An improved weighted nuclear norm minimization method for image denoising

Patch-based low rank matrix approximation has shown great potential in image denoising. Among state-of-the-art methods in this topic, the weighted nuclear norm minimization (WNNM) has been attracting significant attention due to its competitive denoising performance. For each local patch in an image, the WNNM method groups nonlocal similar patches by block matching to formulate a low-rank matrix. However, the WNNM often chooses irrelevant patches such that it may lose fine details of the image, resulting in undesirable artifacts in the final reconstruction. In this regards, this paper aims to provide a denoising algorithm which further improves the performance of the WNNM method. For this purpose, we develop a new nonlocal similarity measure by exploiting both pixel intensities and gradients and present a filter that enhances edge information in a patch to improve the performance of low rank approximation. The experimental results on widely used test images demonstrate that the proposed denoising algorithm performs better than other state-of-the-art denoising algorithms in terms of PSNR and SSIM indices as well as visual quality.