Weighted Tensor Nuclear Norm Minimization for Color Image Restoration

Non-local self-similarity (NLSS) is widely used as prior information in an image restoration method. In particular, a low-rankness-based prior has a significant effect on performance. On the other hand, a number of color extensions of NLSS-based grayscale image restoration methods have been developed. These extensions focus on the pixel-wise correlation among color channels. However, a natural color image also has a complex dependency, known as an inter-channel dependency, among local regions from different color channels. As a result, color artifacts appear in a denoised image obtained by using the existing methods. In this paper, we propose a novel non-local and inter-channel dependency-aware prior called the weighted tensor nuclear norm (WTNN). The proposed prior is derived by incorporating inter-channel dependency to low-rank-based NLSS prior. The WTNN is a low-rankness-of-the-third-order patch tensor, and we apply it to the tensors constructed with non-local similar patches. It enables us to naturally represent the higher-order dependencies among similar color patches. We propose an image denoising algorithm using the WTNN and image restoration algorithm by using a non-trivial generalization of this algorithm. The experimental results clearly show that the proposed WTNN-based color image denoising and restoration algorithms outperform state-of-the-art methods.