메뉴 건너뛰기




Volumn 30, Issue 11, 2014, Pages

Maximum a posteriori estimates in linear inverse problems with log-concave priors are proper Bayes estimators

Author keywords

Bayes cost; Bregman distance; CM estimation; MAP estimation; sparsity

Indexed keywords

COST BENEFIT ANALYSIS; COST FUNCTIONS; COSTS; DIFFERENTIAL EQUATIONS; INVERSE PROBLEMS; MEAN SQUARE ERROR; VARIATIONAL TECHNIQUES;

EID: 84908587167     PISSN: 02665611     EISSN: 13616420     Source Type: Journal    
DOI: 10.1088/0266-5611/30/11/114004     Document Type: Article
Times cited : (63)

References (39)
  • 1
    • 77749311485 scopus 로고    scopus 로고
    • Hierarchical regularization for edge-preserving reconstruction of PET images
    • Bardsley J, Calvetti D and Somersalo E 2010 Hierarchical regularization for edge-preserving reconstruction of PET images Inverse Problems 26 035010
    • (2010) Inverse Problems , vol.26 , Issue.3
    • Bardsley, J.1    Calvetti, D.2    Somersalo, E.3
  • 2
    • 84908603293 scopus 로고    scopus 로고
    • Benning M 2011 Singular regularization of inverse problems PhD thesis University of Muenster
    • (2011) PhD Thesis
    • Benning, M.1
  • 3
    • 6444243748 scopus 로고    scopus 로고
    • Convergence rates of convex variational regularization
    • Burger M and Osher S 2004 Convergence rates of convex variational regularization Inverse Problems 20 1411-21
    • (2004) Inverse Problems , vol.20 , Issue.5 , pp. 1411-1421
    • Burger, M.1    Osher, S.2
  • 5
    • 36549078210 scopus 로고    scopus 로고
    • Error estimation for Bregman iterations and inverse scale space methods in image restoration
    • Burger M, Resmerita E and He L 2007 Error estimation for Bregman iterations and inverse scale space methods in image restoration Computing 81 109-35
    • (2007) Computing , vol.81 , pp. 109-135
    • Burger, M.1    Resmerita, E.2    He, L.3
  • 6
    • 80055063784 scopus 로고    scopus 로고
    • Bayesian calibration of a large-scale geothermal reservoir model by a new adaptive delayed acceptance Metropolis Hastings algorithm
    • Cui T, Fox C and O'Sullivan M J 2011 Bayesian calibration of a large-scale geothermal reservoir model by a new adaptive delayed acceptance Metropolis Hastings algorithm Water Resour. Res. 47 W10521
    • (2011) Water Resour. Res. , vol.47 , pp. 10521
    • Cui, T.1    Fox, C.2    O'Sullivan, M.J.3
  • 7
    • 84884126479 scopus 로고    scopus 로고
    • Map estimators and their consistency in bayesian nonparametric inverse problems
    • Dashti M, Law K J H, Stuart A M and Voss J 2013 Map estimators and their consistency in bayesian nonparametric inverse problems Inverse Problems 29 095017
    • (2013) Inverse Problems , vol.29 , Issue.9
    • Dashti, M.1    Law, K.J.H.2    Stuart, A.M.3    Voss, J.4
  • 10
    • 84969334819 scopus 로고    scopus 로고
    • The split Bregman method for L1-regularized problems
    • Goldstein T and Osher S 2009 The split Bregman method for L1-regularized problems SIAM J. Imaging Sci. 2 323-43
    • (2009) SIAM J. Imaging Sci. , vol.2 , pp. 323-343
    • Goldstein, T.1    Osher, S.2
  • 11
    • 79954564965 scopus 로고    scopus 로고
    • Should penalized least squares regression be interpreted as maximum a posteriori estimation?
    • Gribonval R 2011 Should penalized least squares regression be interpreted as maximum a posteriori estimation? IEEE Trans. Signal Process 59 2405-10
    • (2011) IEEE Trans. Signal Process , vol.59 , pp. 2405-2410
    • Gribonval, R.1
  • 12
    • 84863937465 scopus 로고    scopus 로고
    • Compressible distributions for high-dimensional statistics
    • Gribonval R, Cevher V and Davies M 2012 Compressible distributions for high-dimensional statistics IEEE Trans. Inf. Theory 58 5016-34
    • (2012) IEEE Trans. Inf. Theory , vol.58 , pp. 5016-5034
    • Gribonval, R.1    Cevher, V.2    Davies, M.3
  • 14
    • 3543035224 scopus 로고    scopus 로고
    • Markov chain Monte Carlo methods for high dimensional inversion in remote sensing
    • B
    • Haario H, Laine M, Lehtinen M, Saksman E and Tamminen J 2004 Markov chain Monte Carlo methods for high dimensional inversion in remote sensing J. R. Stat. Soc. B 66 591-607
    • (2004) J. R. Stat. Soc. , vol.66 , pp. 591-607
    • Haario, H.1    Laine, M.2    Lehtinen, M.3    Saksman, E.4    Tamminen, J.5
  • 16
    • 73649128596 scopus 로고    scopus 로고
    • On infinite-dimensional hierarchical probability models in statistical inverse problems
    • Helin T 2010 On infinite-dimensional hierarchical probability models in statistical inverse problems Inverse Probl. Imaging 3 567-97
    • (2010) Inverse Probl. Imaging , vol.3 , pp. 567-597
    • Helin, T.1
  • 18
    • 62749199713 scopus 로고    scopus 로고
    • Selecting forward models for MEG source-reconstruction using model-evidence
    • Henson R N, Mattout J, Phillips C and Friston K J 2009 Selecting forward models for MEG source-reconstruction using model-evidence Neuroimage 46 168-76
    • (2009) Neuroimage , vol.46 , pp. 168-176
    • Henson, R.N.1    Mattout, J.2    Phillips, C.3    Friston, K.J.4
  • 19
    • 79953706294 scopus 로고    scopus 로고
    • The Bayesian framework for inverse problems in heat transfer
    • Kaipio J P and Fox C 2011 The Bayesian framework for inverse problems in heat transfer Heat Transfer Eng. 32 718-53
    • (2011) Heat Transfer Eng. , vol.32 , pp. 718-753
    • Kaipio, J.P.1    Fox, C.2
  • 21
    • 33748749612 scopus 로고    scopus 로고
    • Statistical inverse problems: Discretization, model reduction and inverse crimes
    • Kaipio J P and Somersalo E 2007 Statistical inverse problems: discretization, model reduction and inverse crimes J. Comput. Appl. Math. 198 493-504
    • (2007) J. Comput. Appl. Math. , vol.198 , pp. 493-504
    • Kaipio, J.P.1    Somersalo, E.2
  • 25
    • 70450218926 scopus 로고    scopus 로고
    • Discretization invariant Bayesian inversion and Besov space priors
    • Lassas M, Saksman E and Siltanen S 2009 Discretization invariant Bayesian inversion and Besov space priors Inverse Probl. Imaging 3 87-122
    • (2009) Inverse Probl. Imaging , vol.3 , pp. 87-122
    • Lassas, M.1    Saksman, E.2    Siltanen, S.3
  • 26
    • 6344231795 scopus 로고    scopus 로고
    • Can one use total variation prior for edge-preserving Bayesian inversion?
    • Lassas M and Siltanen S 2004 Can one use total variation prior for edge-preserving Bayesian inversion? Inverse Problems 20 1537-63
    • (2004) Inverse Problems , vol.20 , Issue.5 , pp. 1537-1563
    • Lassas, M.1    Siltanen, S.2
  • 27
    • 84890446484 scopus 로고    scopus 로고
    • Correction of approximation errors with random forests applied to modelling of cloud droplet formation
    • Lipponen A, Kolehmainen V, Romakkaniemi S and Kokkola H 2013 Correction of approximation errors with random forests applied to modelling of cloud droplet formation Geosci. Model Dev. 6 2087-98
    • (2013) Geosci. Model Dev. , vol.6 , pp. 2087-2098
    • Lipponen, A.1    Kolehmainen, V.2    Romakkaniemi, S.3    Kokkola, H.4
  • 28
    • 84891063370 scopus 로고    scopus 로고
    • Posterior expectation of the total variation model: Properties and experiments
    • Louchet C and Moisan L 2013 Posterior expectation of the total variation model: properties and experiments SIAM J. Imaging Sci. 6 2640-84
    • (2013) SIAM J. Imaging Sci. , vol.6 , pp. 2640-2684
    • Louchet, C.1    Moisan, L.2
  • 29
    • 84870416863 scopus 로고    scopus 로고
    • Fast Markov chain Monte Carlo sampling for sparse Bayesian inference in high-dimensional inverse problems using L1-type priors
    • Lucka F 2012 Fast Markov chain Monte Carlo sampling for sparse Bayesian inference in high-dimensional inverse problems using L1-type priors Inverse Problems 28 125012
    • (2012) Inverse Problems , vol.28 , Issue.12
    • Lucka, F.1
  • 30
    • 84861361414 scopus 로고    scopus 로고
    • Hierarchical Bayesian inference for the EEG inverse problem using realistic FE head models: Depth localization and source separation for focal primary currents
    • Lucka F, Pursiainen S, Burger M and Wolters C H 2012 Hierarchical Bayesian inference for the EEG inverse problem using realistic FE head models: depth localization and source separation for focal primary currents Neuroimage 61 1364-82
    • (2012) Neuroimage , vol.61 , pp. 1364-1382
    • Lucka, F.1    Pursiainen, S.2    Burger, M.3    Wolters, C.H.4
  • 31
    • 84873888819 scopus 로고    scopus 로고
    • Moeller M 2012 Multiscale methods for generalized sparse recovery and applications in high dimensional imaging, PhD thesis University of Muenster
    • (2012) PhD Thesis
    • Moeller, M.1
  • 32
    • 79551577471 scopus 로고    scopus 로고
    • Compensation of modelling errors due to unknown domain boundary in electrical impedance tomography
    • Nissinen A, Kolehmainen V and Kaipio J 2011 Compensation of modelling errors due to unknown domain boundary in electrical impedance tomography IEEE Trans. Med. Imaging 30 231-42
    • (2011) IEEE Trans. Med. Imaging , vol.30 , pp. 231-242
    • Nissinen, A.1    Kolehmainen, V.2    Kaipio, J.3
  • 33
    • 84878543914 scopus 로고    scopus 로고
    • Iterative alternating sequential (IAS) method for radio tomography of asteroids in 3D
    • Pursiainen S and Kaasalainen M 2013 Iterative alternating sequential (IAS) method for radio tomography of asteroids in 3D Planet Space Sci. 82-83 84-98
    • (2013) Planet Space Sci. , vol.82-83 , pp. 84-98
    • Pursiainen, S.1    Kaasalainen, M.2
  • 35
    • 77951793592 scopus 로고    scopus 로고
    • Inverse problems: A Bayesian perspective
    • Stuart A M 5 2010 Inverse problems: a Bayesian perspective Acta Numer. 19 451-559
    • (2010) Acta Numer. , vol.19 , pp. 451-559
    • Stuart, A.M.1
  • 37
    • 80053956257 scopus 로고    scopus 로고
    • Bayesian inference in physics
    • Toussaint U 2011 Bayesian inference in physics Rev. Mod. Phys. 83 943-99
    • (2011) Rev. Mod. Phys. , vol.83 , pp. 943-999
    • Toussaint, U.1
  • 39
    • 84890101399 scopus 로고    scopus 로고
    • A hierarchical Bayesian approach for aerosol retrieval using MISR data
    • Wang Y, Jiang X, Yu B and Jiang M 2013 A hierarchical Bayesian approach for aerosol retrieval using MISR data J. Am. Stat. Assoc. 108 483-93
    • (2013) J. Am. Stat. Assoc. , vol.108 , pp. 483-493
    • Wang, Y.1    Jiang, X.2    Yu, B.3    Jiang, M.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.