Author:
Kiefer Lukas,Storath Martin,Weinmann Andreas
Abstract
AbstractSignals and images with discontinuities appear in many problems in such diverse areas as biology, medicine, mechanics and electrical engineering. The concrete data are often discrete, indirect and noisy measurements of some quantities describing the signal under consideration. A frequent task is to find the segments of the signal or image which corresponds to finding the discontinuities or jumps in the data. Methods based on minimizing the piecewise constant Mumford–Shah functional—whose discretized version is known as Potts energy—are advantageous in this scenario, in particular, in connection with segmentation. However, due to their non-convexity, minimization of such energies is challenging. In this paper, we propose a new iterative minimization strategy for the multivariate Potts energy dealing with indirect, noisy measurements. We provide a convergence analysis and underpin our findings with numerical experiments.
Funder
Hochschule Darmstadt University of Applied Sciences
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computational Theory and Mathematics,Computational Mathematics,Analysis
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