Research On Image Reconstruction Algorithms Based On Compressed Sensing And Non Local Self-similarity

Images have a very wide range of applications in real life.Considering the damage and noise effects during image transmission,the research on image reconstruction and denoising has important theoretical and practical significance.Firstly,since larger singular values in an image contain more important information,while smaller singular values usually contain some invalid information such as noise,different processing methods should be adopted for different singular values.Images with larger singular values should be retained as much as possible,and some with smaller singular values should be eliminated as much as possible.Therefore,in order to avoid the limitations of kernel norms,we use non-convex regularization functions instead of kernel norms to establish a new model for solving image reconstruction problems.Secondly,for noisy images,in order to overcome the impact of noise on the image,a new model which leads to total variation based on the original model is proposed to solve the problem of image denoising.Finally,we use the alternating direction multiplier method(ADMM)to solve the proposed models and prove the convergence of the algorithms under appropriate conditions.The numerical experiment results show that our models are superior to the existing ones.