Structural properties of solutions to total variation regularization problems

被引：103
|
作者：
Ring, W [1 ]
机构：
[1] Graz Univ, Inst Math, A-8010 Graz, Austria
来源：
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE | 2000年 / 34卷 / 04期
关键词：
total variation regularization; piecewise constant function; convex optimization; Lebesgue decomposition; singular measures;
D O I：
10.1051/m2an:2000104
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In dimension one it is proved that the solution to a total variation-regularized least-squares problem is always a function which is "constant almost everywhere", provided that the data are in a certain sense outside the range of the operator to be inverted. A similar, but weaker result is derived in dimension two.
引用
收藏
页码：799 / 810
页数：12
相关论文
共 50 条
  • [1] A function space framework for structural total variation regularization with applications in inverse problems
    Hintermuller, Michael
    Holler, Martin
    Papafitsoros, Kostas
    [J]. INVERSE PROBLEMS, 2018, 34 (06)
  • [2] Regularization of linear inverse problems with total generalized variation
    Bredies, Kristian
    Holler, Martin
    [J]. JOURNAL OF INVERSE AND ILL-POSED PROBLEMS, 2014, 22 (06): : 871 - 913
  • [3] ON THE KANTOROVICH THEOREM AND THE REGULARIZATION OF TOTAL VARIATION DENOISING PROBLEMS
    Melara, L. A.
    Kearsley, A. J.
    [J]. ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 2010, 40 (02) : 595 - 607
  • [4] Properties of exact solutions to the problem of regularization of the total variation of one-variable functions
    S. M. Voronin
    A. Yu. Makovetsky
    V. I. Kober
    V. N. Karnaukhov
    [J]. Journal of Communications Technology and Electronics, 2015, 60 : 1356 - 1359
  • [5] Properties of exact solutions to the problem of regularization of the total variation of one-variable functions
    Voronin, S. M.
    Makovetsky, A. Yu.
    Kober, V. I.
    Karnaukhov, V. N.
    [J]. JOURNAL OF COMMUNICATIONS TECHNOLOGY AND ELECTRONICS, 2015, 60 (12) : 1356 - 1359
  • [6] Parametric derivatives in inverse conductivity problems with total variation regularization
    Wade, J. Gordon
    Senior, Kenneth
    Seubert, Steven
    [J]. INTERNATIONAL JOURNAL OF APPLIED ELECTROMAGNETICS AND MECHANICS, 2022, 69 (03) : 431 - 442
  • [7] Total Deep Variation: A Stable Regularization Method for Inverse Problems
    Kobler, Erich
    Effland, Alexander
    Kunisch, Karl
    Pock, Thomas
    [J]. IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, 2022, 44 (12) : 9163 - 9180
  • [8] Inverse Potential Problems for Divergence of Measures with Total Variation Regularization
    L. Baratchart
    C. Villalobos Guillén
    D. P. Hardin
    M. C. Northington
    E. B. Saff
    [J]. Foundations of Computational Mathematics, 2020, 20 : 1273 - 1307
  • [9] SEMI-LOCAL TOTAL VARIATION FOR REGULARIZATION OF INVERSE PROBLEMS
    Condat, Laurent
    [J]. 2014 PROCEEDINGS OF THE 22ND EUROPEAN SIGNAL PROCESSING CONFERENCE (EUSIPCO), 2014, : 1806 - 1810
  • [10] Inverse Potential Problems for Divergence of Measures with Total Variation Regularization
    Baratchart, L.
    Guillen, C. Villalobos
    Hardin, D. P.
    Northington, M. C.
    Saff, E. B.
    [J]. FOUNDATIONS OF COMPUTATIONAL MATHEMATICS, 2020, 20 (05) : 1273 - 1307
12345