GRPCA21 for recovering a corrupted low-rank matrix

Robust principal component analysis (RPCA) based methods via decomposition into low-rank plus sparse matrices offer a wide range of applications for image processing, video processing and 3D computer vision. Most of the time the observed imagery data is often arbitrarily corrupted by anything such as large sparse noise, small dense noise and other unknown fraction, which we call mixed noise in this paper. However, low rank matrix recovery by RPCA is born for the existence of large sparse noise, so its performance and applicability are limited in the presence of mixed noise. In this paper, a generalized robust principal component analysis with norm \(l_{2,1}\) model is proposed to solve the problem of low-rank matrix recovery under mixed large sparse noise and small dense noise. The corrupted matrix is written as a combination that minimizes the nuclear norm, the 1-norm and the norm \(l_{2,1}\), which has high efficiency, flexibility and robustness for low rank matrix recovery from mixed noise. Then a novel and efficient algorithm called random permutation alternative direction of multiplier method is applied to solve the model. Experiments with simulations and real datasets demonstrate efficiency and robustness of this model and algorithm.