Semi-Linearized Proximal Alternating Minimization for a Discrete MumfordÎÜShah Model


Mumford-Shah is a typical model in image segmentation, and various approximations have been made because of the difficulties of the model. Joint picture restoration and contour detection are the primary goals of this functional. Mumford-nonsmooth Shah's penalizations, as well as the assumptions of Proximal Alternating Linearized Minimization (PALM), need a discrete formulation of the Mumford-Shah functional, which we present here. In a second contribution, we loosen some of the functionals' assumptions to construct an unique Semi-Linearized Proximal Alternated Minimization method with proven convergence. For denoising, picture restoration, and RGB-color denoising, we compare the algorithm's performance with other nonsmooth penalizations, including Gaussian and Poisson denoising. With respect to the Mumford-Shah functional and a discrete version of the Ambrosio-Tortorelli functional, the findings are compared. When it comes to denoising and segmentation, SL-PAM outperforms the original PALM method by a wide margin.

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