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Overlapping and nonoverlapping domain decomposition methods for image restoration

Zeghbib Fatima Zohra, Maouni Messaoud, Nouri Fatima Zohra


In concrete applications for image processing, one might be interested to recover at best a digital image provided only partial linear or nonlinear measurements, possibly corrupted by noise. Given the observation that natural and man-made images are characterized by a relatively small number of edges and extensive relatively uniform parts, one may want to help the reconstruction by imposing that the interesting solution is the one which matches the given data and has also a few discontinuities localized on sets of lower dimension. In this paper we review concisely both nonoverlapping and overlapping domain decomposition methods for total variation minimization and we provide their properties of convergence to global minimizers. Moreover, we show numerical applications in classical problems of signal and image processing.

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