TY - GEN A1 - Daubechies, Ingrid A1 - Teschke, Gerd A1 - Vese, Luminita T1 - Iteratively Solving Linear Inverse Problems under General Convex Contraints N2 - 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. T3 - ZIB-Report - 06-36 KW - Linear Inverse Problems KW - Landweber Iteration KW - Besov- and BV Image Restoration Y1 - 2006 UR - https://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/930 UR - https://nbn-resolving.org/urn:nbn:de:0297-zib-9304 ER -