Adaptive regularizer learning for low rank approximation with application to image denoising

In this paper, we propose an adaptive regularizer learning method in the framework of MAP for low rank approximation (ARLLR). We assume that the prior distribution of the singular values is Laplacian with varying scale parameters. By using a full maximize a posterior (MAP) we learn the optimal scale parameters iteratively. We indicate that ARLLR is equivalent to low rank approximation regularized by Logarithm on singular values. In theory, we prove that ARLLR (Logarithm regularization) although being non-convex can be solved in closed form, and we further prove that local minimum can be easily obtained. Finally, ARLLR is applied to image de-noising. Experimental results show that the proposed method enhances image denoising compared with state-of-the-art image denoising algorithms(especially for BM3D, SAIST and WNNM) in both quantity value (PSNR) and visual quality.