Iteratively Solving Linear Inverse Problems under General Convex Contraints
Please always quote using this URN: urn:nbn:de:0297-zib-9304
- We consider linear inverse problems where the solution is assumed to fulfill some general homogeneous convex constraint. We develop an algorithm that amounts to a projected Landweber iteration and that provides and iterative approach to the solution of this inverse problem. For relatively moderate assumptions on the constraint we can always prove weak convergence of the iterative scheme. In certain cases, i.e. for special families of convex constraints, weak convergence implies norm convergence. The presented approach covers a wide range of problems, e.g. Besov- or BV-restoration for which we present also numerical experiments in the context of image processing.
| Author: | Ingrid Daubechies, Gerd Teschke, Luminita Vese |
|---|---|
| Document Type: | ZIB-Report |
| Tag: | Besov- and BV Image Restoration; Landweber Iteration; Linear Inverse Problems |
| MSC-Classification: | 45-XX INTEGRAL EQUATIONS / 45Qxx Inverse problems / 45Q05 Inverse problems |
| Date of first Publication: | 2006/06/27 |
| Series (Serial Number): | ZIB-Report (06-36) |
| ZIB-Reportnumber: | 06-36 |
| Published in: | Appeared under the title "Iteratively solving linear inverse problems with general convex constraints" in: Inverse Problems and Imaging, 1(1), 29-46, 2007 |
