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Volumn 40, Issue 3, 2002, Pages 965-994

Minimizers of cost-functions involving nonsmooth data-fidelity terms. Application to the processing of outliers

Author keywords

Inverse problems; MAP estimation; Nonsmooth analysis; Outliers; Perturbation analysis; Proximal analysis; Reconstruction; Regularization; Stabilization; Total variation; Variational methods

Indexed keywords

INVERSE PROBLEMS; MATHEMATICAL MODELS; PERTURBATION TECHNIQUES; SIGNAL PROCESSING;

EID: 0038042413     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142901389165     Document Type: Article
Times cited : (286)

References (39)
  • 1
    • 36149030663 scopus 로고
    • Analysis of bounded variation penalty methods for ill-posed problems
    • R. ACAR AND C. VOGEL, Analysis of bounded variation penalty methods for ill-posed problems, IEEE Trans. Image Process.. 10 (1994), pp. 1217-1229.
    • (1994) IEEE Trans. Image Process. , vol.10 , pp. 1217-1229
    • Acar, R.1    Vogel, C.2
  • 2
    • 0027609052 scopus 로고
    • Digital filters as absolute norm regularizes
    • S. ALLINEY, Digital filters as absolute norm regularizes, IEEE Trans. Medical Imaging, 12 (1993), pp. 173-181.
    • (1993) IEEE Trans. Medical Imaging , vol.12 , pp. 173-181
    • Alliney, S.1
  • 3
    • 0031124308 scopus 로고    scopus 로고
    • A property of the minimum vectors of a regularizing functional defined by means of absolute norm
    • S. ALLINEY, A property of the minimum vectors of a regularizing functional defined by means of absolute norm, IEEE Trans. Signal Process., 45 (1997), pp. 913-917.
    • (1997) IEEE Trans. Signal Process. , vol.45 , pp. 913-917
    • Alliney, S.1
  • 6
    • 0000013152 scopus 로고
    • On the statistical analysis of dirty pictures (with discussion)
    • J. E. BESAG, On the statistical analysis of dirty pictures (with discussion), J. Roy. Statist. Soc. Ser. B, 48 (1986), pp. 259-302.
    • (1986) J. Roy. Statist. Soc. Ser. B , vol.48 , pp. 259-302
    • Besag, J.E.1
  • 7
    • 0030194054 scopus 로고    scopus 로고
    • On the unification of line processes, outlier rejection, and robust statistics with applications to early vision
    • M. BLACK AND A. RANGARAJAN, On the unification of line processes, outlier rejection, and robust statistics with applications to early vision, Internat. J. Computer Vision, 19 (1996), pp. 57-91.
    • (1996) Internat. J. Computer Vision , vol.19 , pp. 57-91
    • Black, M.1    Rangarajan, A.2
  • 9
    • 0027624429 scopus 로고
    • A generalized Gaussian image model for edge-preserving MAP estimation
    • C. BOUMAN AND K. SAUER, A generalized Gaussian image model for edge-preserving MAP estimation. IEEE Trans. Image Process., 2 (1993), pp. 296-310.
    • (1993) IEEE Trans. Image Process. , vol.2 , pp. 296-310
    • Bouman, C.1    Sauer, K.2
  • 10
    • 0030109399 scopus 로고    scopus 로고
    • A unified approach to statistical tomography using coordinate descent optimization
    • C. BOUMAN AND K. SAUER, A unified approach to statistical tomography using coordinate descent optimization, IEEE Trans, Image Process., 5 (1996), pp. 480-492.
    • (1996) IEEE Trans. Image Process. , vol.5 , pp. 480-492
    • Bouman, C.1    Sauer, K.2
  • 11
    • 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., 76 (1997), pp. 167-188.
    • (1997) Numer. Math. , vol.76 , pp. 167-188
    • Chambolle, A.1    Lions, P.-L.2
  • 12
    • 0032028980 scopus 로고    scopus 로고
    • Total variation blind deconvolution
    • T. F. CHAN AND C. K. WONG, Total variation blind deconvolution, IEEE Trans. Image Process., 7 (1998), pp. 370-375.
    • (1998) IEEE Trans. Image Process. , vol.7 , pp. 370-375
    • Chan, T.F.1    Wong, C.K.2
  • 13
    • 0024928175 scopus 로고
    • Image reconstruction and restoration: Overview of common estimation structure and problems
    • G. DEMOMENT, Image reconstruction and restoration: Overview of common estimation structure and problems, IEEE Trans. Acoust. Speech Signal Process., 37 (1989), pp. 2024-2036.
    • (1989) IEEE Trans. Acoust. Speech Signal Process. , vol.37 , pp. 2024-2036
    • Demoment, G.1
  • 14
    • 0030212858 scopus 로고    scopus 로고
    • Recovery of blocky images from noisy and blurred data
    • D. DOBSON AND F. SANTOSA, Recovery of blocky images from noisy and blurred data, SIAM J. Appl. Math.. 56 (1996), pp. 1181-1199.
    • (1996) SIAM J. Appl. Math. , vol.56 , pp. 1181-1199
    • Dobson, D.1    Santosa, F.2
  • 17
    • 0003275328 scopus 로고
    • Random fields and inverse problems in imaging
    • École d'Été de Probabilités de Saint-Flour XVIIT, Springer-Verlag, Berlin
    • D. GEMAN, Random fields and inverse problems in imaging, in École d'Été de Probabilités de Saint-Flour XVIIT 1988, Lecture Notes in Math. 1427, Springer-Verlag, Berlin, 1990, pp. 117-193.
    • (1988) Lecture Notes in Math. , vol.1427 , pp. 117-193
    • Geman, D.1
  • 19
    • 0029341230 scopus 로고
    • Nonlinear image recovery with half-quadratic regularization
    • D. GEMAN AND C. YANG, Nonlinear image recovery with half-quadratic regularization, IEEE Trans. Image Process., 4 (1995), pp. 932-946.
    • (1995) IEEE Trans. Image Process. , vol.4 , pp. 932-946
    • Geman, D.1    Yang, C.2
  • 20
    • 0002200424 scopus 로고
    • Statistical methods for tomographic image reconstruction
    • Proceedings of the 46th Session of the International Statistical Institute, Vol. 4 (Tokyo, 1987)
    • S. GEMAN AND D. McCLURE, Statistical methods for tomographic image reconstruction, in Proceedings of the 46th Session of the International Statistical Institute, Vol. 4 (Tokyo, 1987), Bull. Inst. Internat. Statist., 52 (1987), pp. 5-21.
    • (1987) Bull. Inst. Internat. Statist. , vol.52 , pp. 5-21
    • Geman, S.1    McClure, D.2
  • 21
    • 0025404969 scopus 로고
    • Bayesian reconstructions from emission tomography data using a modified EM algorithm
    • P. J. GREEN, Bayesian reconstructions from emission tomography data using a modified EM algorithm, IEEE Trans. Medical Imaging, 9 (1990), pp. 84-93.
    • (1990) IEEE Trans. Medical Imaging , vol.9 , pp. 84-93
    • Green, P.J.1
  • 22
    • 0016033438 scopus 로고
    • A view of three decades of linear filtering theory
    • T. KAILATH, A view of three decades of linear filtering theory, IEEE Trans. Inform. Theory, 20 (1974), pp. 146-181.
    • (1974) IEEE Trans. Inform. Theory , vol.20 , pp. 146-181
    • Kailath, T.1
  • 25
    • 0002902522 scopus 로고
    • Least squares methods for ill-posed problems with a prescribed bound
    • K. S. MILLER, Least squares methods for ill-posed problems with a prescribed bound, SIAM J. Math. Anal., 1 (1970), pp. 52-74.
    • (1970) SIAM J. Math. Anal. , vol.1 , pp. 52-74
    • Miller, K.S.1
  • 26
    • 0031231822 scopus 로고    scopus 로고
    • Estimées localement fortement homogènes
    • M. NIKOLOVA, Estimées localement fortement homogènes, C. R. Acad. Sci. Paris Sér. I Math., 325 (1997), pp. 665-670.
    • (1997) C. R. Acad. Sci. Paris Sér. I Math. , vol.325 , pp. 665-670
    • Nikolova, M.1
  • 27
    • 0142176890 scopus 로고    scopus 로고
    • Local strong homogeneity of a regularized estimator
    • M. NIKOLOVA, Local strong homogeneity of a regularized estimator, SIAM J. Appl. Math., 61 (2000), pp. 633-658.
    • (2000) SIAM J. Appl. Math. , vol.61 , pp. 633-658
    • Nikolova, M.1
  • 28
    • 0038200269 scopus 로고    scopus 로고
    • Weakly constrained minimization. Application to the estimation of images and signals involving constant regions
    • CMLA - ENS de Cachan, France
    • M. NIKOLOVA, Weakly Constrained Minimization. Application to the Estimation of Images and Signals Involving Constant Regions, Tech. report, CMLA - ENS de Cachan, France, 2001. Available online at http://www.cmla.ens-cachan.fr/Cmla/index.html
    • (2001) Tech. Report
    • Nikolova, M.1
  • 31
    • 0001074359 scopus 로고
    • Norms for smoothing and estimation
    • J. R. RICE AND J. S. WHITE, Norms for smoothing and estimation, SIAM Rev., 6 (1964), pp. 243-256.
    • (1964) SIAM Rev. , vol.6 , pp. 243-256
    • Rice, J.R.1    White, J.S.2
  • 33
    • 44049111982 scopus 로고
    • Nonlinear total variation based noise removal algorithm
    • L. RUDIN, S. OSHER, AND C. FATEMI, Nonlinear total variation based noise removal algorithm, Phys. D, 60 (1992), pp. 259-268.
    • (1992) Phys. D , vol.60 , pp. 259-268
    • Rudin, L.1    Osher, S.2    Fatemi, C.3
  • 34
    • 0027542459 scopus 로고
    • A local update strategy for iterative reconstruction from projections
    • K. SAUER AND C. BOUMAN, A local update strategy for iterative reconstruction from projections, IEEE Trans. Signal Process., 41 (1993). pp. 534-548.
    • (1993) IEEE Trans. Signal Process. , vol.41 , pp. 534-548
    • Sauer, K.1    Bouman, C.2
  • 36
    • 0032022521 scopus 로고    scopus 로고
    • Variational approach for edge-preserving regularization using coupled PDE's
    • S. TEBOUL, L. BLANC-FÉRAUD, G. AUBERT, AND M. BARLAUD, Variational approach for edge-preserving regularization using coupled PDE's, IEEE Trans. Image Process., 7 (1998). pp. 387-397.
    • (1998) IEEE Trans. Image Process. , vol.7 , pp. 387-397
    • Teboul, S.1    Blanc-Féraud, L.2    Aubert, G.3    Barlaud, M.4
  • 38
    • 0032096686 scopus 로고    scopus 로고
    • Fast, robust total variation-based reconstruction of noisy, blurred images
    • C. R. VOGEL AND M. E. OMAN, Fast, robust total variation-based reconstruction of noisy, blurred images, IEEE Trans. Image Process., 7 (1998), pp. 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.