  Signals 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
functional -- are advantageous in this scenario, in particular, in connection
with segmentation. However, due to their non-convexity, minimization of such
functionals is challenging. In this paper we propose a new iterative
minimization strategy for the multivariate Potts functional dealing with
indirect, noisy measurements. We provide a convergence analysis and underpin
our findings with numerical experiments.
