Non-smooth SOR for L1-Fitting: Convergence Study and Discussion of Related Issues

Authors:
R. Glowinski;T. Kärkkäinen;T. Valkonen;A. Ivannikov
Affiliations:
Department of Mathematics, University of Houston, Houston, USA 77204-3008;Department of Mathematical Information Technology, Universify of Jyväskylä, University of Jyväskylä, Finland 40014;Department of Mathematical Information Technology, Universify of Jyväskylä, University of Jyväskylä, Finland 40014;Department of Mathematical Information Technology, Universify of Jyväskylä, University of Jyväskylä, Finland 40014
Venue:
Journal of Scientific Computing
Year:
2008

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Abstract

In this article, the denoising of smooth (H 1-regular) images is considered. To reach this objective, we introduce a simple and highly efficient over-relaxation technique for solving the convex, non-smooth optimization problems resulting from the denoising formulation. We describe the algorithm, discuss its convergence and present the results of numerical experiments, which validate the methods under consideration with respect to both efficiency and denoising capability. Several issues concerning the convergence of an Uzawa algorithm for the solution of the same problem are also discussed.