A Tikhonov-based projection iteration for nonlinear Ill-posed problems with sparsity constraints

Authors:
Ronny Ramlau;Gerd Teschke
Affiliations:
Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences, Altenbergerstrasse 69, 4040, Linz, Austria;Konrad–Zuse–Zentrum für Informationstechnik Berlin (ZIB), Takustr. 7, 14195, Berlin-Dahlem, Germany
Venue:
Numerische Mathematik
Year:
2006

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Abstract

In this paper, we consider nonlinear inverse problems where the solution is assumed to have a sparse expansion with respect to a preassigned basis or frame. We develop a scheme which allows to minimize a Tikhonov functional where the usual quadratic regularization term is replaced by a one-homogeneous (typically weighted ℓ p ) penalty on the coefficients (or isometrically transformed coefficients) of such expansions. For (p