Author:
Hilb Stephan,Langer Andreas,Alkämper Martin
Abstract
AbstractBased on the Fenchel duality we build a primal-dual framework for minimizing a general functional consisting of a combined$$L^1$$L1and$$L^2$$L2data-fidelity term and a scalar or vectorial total variation regularisation term. The minimization is performed over the space of functions of bounded variations and appropriate discrete subspaces. We analyze the existence and uniqueness of solutions of the respective minimization problems. For computing a numerical solution we derive a semi-smooth Newton method on finite element spaces and highlight applications in denoising, inpainting and optical flow estimation.
Funder
Ministerium für Wissenschaft, Forschung und Kunst Baden-Württemberg
Deutsche Forschungsgemeinschaft
Publisher
Springer Science and Business Media LLC
Subject
Computational Theory and Mathematics,General Engineering,Theoretical Computer Science,Software,Applied Mathematics,Computational Mathematics,Numerical Analysis
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