Research On Low Rank Denoising Method Based On SVD Decomposition And Dual Domain Filtering

With the development and progress of computer information technology and the Internet,digital images have gradually become an important intermediary and means for people to obtain and use visual information.Compared to text and sound,digital images contain more information and are more intuitive.However,the image will be contaminated by a certain amount of noise during the process of generation and transmission.This will not only damage the quality of the image,affect people's visual effects,but also be detrimental to the subsequent processing of the image.Therefore,how to remove complex noise and obtain useful information from the image effectively has become a hot issue in the current study,which also has very important theoretical and practical values.In recent years,the sparse representation theory and the low-rank approximation model have been widely used in fields such as signal and image processing,and have become a kind of important advanced technology and method in this field.In the study of natural image denoising,non-local similarity enhances the correlation of grouped image blocks,and a low rank prior is used to devise a bilateral sparse representation of the image matrix,consequently achieving the purpose of removing image noise.However,many problems,such as how to select the threshold in the singular value shrinkage to adapt to different noise levels,and how to eliminate image artifacts in removing noise with high levels,have not been well solved,which reduces the denoising effect of the sparse low-rank algorithm.In this thesis,a low rank denoising algorithm based on SVD decomposition and double domain filtering is proposed,which uses random matrix and asymptotic matrix reconstruction theory to scientifically select the threshold of singular value thresholding,and measures the self-similarity by absolute and relative differences of image blocks.At the same time,a dual domain filtering method is used to process the artifacts after image denoising.The main work of this thesis includes the following three aspects.(1)An adaptive threshold selection method based on random matrix and asymptotic matrix reconstruction theory.A general low rank denoising algorithm is based on the soft threshold shrinkage of singular values,where the selection of the threshold is inversely proportional to the corresponding singular value,which results in the larger corresponding threshold to the small singular value,and many potential image feature information cannot be recovered.In this thesis,using non-local similarity and low-rank approximation techniques we propose an adaptive singular value thresholding method based on the random matrix optimizing the selection of singular value threshold.By this way,when the smooth area of image is restored,edge,texture and other detailed features are well restored.(2)A similar block matching method using absolute and relative differences of image blocks.In order to better describe the similarity between image blocks and to enhance the ability of the sparse expression of image,in the thesis absolute and relative differences of image blocks are combined to measure the similarity of image blocks,which further enhances effectiveness and timeliness of the proposed denoising algorithm.(3)Denoising enhancement using dual domain filtering.In the case of higher noise levels,the low rank denoising method produces more serious artificial artifacts,which is a degenerative phenomenon caused by the singular threshold shrinkage during image denoising.In order to improve the processing of high-contrast image features in the transform domain,we use a double-domain filtering to improve the low rank denoising method,weakening the influence of artificial artifacts on image quality,and obtain better image denoising performance.Using the low rank denoising algorithm based on SVD decomposition and dual domain filtering,we denoised and enhanced a large number of natural images.The experimental results show that the proposed algorithm has a certain improvement in subjective visual effects and objective quantitative indicators compared with some related advanced denoising algorithms.The research of this dissertation further strengthens the collaborative innovation between computational mathematics and information science,deepens and enriches the research of image denoising technology,and is expected to be further extended to medical image processing and other application fields.