Denoising of Smooth Images Using L1-Fitting

Authors:
T. Kärkkäinen;K. Kunisch;K. Majava
Affiliations:
Department of Mathematical Information Technology, University of Jyväskylä, P.O. Box 35 (Agora), 40014, Jyväskylä, Finland;Institute for Mathematics, University of Graz, P.O. Box 35 (Agora), Heinrichstr. 36, 8010, Graz, Austria;Department of Mathematical Information Technology, University of Jyväskylä, P.O. Box 35 (Agora), Heinrichstr. 36, 40014, Jyväskylä, Finland
Venue:
Computing
Year:
2005

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Abstract

In this paper, denoising of smooth (H10-regular) images is considered. The purpose of the paper is basically twofold. First, to compare the denoising methods based on L1- and L2-fitting. Second, to analyze and realize an active-set method for solving the non-smooth optimization problem arising from the former approach. More precisely, we formulate the algorithm, proof its convergence, and give an efficient numerical realization. Several numerical experiments are presented, where the convergence of the proposed active-set algorithm is studied and the denoising properties of the methods based on L1- and L2-fitting are compared. Also a heuristic method for determining the regularization parameter is presented and tested.