Sparsity Regularization for Radon Measures

Authors:
Otmar Scherzer;Birgit Walch
Affiliations:
Department of Mathematics, University of Innsbruck, Innsbruck, Austria A-6020 and Radon Institute of Computational and Applied Mathematics, Linz, Austria A-4040;Department of Mathematics, University of Innsbruck, Innsbruck, Austria A-6020
Venue:
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
Year:
2009

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Abstract

In this paper we establish a regularization method for Radon measures. Motivated from sparse L 1 regularization we introduce a new regularization functional for the Radon norm, whose properties are then analyzed. We, furthermore, show well-posedness of Radon measure based sparsity regularization. Finally we present numerical examples along with the underlying algorithmic and implementation details. We shall, here, see that the number of iterations turn out of utmost importance when it comes to obtain reliable reconstructions of sparse data with varying intensities.