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Volumn 18, Issue 6, 2010, Pages 677-699

Theory and examples of variational regularization with non-metric fitting functionals

Author keywords

Convergence rates; Poisson noise; Variational inequalities; Variational regularization

Indexed keywords


EID: 78650735752     PISSN: 09280219     EISSN: None     Source Type: Journal    
DOI: 10.1515/JIIP.2010.031     Document Type: Article
Times cited : (35)

References (25)
  • 2
    • 84864760335 scopus 로고    scopus 로고
    • An extension of the variational inequality approach for nonlinear ill-posed problems
    • R. I. Boţ and B. Hofmann, An extension of the variational inequality approach for nonlinear ill-posed problems, Journal of Integral Equations and Applications 22 (2010), 369-392.
    • (2010) Journal of Integral Equations and Applications , vol.22 , pp. 369-392
    • Boţ, R.I.1    Hofmann, B.2
  • 3
    • 70350634124 scopus 로고    scopus 로고
    • Regularization with non-convex separable constraints
    • K. Bredies and D. A. Lorenz, Regularization with non-convex separable constraints, Inverse Problems 25 (2009), 085011, 14pp.
    • (2009) Inverse Problems , vol.25
    • Bredies, K.1    Lorenz, D.A.2
  • 4
    • 6444243748 scopus 로고    scopus 로고
    • Convergence rates of convex variational regularization
    • M. Burger and S. Osher, Convergence rates of convex variational regularization, Inverse Problems (2004), 1411-1421.
    • (2004) Inverse Problems , pp. 1411-1421
    • Burger, M.1    Osher, S.2
  • 5
    • 0343650333 scopus 로고
    • Maximum Entropy Regularization for Fredholm Integral Equations of the First Kind
    • P. P. B. Eggermont, Maximum Entropy Regularization for Fredholm Integral Equations of the First Kind, SIAM Journal on Mathematical Analysis 24 (1993), 1557-1576.
    • (1993) SIAM Journal on Mathematical Analysis , vol.24 , pp. 1557-1576
    • Eggermont, P.P.B.1
  • 6
    • 0003277393 scopus 로고    scopus 로고
    • Regularization of Inverse Problems
    • Kluwer Academic Publishers, Dordrecht
    • H. W. Engl, M. Hanke and A. Neubauer, Regularization of Inverse Problems, Mathematics and its Applications 375, Kluwer Academic Publishers, Dordrecht, 1996.
    • (1996) Mathematics and Its Applications , vol.375
    • Engl, H.W.1    Hanke, M.2    Neubauer, A.3
  • 7
    • 36149030945 scopus 로고
    • Convergence rates for Tikhonov regularization of non-linear ill-posed problems
    • H. W. Engl, K. Kunisch and A. Neubauer, Convergence rates for Tikhonov regularization of non-linear ill-posed problems, Inverse Problems 5 (1989), 523-540.
    • (1989) Inverse Problems , vol.5 , pp. 523-540
    • Engl, H.W.1    Kunisch, K.2    Neubauer, A.3
  • 8
    • 77951994600 scopus 로고    scopus 로고
    • A New Approach to Source Conditions in Regularization with General Residual Term
    • J. Flemming and B. Hofmann, A New Approach to Source Conditions in Regularization with General Residual Term, Numerical Functional Analysis and Optimization 31 (2010), 254-284.
    • (2010) Numerical Functional Analysis and Optimization , vol.31 , pp. 254-284
    • Flemming, J.1    Hofmann, B.2
  • 11
    • 78049421232 scopus 로고    scopus 로고
    • Generalized Bregman distances and convergence rates for non-convex regularization methods
    • M. Grasmair, Generalized Bregman distances and convergence rates for non-convex regularization methods, Inverse Problems 26 (2010), 115014 (16pp).
    • (2010) Inverse Problems , vol.26
    • Grasmair, M.1
  • 13
    • 70350327168 scopus 로고    scopus 로고
    • Approximate source conditions for nonlinear ill-posed problems - Chances and limitations
    • T. Hein and B. Hofmann, Approximate source conditions for nonlinear ill-posed problems - chances and limitations, Inverse Problems 25 (2009), 035003, 16pp.
    • (2009) Inverse Problems , vol.25
    • Hein, T.1    Hofmann, B.2
  • 14
    • 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. Pöschl and O. Scherzer, A convergence rates result for Tikhonov regularization in Banach spaces with non-smooth operators, Inverse Problems 23 (2007), 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
  • 15
    • 14844311918 scopus 로고    scopus 로고
    • On maximum entropy regularization for a specific inverse problem of option pricing
    • DOI 10.1163/1569394053583739
    • B. Hofmann and R. Krämer, On maximum entropy regularization for a specific inverse problem of option pricing, Jounal of Inverse and Ill-posed Problems 13 (2005), 41-63. (Pubitemid 40349993)
    • (2005) Journal of Inverse and Ill-Posed Problems , vol.13 , Issue.1 , pp. 41-63
    • Hofmann, B.1    Kramer, R.2
  • 16
    • 77749289494 scopus 로고    scopus 로고
    • On the interplay of source conditions and variational inequalities for nonlinear ill-posed problems
    • B. Hofmann and M. Yamamoto, On the interplay of source conditions and variational inequalities for nonlinear ill-posed problems, Applicable Analysis 89 (2010), 1705-1727.
    • (2010) Applicable Analysis , vol.89 , pp. 1705-1727
    • Hofmann, B.1    Yamamoto, M.2
  • 17
    • 77956031093 scopus 로고    scopus 로고
    • Department of Mathematics, Chinese University of Hong Kong, Technical report no. 2010-02 (369), Shatin, Hong Kong, Feb.
    • B. Jin and J. Zou, Iterative Parameter Choice by Discrepancy Principle, Department of Mathematics, Chinese University of Hong Kong, Technical report no. 2010-02 (369), Shatin, Hong Kong, Feb. 2010.
    • (2010) Iterative Parameter Choice by Discrepancy Principle
    • Jin, B.1    Zou, J.2
  • 18
    • 84860523889 scopus 로고    scopus 로고
    • Computational and Statistical Inverse Problems
    • Springer
    • J. Kaipio and E. Somersalo, Computational and Statistical Inverse Problems, Applied Mathematical Science 160, Springer, 2005.
    • (2005) Applied Mathematical Science , vol.160
    • Kaipio, J.1    Somersalo, E.2
  • 19
    • 34247500347 scopus 로고    scopus 로고
    • A variational approach to reconstructing images corrupted by poisson noise
    • DOI 10.1007/s10851-007-0652-y
    • T. Le, R. Chartrand and T. J. Asaki, A Variational Approach to Reconstructing Images Corrupted by Poisson Noise, Journal of Mathematical Imaging and Vision 27 (2007), 257-263. (Pubitemid 46664094)
    • (2007) Journal of Mathematical Imaging and Vision , vol.27 , Issue.3 , pp. 257-263
    • Le, T.1    Chartrand, R.2    Asaki, T.J.3
  • 20
    • 77957906834 scopus 로고    scopus 로고
    • Improved and extended results for enhanced convergence rates of Tikhonov regularization in Banach spaces
    • A. Neubauer, T. Hein, B. Hofmann, S. Kindermann and U. Tautenhahn, Improved and extended results for enhanced convergence rates of Tikhonov regularization in Banach spaces, Applicable Analysis 89 (2010), 1729-1743.
    • (2010) Applicable Analysis , vol.89 , pp. 1729-1743
    • Neubauer, A.1    Hein, T.2    Hofmann, B.3    Kindermann, S.4    Tautenhahn, U.5
  • 22
    • 23244453192 scopus 로고    scopus 로고
    • Regularization of ill-posed problems in Banach spaces: Convergence rates
    • DOI 10.1088/0266-5611/21/4/007, PII S0266561105930761
    • E. Resmerita, Regularization of ill-posed problems in Banach spaces: convergence rates, Inverse Problems 21 (2005), 1303-1314. (Pubitemid 41090541)
    • (2005) Inverse Problems , vol.21 , Issue.4 , pp. 1303-1314
    • Resmerita, E.1
  • 23
    • 34547616147 scopus 로고    scopus 로고
    • Joint additive Kullback-Leibler residual minimization and regularization for linear inverse problems
    • DOI 10.1002/mma.855
    • E. Resmerita and R. S. Anderssen, Joint additive Kullback-Leibler residual minimization and regularization for linear inverse problems, Mathematical Methods in the Applied Sciences 30 (2007), 1527-1544. (Pubitemid 47204318)
    • (2007) Mathematical Methods in the Applied Sciences , vol.30 , Issue.13 , pp. 1527-1544
    • Resmerita, E.1    Anderssen, R.S.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.