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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 nonconvex 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 subproblemsdoi:10.1088/0266-5611/31/11/115011 fatcat:gdces3rkkvdulkoqyo2ty52ndy