University of Guilan Journal of Mathematical Modeling 2345-394X 9 1 2021 01 01 A combined dictionary learning and TV model for image restoration with convergence analysis 13 30 4187 10.22124/jmm.2020.15408.1369 EN Souad Mohaoui Department of mathematics, University of Cadi Ayad, Marrakesh, Morocco Abdelilah Hakim Department of mathematics, University of Cadi Ayad, Marrakesh, Morocco Said Raghay Department of mathematics, University of Cadi Ayad, Marrakesh, Morocco Journal Article 2020 01 09 We consider in this paper the $l_0$-norm based dictionary learning approach combined with total variation regularization for the image restoration problem. It is formulated as a nonconvex nonsmooth optimization problem. Despite that this image restoration model has been proposed in many works, it remains important to ensure that the considered minimization method satisfies the global convergence property, which is the main objective of this work. Therefore, we employ the proximal alternating linearized minimization method whereby we demonstrate the global convergence of the generated sequence to a critical point. The results of several experiments demonstrate the performance of the proposed algorithm for image restoration. Image deblurring dictionary learning sparse approximation total variation proximal methods nonconvex optimization https://jmm.guilan.ac.ir/article_4187_8d48376485cc61654259b0f2dd2b02e0.pdf