Research On Image Restoration Algorithms Based On Nonlocal And Low-rank Matrix Approximation

In today's age of big data,images are widely utilized in many fields.However,images will be degraded by various factors such as missing and noise,which can reduce the fidelity of the image.Therefore,how to restore the degraded image is of great significance in digital image processing.This dissertation focuses on the completion algorithm based on nonlocal and low-rank matrix approximation in image inpainting and image denoising.1)Aiming at the problem of the completion algorithm for low-rank matrix approximation algorithm has a good completion effect when applied to the low-rank numerical matrix and a poor recovery effect when applied to natural images of approximately low-rank,inspired by the nonlocal self-similarity of natural image and low-rank matrix approximation algorithm,a completion algorithm based on nonlocal self-similarity and low-rank matrix approximation was proposed and a concise theoretical analysis of the algorithm is carried out.Firstly,the nonlocal similar patches corresponding to the local patches in the image were found through similarity measurement,and the corresponding grayscale matrices were vectorized to construct the nonlocal similar patch matrix.Secondly,aiming at the low rank property of the obtained similarity matrix,low-rank matrix approximation was carried out.Finally,the completion results were recombined to achieve the goal of inpainting the original image.2)Extend the nonlocal self-similarity and low-rank matrix approximation algorithm to image denoising.Compared with the matrix completion problem of known real data matrix,image denoising problems are often unknown to the real image data.Based on the above question,we have made a concise analysis of the feasibility of applying nonlocal and low-rank matrix approximation algorithms to image denoising problem.Furthermore,an image denoising algorithm based on nonlocal and low-rank matrix approximation is proposed and a concise theoretical analysis of the algorithm is carried out.At the same time,inspired by the weighted nuclear norm algorithm,we set different truncation thresholds for different singular values in the algorithm,and adopted the idea of over-relaxation to achieve obvious denoising effect in the initial attempt of image denoising.In summary,the main work of this dissertation is to propose two applications of image restoration and image denoising algorithms based on nonlocal and low-rank matrix approximation and make a concise theoretical analysis.The experimental results show that the proposed algorithm has obvious effects in image restoration and image denoising.