Outlier-robust image inpainting via nuclear norm-guided bilinear factorization

Matrix factorization (MF)-based methods are very popular in image inpainting fields. However, the existing MF-based methods are mainly considered in the noiseless case or the cases where the noise is of Gaussian type. Although there exist a few MF-based methods that were proposed to resist the outliers and impulsive noise, they do not well pose some effective constraints on the factor matrices, which to some extent limits the resultant restoration performance. Inspired by a HOAT (half-quadratic optimization based on additive form for truncated quadratic function) algorithm proposed recently, we first consider adding a nuclear norm-guided bilinear factorization constraint into it, and based on the popular block coordinate descent framework; thus, we propose an improved HOAT algorithm to deal with the outlier-robust image inpainting tasks. Surprisingly, this small modification makes our algorithm possess the capability to perform much better than the HOAT algorithm in both restoration accuracy and running time when the rank estimate tends to be large. By contrast, the HOAT algorithm will result in much worse performance under the same settings of rank estimate. Extensive experiments on outlier-robust image inpainting with random/non-random masks further verify the effectiveness of the proposed algorithm when it is compared with some state-of-the-art MF-based algorithms.