2    Wen, Y.W.3
  • 20
    • 0031190440 scopus 로고    scopus 로고
    • Proximal minimization methods with generalized Bregman functions
    • K. C. KlWIEL, Proximal minimization methods with generalized Bregman functions, SIAM J. Control Optim., 35(1997), pp. 1142-1168.
    • (1997) SIAM J. Control Optim. , vol.35 , pp. 1142-1168
    • Klwiel, K.C.1
  • 21
    • 51749124719 scopus 로고    scopus 로고
    • Convergence rates and source conditions for Tikhonov regularization with sparsity constraints
    • D. A. LORENZ, Convergence rates and source conditions for Tikhonov regularization with sparsity constraints, J. Inverse Ill-Posed Probl., 16 (2008), pp. 463-478.
    • (2008) J. Inverse Ill-Posed Probl. , vol.16 , pp. 463-478
    • Lorenz, D.A.1
  • 22
    • 54749132261 scopus 로고    scopus 로고
    • Optimal convergence rates for Tikhonov regularization in Besov scales
    • D. A. LORENZ AND D. TREDE, Optimal convergence rates for Tikhonov regularization in Besov scales. Inverse Problems, 24 (2008), 055010.
    • (2008) Inverse Problems , vol.24 , pp. 055010
    • Lorenz, D.A.1    Trede, D.2
  • 25
    • 0004865563 scopus 로고    scopus 로고
    • On converse and saturation results for tikhonov regulartzatton of linear ill-posed problems
    • A. NEUBAUER, On converse and saturation results for Tikhonov regularization of linear ill-posed problems, SIAM J. Numer. Anal., 34 (1997), pp. 517-527. (Pubitemid 127463077)
    • (1997) SIAM Journal on Numerical Analysis , vol.34 , Issue.2 , pp. 517-527
    • Neubauer, A.1
  • 26
    • 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. Simul., 4 (2005), pp. 460-489. (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
  • 27
    • 77951980928 scopus 로고    scopus 로고
    • PhD thesis, Department of Mathematics, Computer Science, and Physics, Leopold-Franzens-Universitat Innsbruck
    • C. POSCHL, Tikhonov regularization with general residual term, PhD thesis, Department of Mathematics, Computer Science, and Physics, Leopold-Franzens-Universitat Innsbruck, 2008.
    • (2008) Tikhonov Regularization with General Residual Term
    • Poschl, C.1
  • 28
    • 33744766866 scopus 로고    scopus 로고
    • Error estimates for non-quadratic regularization and the relation to enhancement
    • DOI 10.1088/0266-5611/22/3/004, PII S0266561106147826
    • E. RESMERITA AND O. SCHERZER, Error estimates for non-quadratic regularization and the relation to enhancing, Inverse Problems, 22 (2006), pp. 801-814. (Pubitemid 43821177)
    • (2006) Inverse Problems , vol.22 , Issue.3 , pp. 801-814
    • Resmerita, E.1    Scherzer, O.2
  • 29
    • 44049111982 scopus 로고
    • Nonlinear total variation based noise removal algorithms
    • L. RUDIN, S. OSHER, AND E. FATEMI, Nonlinear total variation based noise removal algorithms, Physica D, 60 (1992), pp. 259-268.
    • (1992) Physica D , vol.60 , pp. 259-268
    • Rudin, L.1    Osher, S.2    Fatemi, E.3
  • 30
    • 84907734262 scopus 로고    scopus 로고
    • 4 nonlinear inverse scale space method for a convex multiplicative noise model
    • J. SHI AND S. OSHER, 4 nonlinear inverse scale space method for a convex multiplicative noise model, SIAM J. Imaging Sci., 1 (2008), pp. 294-321.
    • (2008) SIAM J. Imaging Sci. , vol.1 , pp. 294-321
    • Shi, J.1    Osher, S.2
  • 31
    • 79951763545 scopus 로고    scopus 로고
    • Augmented Lagrangian method for total variation restoration with non-quadratic fidelity
    • C. Wu, J. ZHANG, AND X. TAI, Augmented Lagrangian method for total variation restoration with non-quadratic fidelity, Inverse Problems and Imaging, 5 (2011), pp. 237-261.
    • (2011) Inverse Problems and Imaging , vol.5 , pp. 237-261
    • Wu, C.1    Zhang, J.2    Tai, X.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.