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Regularization by Functions of Bounded Variation and Applications to Image Enhancement
Authors:E Casas  K Kunisch  C Pola
Institution:(1) Departamento de Matemática Aplicada y Ciencias de la Computación, E.T.S.I. Industriales y de Telecomunicación, Universidad de Cantabria, Av. Los Castros s/n, 39071 Santander, Spain , ES;(2) Institut für Mathematik, Universität Graz, Heinrichstrasse 36, A-8010 Graz, Austria , AT;(3) Departamento de Matemáticas, Estadistica y Computación, Facultad de Ciencias, Universidad de Cantabria, Av. Los Castros s/n, 39071 Santander, Spain , ES
Abstract:Optimization problems regularized by bounded variation seminorms are analyzed. The optimality system is obtained and finite-dimensional approximations of bounded variation function spaces as well as of the optimization problems are studied. It is demonstrated that the choice of the vector norm in the definition of the bounded variation seminorm is of special importance for approximating subspaces consisting of piecewise constant functions. Algorithms based on a primal—dual framework that exploit the structure of these nondifferentiable optimization problems are proposed. Numerical examples are given for denoising of blocky images with very high noise. Accepted 29 March 1998
Keywords:, Bounded variation functions, Image enhancement, Optimality conditions, Numerical approximation, AMS Classification,,,,,,26A45, 49J45, 49K99, 49M29,
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