Research On Image Denoising Algorithm Based On Low-rank Approximation And Sparse Coding

With the rapid development of multimedia technology in the 21 th century,great changes have taken place in the way humans transmit information.Paperless digital information exchange has largely replaced cumbersome and complicated correspondence.As one of the main carriers of digital information,images have been widely used in all walks of life.However,due to imperfect equipment and external interference,noise will inevitably be introduced in the process of image acquisition and transmission,which brings certain difficulties in correcting understanding the image content.Therefore,in the past few decades,image denoising has been a hot research topic of many researchers.Essentially,image denoising is an ill-posed inverse problem.In order to obtain a visually stable solution,it is necessary to mine the prior knowledge of natural images,and then establish a regularization term to constrain the solution space.This thesis takes the non-local self-similarity prior of the image as the starting point,adopts the non-local self-similar group as the basic processing unit,and proposes two image denoising algorithms based on low-rank approximation and two image denoising algorithms based on sparse coding.On this basis,an image denoising algorithm combining sparse coding with low-rank approximation constraints is proposed.In this thesis,the suppression of the ringing phenomenon and the preservation of the edge and texture information in image denoising are deeply studied.The main research work is as follows:(1)The first image denoising algorithm that is proposed is based on group low-rank approximation.In the traditional weighted nuclear norm minimization algorithm,only the Euclidean distance is used to measure the similarity between noisy image patches,and a fixed method noise coefficient is used to feedback and adjust images contaminated with different noise levels,and a fixed number of iterations is used as the termination condition for images with different contents,which usually yields sub-optimal denoising results.Aiming at the above problems,an image denoising algorithm based on group low-rank approximation is proposed.First,grey theory is introduced to measure the correlation coefficient between noisy image patches,and Euclidean distance is used jointly to measure the similarity between noisy patches.Second,using statistical analysis,the feedback coefficients of the method noise are adaptively added for different noise levels.Finally,residual noise is used to design iteration termination conditions.Extensive experiments are conducted and the results show that,compared with various classical image denoising algorithms,the proposed algorithm can better preserve the structure of the image.(2)The second algorithm that is proposed is a multi-scale group low-rank approximation image denoising algorithm.The non-local self-similarity of images has been widely used in image denoising algorithms,but the existing mainstream algorithms only consider the self-similarity of a single scale,and for local regions that do not possess sufficient similar structures in the image,these algorithms usually produce ringing artifacts.To overcome this problem,a multi-scale group low-rank approximation image denoising algorithm is proposed.First,similar image patches are selected from different scales to make full use of the multi-scale non-local self-similar prior of the image.Then,a constrained nuclear norm minimization model is introduced to mine low-rank prior characteristics.Finally,the eigenvalue thresholding technique is used to obtain the closed-form solution of the algorithm.Experimental results demonstrate that the proposed algorithm can better suppress ringing artifacts than image denoising algorithms based on single-scale self-similar prior.(3)The third denoising algorithm that is proposed is based on group bilateral weighted sparse coding.When the traditional sparse coding model is applied to image denoising,it ignores the noise variation characteristics of different similar patch groups and the sparse characteristics of natural images,and obtains sub-optimal objective values and visual quality.To overcome this problem,an image denoising algorithm based on group bilateral weighted sparse coding is proposed.First,on the basis of traditional sparse coding,a weight matrix is introduced to consider the noise variation characteristics of different similar patch groups.Then,another weight matrix is introduced to make full use of the sparse prior characteristics of natural images.Finally,maximum a posteriori estimation is used to obtain the closed-form solution of the algorithm.The experimental results show that the proposed algorithm achieves better objective numerical values and subjective visual quality than a variety of classical image denoising algorithms do.(4)A multi-scale weighted group sparse coding algorithm is proposed next.Existing image denoising algorithms based on sparse coding exploit the non-local self-similarity of images in a single scale only,and for some image patches that do not have enough repetitive structures,undesirable ringing artifacts will occur in the restored results,and even the image content may be lost.Aiming at this problem,a multi-scale weighted group sparse coding algorithm is proposed.First,similar image patches are selected from different scales to make use of multi-scale non-local self-similarity priors.Then,a weighted sparse coding algorithm is built with multi-scale self-similar groups as the basic unit.Finally,an alternative minimization method is developed to obtain the solution of the algorithm.The experimental results show that,compared with various classical denoising algorithms,the proposed algorithm can better restore the image structure and edges contaminated by noise.(5)Finally,an image denoising algorithm based on low-rank approximation combined with sparse coding constraints is proposed.Groups formed by stacking similar image patches not only have low-rank characteristics,but also have sparse characteristics.Existing image denoising algorithms often use only one of the two to achieve sub-optimal results.Aiming at these problems,an image denoising algorithm that utilizes a low-rank approximation combined with sparse coding constraints is proposed.First,the regularization term in the objective function is established according to the low-rank characteristic and the sparse characteristic,respectively.Then,a three-step block coordinate descent method is developed to solve the algorithm.The experimental results of noise reduction on different scenes including grayscale images and color images show that,compared with many existing classical algorithms,the proposed algorithm achieves results that are better in terms of both the objective metrics and subjective visual quality than the existing ones,and can better restore image edges and textures.