Real Color Image Denoising Using t-Product-Based Weighted Tensor Nuclear Norm Minimization

Color images can be seen as third-order tensors with column, row and color modes. Considering two inherent characteristics of a color image including the non-local self-similarity (NSS) and the cross-channel correlation, we extract non-local similar patch groups from a color image and treat these groups as tensors with each color channel corresponding to the frontal slice of the tensor to exploit the information within and cross channel correlation. Inspired by recently proposed tensor-tensor product (t-product), t-SVD, tensor tubal rank and rigorously deduced tensor nuclear norm, a novel t-product based weighted tensor nuclear norm minimization (WTNNM) is proposed to model the extracted non-local similar patch group tensor (NPGT). Considering the NPGT is of low tubal rank, we formulate real color image denoising as a low tubal rank tensor recovery problem and solve it with the weighted tensor nuclear norm minimization. Experiments on both simulated and realistic noisy images verify the effectiveness of our method.