Showing a limited preview of this publication:
Abstract
This paper is concerned with iterated soft shrinkage for minimizing Tikhonov functionals with sparsity constraints. Motivated by parameter identification problems for partial differential equations we assume, that only adaptive operator evaluations [Ax]h are available. Adaptive refinement strategies lead to different realizations of [A]h in every iteration step, hence, we cannot assume a bound on the approximation error in the operator norm.
We will develop the basic convergence and regularization results for linear inverse problems with adaptive operator evaluations and penalty terms for 1 < p ≤ 2.
Key words.: regularization of ill-posed problems; sparsity; iterated soft shrinkage; adaptive operator evaluations
Received: 2008-02-25
Published Online: 2009-06-16
Published in Print: 2009-June
© de Gruyter 2009
