Simultaneous image denoising and completion through convolutional sparse representation and nonlocal self-similarity

Low rank matrix approximation (LRMA) has been widely studied due to its capability of approximating original image from the degraded image. According to the characteristics of degraded images, image denoising and image completion have become research objects. Existing methods are usually designed for a single task. In this paper, focusing on the task of simultaneous image denoising and completion, we propose a weighted low rank sparse representation model and the corresponding efficient algorithm based on LRMA. The proposed method integrates convolutional analysis sparse representation (ASR) and nonlocal statistical modeling to maintain local smoothness and nonlocal self-similarity (NLSM) of natural images. More importantly, we explore the alternating direction method of multipliers (ADMM) to solve the above inverse problem efficiently due to the complexity of simultaneous image denoising and completion. We conduct experiments on image completion for partial random samples and mask removal with different noise levels. Extensive experiments on four datasets, i.e., Set12, Kodak, McMaster, and CBSD68, show that the proposed method prevents the transmission of noise while completing images and has achieved better quantitative results and human visual quality compared to 17 methods. The proposed method achieves (1.9%, 1.8%, 4.2%, and 3.7%) gains in average PSNR and (4.2%, 2.9%, 6.7%, and 6.6%) gains in average SSIM over the sub-optimal method across the four datasets, respectively. We also demonstrate that our method can handle the challenging scenarios well. Source code is available at https://github.com/weimin581/demo_CSRNS.