Non-Local Robust Quaternion Matrix Completion for Color Images and Videos Inpainting
This work provides a theoretical basis for the NSS prior in image processing, which is beneficial for researchers and practitioners working on image and video inpainting.
This paper explores the relationship between non-local self-similarity (NSS) and the low-rank property of color images, proposing a new patch group based NSS prior scheme. The method achieves high PSNR and SSIM measures, along with better visual quality, outperforming state-of-the-art methods for color image and video inpainting.
The image nonlocal self-similarity (NSS) prior refers to the fact that a local patch often has many nonlocal similar patches to it across the image and has been widely applied in many recently proposed machining learning algorithms for image processing. However, there is no theoretical analysis on its working principle in the literature. In this paper, we discover a potential causality between NSS and low-rank property of color images, which is also available to grey images. A new patch group based NSS prior scheme is proposed to learn explicit NSS models of natural color images. The numerical low-rank property of patched matrices is also rigorously proved. The NSS-based QMC algorithm computes an optimal low-rank approximation to the high-rank color image, resulting in high PSNR and SSIM measures and particularly the better visual quality. A new tensor NSS-based QMC method is also presented to solve the color video inpainting problem based on quaternion tensor representation. The numerical experiments on color images and videos indicate the advantages of NSS-based QMC over the state-of-the-art methods.