Iterative thresholding algorithms

被引：122

作者：

Fornasier, Massimo ^{[2
]}

Rauhut, Holger ^{[1
]}

机构：

[1] Univ Vienna, Dept Math, Numer Harmon Anal Grp, A-1090 Vienna, Austria

[2] Princeton Univ, Program Appl & Computat Math, Princeton, NJ 08544 USA

来源：

APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS | 2008年 / 25卷 / 02期

关键词：

linear inverse problems; joint sparsity; thresholded Landweber iterations; frames; variational calculus on sequence spaces; Gamma-convergence;

D O I：

10.1016/j.acha.2007.10.005

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This article provides a variational formulation for hard and firm thresholding. A related functional can be used to regularize inverse problems by sparsity constraints. We show that a damped hard or firm thresholded Landweber iteration converges to its minimizer. This provides an alternative to an algorithm recently studied by the authors. We prove stability of minimizers with respect to the parameters of the functional by means of Gamma-convergence. All investigations are done in the general setting of vector-valued (multi-channel) data. (c) 2007 Elsevier Inc. All rights reserved.

引用

页码：187 / 208

页数：22

共 38 条

[1]

ANTHOINE S, 2005, THESIS PRINCETON U

[2]

Baron D., 2005, DISTRIBUTED COMPRESS

[3]

Blumensath T., 2007, P IEEE INT C AC SPEE

[4] Stable signal recovery from incomplete and inaccurate measurements [J].

Candes, Emmanuel J. ;

Romberg, Justin K. ;

Tao, Terence .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2006, 59 (08) :1207-1223

[5] Image recovery via total variation minimization and related problems [J].

Chambolle, A ;

Lions, PL .

NUMERISCHE MATHEMATIK, 1997, 76 (02) :167-188

[6] Nonlinear wavelet image processing: Variational problems, compression, and noise removal through wavelet shrinkage [J].

Chambolle, A ;

DeVore, RA ;

Lee, NY ;

Lucier, BJ .

IEEE TRANSACTIONS ON IMAGE PROCESSING, 1998, 7 (03) :319-335

[7]

Christensen O., 2003, An Introduction to Frames and Riesz Bases, DOI [10.1007/978-0-8176-8224-8, DOI 10.1007/978-0-8176-8224-8]

[8]

Dal Maso G., 1993, INTRO GAMMA CONVERGE

[9] Variational image restoration by means of wavelets: Simultaneous decomposition, deblurring, and denoising [J].

Daubechies, I ;

Teschke, G .

APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS, 2005, 19 (01) :1-16

[10] An iterative thresholding algorithm for linear inverse problems with a sparsity constraint [J].

Daubechies, I ;

Defrise, M ;

De Mol, C .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2004, 57 (11) :1413-1457

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