Jump to ContentJump to Main Navigation
Show Summary Details

Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

6 Issues per year

IMPACT FACTOR increased in 2015: 0.987
Rank 59 out of 312 in category Mathematics and 93 out of 254 in Applied Mathematics in the 2015 Thomson Reuters Journal Citation Report/Science Edition

SCImago Journal Rank (SJR) 2015: 0.583
Source Normalized Impact per Paper (SNIP) 2015: 1.106
Impact per Publication (IPP) 2015: 0.712

Mathematical Citation Quotient (MCQ) 2015: 0.43

See all formats and pricing
Volume 17, Issue 1 (Jan 2009)


An iterative thresholding-like algorithm for inverse problems with sparsity constraints in Banach space

K. Bredies
  • Center for Industrial Mathematics / Fachbereich 3, University of Bremen, Postfach 33 04 40, D-28334 Bremen, Germany. Email:
Published Online: 2009-02-04 | DOI: https://doi.org/10.1515/JIIP.2009.003


This paper addresses the problem of computing the minimizers for Tikhonov functionals associated with inverse problems with sparsity constraints in general Banach spaces. We present, based on splitting the Tikhonov functional into a smooth and a non-smooth part, a general iterative procedure for the Banach-space setting. In case of sparsity constraints, this algorithm yields a successive application of thresholding-like functions which generalizes the well-known iterative soft-thresholding procedure. The convergence properties of the proposed method are studied. Depending on the smoothness and convexity of the underlying spaces, convergence of asymptotic rate is obtained with the help of Bregman and Bregman–Taylor distance estimates. In particular, strong convergence can be achieved for a large class of linear inverse problems with sparsity constraints in Banach space.

Key words.: Iterative thresholding; sparsity constraints; Banach space; generalized gradient projection method; convergence analysis

About the article

Received: 2008-07-25

Published Online: 2009-02-04

Published in Print: 2009-02-01

Citation Information: Journal of Inverse and Ill-posed Problems, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/JIIP.2009.003. Export Citation

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

Esther Klann, Eric Todd Quinto, and Ronny Ramlau
Inverse Problems, 2015, Volume 31, Number 2, Page 025001
Daniel Gerth and Ronny Ramlau
Inverse Problems, 2014, Volume 30, Number 5, Page 055009
Kristian Bredies and Dirk A Lorenz
Inverse Problems, 2009, Volume 25, Number 8, Page 085011

Comments (0)

Please log in or register to comment.
Log in