Weighted bilinear factorization of low-rank matrix with structural smoothness for image denoising

Low-rank matrix restoration, which aims to recover low-rank structures from degraded observation matrices, has been extensively studied in computer vision. However, the existing methods always suffer from data information loss caused by over shrinkage of the rank component or heavy computation burden brought by singular value decomposition. To simultaneously account for these two issues, in this work we propose a low-rank restoration model based on the bilinear factorization for image denoising. Specifically, the essence of the weighted Schatten 2/3 quasi-norm is defined as the hybrid norm of weighted Frobenius/nuclear, thus is extended to a more solvable optimization problem by harnessing the convexity of both factor matrix terms. Moreover, the weights are introduced to \(\ell _p\) ${\ell }_p$ norm with \(p = 2/3\) $p=2/3$ , which both leverages the solvability of the \(\ell _{2/3}\) ${\ell }_{2/3}$ norm and mitigates the over shrinkage problem. Furthermore, for effectively preserving the edge features of image, the total variation (TV) norm is also integrated into the proposed weighted low-rank restoration model. Collectively, above rationally introduced ingredients enables our algorithm to enhance the structural smoothness and effectively remove large sparse noise in the case of natural images with low rank attributes. Finally, the experiments on several data sets show that the proposed method significantly improve the quality of reconstructed images, compared with existing low-rank methods, which confirms the desired roles of introduced ingredients and the effectiveness of our algorithm.