Tube Methods for BV Regularization

Authors:
Walter Hinterberger;Michael Hintermüller;Karl Kunisch;Markus Von Oehsen;Otmar Scherzer
Affiliations:
Mathconsult GMBH, Altenberger Str. 74, A-4040 Linz, Austria. walter@mathconsult.co.at;Mathematical Institute, University Graz, A-8020 Graz, Austria. michael.hintermueller@uni-graz.ac.at;Mathematical Institute, University Graz, A-8020 Graz, Austria. karl.kunisch@uni-graz.ac.at;Seminar of Applied Mathematics, ETH Zürich, Zürich, Switzerland. mvo@math.ethz.ch;Department of Computer Science, University Innsbruck, Techniker Str. 25, A-6020 Innsbruck, Austria. otmar.scherzer@uibk.ac.at
Venue:
Journal of Mathematical Imaging and Vision
Year:
2003

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Abstract

In this paper tube methods for reconstructing discontinuous data from noisy and blurred observation data are considered. It is shown that discrete bounded variation (BV)-regularization (commonly used in inverse problems and image processing) and the taut-string algorithm (commonly used in statistics) select reconstructions in a tube. A version of the taut-string algorithm applicable for higher dimensional data is proposed. This formulation results in a bilateral contact problem which can be solved very efficiently using an active set strategy. As a by-product it is shown that the Lagrange multiplier of the active set strategy is an efficient parameter for edge detection.