Low-Rank Prior in Single Patches for Nonpointwise Impulse Noise Removal

This paper introduces a low-rank prior in small oriented noise-free image patches. Considering an oriented patch as a matrix, a low-rank matrix approximation is enough to preserve the texture details in the optimally oriented patch. Based on this prior, we propose a single-patch method within a generalized joint low-rank and sparse matrix recovery framework to simultaneously detect and remove nonpointwise random-valued impulse noise (e.g., very small blobs). A weighting matrix is incorporated in the framework to encode an initial estimate of the spatial noise distribution. An accelerated proximal gradient method is adapted to estimate the optimal noise-free image patches. Experiments show the effectiveness of our framework in detecting and removing nonpointwise random-valued impulse noise.