Image Multiplicative Noise Removal Models And Algorithms Based On Non-Convex Low-Rank And Gradient Sparse Priors

With the development of the information age,high-quality images have important applications in photography,aerospace,biomedicine,communications,and resource exploration.However,the image is easily interfered by equipment and the external environment during the acquisition and transmission process,and the resulting image is often degraded such as noise,blurring,downsampling which greatly influence subsequent analysis and application.As a special class of degraded images with multiplicative noise,due to the high image dependence of multiplicative noise,it becomes more difficult and it is a challenge to remove image multiplicative noise.Therefore,studying more effective image multiplicative noise removal method becomes more important.Due to the good theoretical foundation and high flexibility of variational theory,the method of image multiplicative noise removal based on variational theory has become an economical and effective way.By modeling the image multiplicative noise model and mining the geometric prior information of the image,the multiplicative noise removal problem is transformed into a problem of solving the minimum value of the energy functional,and then the numerical solution is the denoising image that needs to be obtained.Therefore,the paper focuses on the problem of image multiplicative noise based on variational theory.Taking image geometric prior modeling as the main line,the characteristics of multiplicative noise are analyzed,and non-convex low-rank prior modeling and gradient feature domain sparsity are studied.We can get an image multiplicative noise removal model and algorithm based on nonconvex low-rank and gradient feature domain sparsity priors are proposed.The main work includes the following aspects:In the first part,on the one hand,the total variation(TV)method based on the first-order gradient of the image is used to easily maintain the important characteristics of the image edge,and on this basis,the self-similar characteristics of the non-local blocks of the image and their similarity image matching are simultaneously mined.Based on the low rank characteristics of block matrix,the rank minimum prior modeling of the similarity image matching block matrix is studied and then an image noise removal model based on non-convex rank minimum and TV prior is proposed.In the second part,aiming at the disadvantage that the TV method based on the first-order gradient of the image leads to the step effect and the high-order TV can solve the step effect.We also take the similarity image matching into consideration.But the block matrix rank minimum prior is non-convex and difficult to solve,so the non-convex low-rank approximation modeling method of the block matrix rank minimum prior for similarity image matching is mainly studied.Furthermore,an image noise removal model based on non-convex low-rank approximation and high-order TV prior is proposed.In the third part,the above two denoising models are solved and simulated by alternate iteration method.The model proposed in this paper can maintain a relatively good image denoising effect,no matter from the perspective of visual or numerical evaluation.