A Derivative-Free Approach to Total Variation Regularization

Carsten Pontow; Otmar Scherzer

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arXiv · 0911.1293

A Derivative-Free Approach to Total Variation Regularization

Carsten Pontow·Otmar Scherzer

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Abstract

The goal of this paper is to present a novel approach for total variation regularization and Sobolev minimization, which are prominent tools for variational imaging. Thereby we use derivative free characterizations of the total variation semi-norm and Sobolev semi-norms of functions recently derived by Bourgain, Brézis, Mironescu and Dávila. Their analysis is to approximate the semi-norms of a function by singular integral operators. With this characterization we derive a series of novel regularization methods for total variation minimization which have as a novel feature a non-local double integral regularization term.

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BibTeX RIS

Carsten Pontow, Otmar Scherzer. 2009-11-06. A Derivative-Free Approach to Total Variation Regularization. https://arxiv.org/abs/0911.1293

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