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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\u2013Shah functional\u2014whose discretized version is known as Potts energy\u2014are 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.<\/jats:p>","DOI":"10.1007\/s10208-020-09466-9","type":"journal-article","created":{"date-parts":[[2020,7,6]],"date-time":"2020-07-06T21:02:43Z","timestamp":1594069363000},"page":"649-694","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Iterative Potts Minimization for the Recovery of Signals with Discontinuities from Indirect Measurements: The Multivariate Case"],"prefix":"10.1007","volume":"21","author":[{"given":"Lukas","family":"Kiefer","sequence":"first","affiliation":[]},{"given":"Martin","family":"Storath","sequence":"additional","affiliation":[]},{"given":"Andreas","family":"Weinmann","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,7,6]]},"reference":[{"key":"9466_CR1","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198502456.001.0001","volume-title":"Functions of bounded variation and free discontinuity problems","author":"L Ambrosio","year":"2000","unstructured":"Ambrosio, L., Fusco, N., Pallara, D.: Functions of bounded variation and free discontinuity problems. 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