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

Markus Grasmair

doi:10.3934/ipi.2009.3.383

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2009, Volume 3, Issue 3: 383-387. Doi: 10.3934/ipi.2009.3.383

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

Markus Grasmair^1,

1.
Department of Mathematics, University of Innsbruck, Technikerstr. 21a, 6020 Innsbruck

Received: July 31, 2008

Revised: April 30, 2009

Published: July 2009

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Abstract

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.

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Mathematics Subject Classification: Primary: 65J20; Secondary: 65J22, 49N45.

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

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