Color Image Denoising via Tensor Robust PCA with Nonconvex and Nonlocal Regularization

Xiaoyu Geng, Qiang Guo, Caiming Zhang

Abstract: Tensor robust principal component analysis (TRPCA) is an important algorithm for color image denoising by treating the whole image as a tensor and shrinking all singular values equally. In this paper, to improve the denoising performance of TRPCA, we propose a variant of TRPCA model. Specifically, we first introduce a nonconvex TRPCA (N-TRPCA) model which can shrink large singular values more and shrink small singular values less, so that the physical meanings of different singular values can be preserved. To take advantage of the structural redundancy of an image, we further group similar patches as a tensor according to nonlocal prior, and then apply the N-TRPCA model on this tensor. The denoised image can be obtained by aggregating all processed tensors. Experimental results demonstrate the superiority of the proposed denoising method beyond state-of-the-arts.