Robust Low-Rank Matrix Recovery Fusing Local-Smoothness

Recovering low-rank matrices by nuclear norm minimization and local-smooth matrices by total variation seminorm minimization are two common methods in the context of compressive sensing. As a matter of fact, the two properties simultaneously exist in many real-world datasets, typically exampling hyperspectral images. The two methods may not perform well in this situation. To better address this issue, in this letter, we study the correlated total variation norm minimization problem both theoretically and numerically. We obtain an error bound for the robust recovery of our method in theory, which reflects that this model indeed benefits from low-rank and local-smooth properties of the matrix to be restored. Experiments on the recovery of hyperspectral images show that this model is superior to many other competing ones.