August  2009, 3(3): 383-387. doi: 10.3934/ipi.2009.3.383

Well-posedness and convergence rates for sparse regularization with sublinear $l^q$ penalty term

1. 

Department of Mathematics, University of Innsbruck, Technikerstr. 21a, 6020 Innsbruck, Austria

Received  August 2008 Revised  May 2009 Published  July 2009

This paper deals with the application of non-convex, sublinear penalty terms to the regularization of possibly non-linear inverse problems the solutions of which are assumed to have a sparse expansion with respect to some given basis or frame. It is shown that this type of regularization is well-posed and yields sparse results. Moreover, linear convergence rates are derived under the additional assumption of a certain range condition.
Citation: Markus Grasmair. Well-posedness and convergence rates for sparse regularization with sublinear $l^q$ penalty term. Inverse Problems & Imaging, 2009, 3 (3) : 383-387. doi: 10.3934/ipi.2009.3.383
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