Optimal Convergence Rates Results for Linear Inverse Problems in Hilbert Spaces

被引：20
|
作者：
Albani, V. [1 ]
Elbau, P. [1 ]
de Hoop, M. V. [2 ,3 ]
Scherzer, O. [1 ,4 ]
机构：
[1] Univ Vienna, Computat Sci Ctr, Oskar Morgenstern Pl 1, A-1090 Vienna, Austria
[2] Rice Univ, Dept Computat & Appl Math, Houston, TX USA
[3] Rice Univ, Dept Earth Sci, Houston, TX USA
[4] Johann Radon Inst Computat & Appl Math RICAM, Linz, Austria
来源：
NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION | 2016年 / 37卷 / 05期
基金：
奥地利科学基金会;
关键词：
Approximative source conditions; convergence rates; linear inverse problems; regularization; variational source conditions; TIKHONOV REGULARIZATION;
D O I：
10.1080/01630563.2016.1144070
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this article, we prove optimal convergence rates results for regularization methods for solving linear ill-posed operator equations in Hilbert spaces. The results generalizes existing convergence rates results on optimality to general source conditions, such as logarithmic source conditions. Moreover, we also provide optimality results under variational source conditions and show the connection to approximative source conditions.
引用
收藏
页码：521 / 540
页数：20
相关论文
共 50 条
  • [21] Towards optimal sensor placement for inverse problems in spaces of measures
    Huynh, Phuoc-Truong
    Pieper, Konstantin
    Walter, Daniel
    INVERSE PROBLEMS, 2024, 40 (05)
  • [22] Convergence of posteriors for structurally non-identified problems using results from the theory of inverse problems
    Radde, Nicole E.
    Offtermatt, Jonas
    JOURNAL OF INVERSE AND ILL-POSED PROBLEMS, 2014, 22 (02): : 251 - 276
  • [23] Gradient method in Hilbert-Besov spaces for the optimal control of parabolic free boundary problems
    Abdulla, Ugur G.
    Bukshtynov, Vladislav
    Hagverdiyev, Ali
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2019, 346 : 84 - 109
  • [24] CONVERGENCE RATES FOR ILL-POSED INVERSE PROBLEMS WITH AN UNKNOWN OPERATOR
    Johannes, Jan
    Van Bellegem, Sebastien
    Vanhems, Anne
    ECONOMETRIC THEORY, 2011, 27 (03) : 522 - 545
  • [25] Convergence rates of general regularization methods for statistical inverse problems and applications
    Bissantz, N.
    Hohage, T.
    Munk, A.
    Ruymgaart, F.
    SIAM JOURNAL ON NUMERICAL ANALYSIS, 2007, 45 (06) : 2610 - 2636
  • [26] Convergence rates for the joint solution of inverse problems with compressed sensing data
    Ebner, Andrea
    Haltmeier, Markus
    INVERSE PROBLEMS, 2023, 39 (01)
  • [27] A note on convergence of solutions of total variation regularized linear inverse problems
    Iglesias, Jose A.
    Mercier, Gwenael
    Scherzer, Otmar
    INVERSE PROBLEMS, 2018, 34 (05)
  • [28] Optimal Adaptation for Early Stopping in Statistical Inverse Problems
    Blanchard, Gilles
    Hoffmann, Marc
    Reiss, Markus
    SIAM-ASA JOURNAL ON UNCERTAINTY QUANTIFICATION, 2018, 6 (03): : 1043 - 1075
  • [29] ON FRACTIONAL ASYMPTOTICAL REGULARIZATION OF LINEAR ILL-POSED PROBLEMS IN HILBERT SPACES
    Zhang, Ye
    Hofmann, Bernd
    FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2019, 22 (03) : 699 - 721
  • [30] Saturation of regularization methods for linear ill-posed problems in Hilbert spaces
    Mathé, P
    SIAM JOURNAL ON NUMERICAL ANALYSIS, 2004, 42 (03) : 968 - 973
12345