Well-posedness and convergence rates for sparse regularization with sublinear $l^q$ penalty term
Markus Grasmair - Department of Mathematics, University of Innsbruck, Technikerstr. 21a, 6020 Innsbruck, Austria (email)
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.
Keywords: Tikhonov Regularization, Sparsity, Convergence Rates.
Received: August 2008; Revised: May 2009; Published: July 2009.
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