A convergent overlapping domain decomposition method for total variation minimization (Q711582)

The authors consider the analysis of convergent sequential and parallel overlapping domain decorrmposition methods for the minimization of functionals formed by a discrepancy term with respect to the data and a total variation constraint of the form \[ J(u):= \| Tu- g\|^2_{L^2(\Omega)}= 2\alpha|D(u)|(\Omega). \] The authors provide several numerical experiments, showing the successful application of the algorithm for the restoration of 1D signals and 2D in interpolation/inpainting problems, respectively, and in a compressed sensing problem, for recovering piecewise constant medical-type images from partial Fourier ensembles.