Iteratively solving linear inverse problems under general convex constraints

Published

Journal Article

© 2007 AIMSciences. 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.

Full Text

Duke Authors

Cited Authors

  • Daubechies, I; Teschke, G; Vese, L

Published Date

  • January 1, 2007

Published In

Volume / Issue

  • 1 / 1

Start / End Page

  • 29 - 46

Electronic International Standard Serial Number (EISSN)

  • 1930-8345

International Standard Serial Number (ISSN)

  • 1930-8337

Digital Object Identifier (DOI)

  • 10.3934/ipi.2007.1.29

Citation Source

  • Scopus