Low-Rank and Total Variation Regularization and Its Application to Image Recovery
This addresses image recovery for applications like computer vision, but it is incremental as it builds on existing low-rank and sparsity models.
The paper tackles image recovery from partial or corrupted observations by proposing a formulation that combines low-rank and sparsity in a transformed domain, with an efficient iterative algorithm that outperforms state-of-the-art methods in experiments.
In this paper, we study the problem of image recovery from given partial (corrupted) observations. Recovering an image using a low-rank model has been an 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 transformed space. In this work, we propose a new problem formulation in such a way that we seek to recover an image that is of low-rank and has sparsity in a transformed domain. We further discuss various non-convex non-smooth surrogates of the rank function, leading to a relaxed problem. Then, we present an efficient iterative scheme to solve the relaxed problem that essentially employs the (weighted) singular value thresholding at each iteration. Furthermore, we discuss the convergence properties of the proposed iterative method. We perform extensive experiments, showing that the proposed algorithm outperforms state-of-the-art methodologies in recovering images.