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This paper is concerned with the analysis of convergent sequential andparallel overlapping domain decomposition methods for the minimization offunctionals formed by a discrepancy term with respect to data and a totalvariation constraint. To our knowledge, this is the first successful attempt ofaddressing such strategy for the nonlinear, nonadditive, and nonsmooth problemof total variation minimization. We provide several numerical experiments,showing the successful application of the algorithm for the restoration of 1Dsignals and 2D images in interpolation/inpainting problems respectively, and ina compressed sensing problem, for recovering piecewise constant medical-typeimages from partial Fourier ensembles.

A Convergent Overlapping Domain Decomposition Method for Total Variation Minimization