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An algorithmic framework for Mumford-Shah regularization of inverse problems in imaging.
Inverse Probl. 31:115011 (2015)
The Mumford–Shah model is a very powerful variational approach for edge preserving regularization of image reconstruction processes. However, it is algorithmically challenging because one has to deal with a non-smooth and non-convex functional. In this paper, we propose a new efficient algorithmic framework for Mumford–Shah regularization of inverse problems in imaging. It is based on a splitting into specific subproblems that can be solved exactly. We derive fast solvers for the subproblems which are key for an efficient overall algorithm. Our method neither requires a priori knowledge of the gray or color levels nor of the shape of the discontinuity set. We demonstrate the wide applicability of the method for different modalities. In particular, we consider the reconstruction from Radon data, inpainting, and deconvolution. Our method can be easily adapted to many further imaging setups. The relevant condition is that the proximal mapping of the data fidelity can be evaluated a within reasonable time. In other words, it can be used whenever classical Tikhonov regularization is possible.
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Publication type Article: Journal article
Document type Scientific Article
Keywords Admm ; Computed Tomography ; Deconvolution ; Dynamic Programming ; Image Reconstruction ; Inverse Problem ; Mumford-shah Functional
ISSN (print) / ISBN 0266-5611
Journal Inverse Problems
Quellenangaben Volume: 31, Issue: 11, Article Number: 115011
Publisher Institute of Physics Publishing (IOP)
Reviewing status Peer reviewed
Institute(s) Institute of Computational Biology (ICB)