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In this paper, we study the problem of image recovery from given partial(corrupted) observations. Recovering an image using a low-rank model has beenan active research area in data analysis and machine learning. But often,images are not only of low-rank but they also exhibit sparsity in a transformedspace. In this work, we propose a new problem formulation in such a way that weseek to recover an image that is of low-rank and has sparsity in a transformeddomain. We further discuss various non-convex non-smooth surrogates of the rankfunction, leading to a relaxed problem. Then, we present an efficient iterativescheme to solve the relaxed problem that essentially employs the (weighted)singular value thresholding at each iteration. Furthermore, we discuss theconvergence properties of the proposed iterative method. We perform extensiveexperiments, showing that the proposed algorithm outperforms state-of-the-artmethodologies in recovering images.

Low-Rank and Total Variation Regularization and Its Application to Image Recovery