# American Institute of Mathematical Sciences

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