Nonlocal Regularization Iamge Restoration Method Based On Augmented Lagangian

In the imaging process, due to the physical or objective factors causing part of image information missing, finally, we get the distortion image. Image restoration is a technology which uses mathematical model and some prior knowledge of an image to reconstruct the real image as much as possible. The modeling and the applications of algorithms have a critical influence on the quality of the reconstructed image.In recent years, methods based on the self-similarity principle of an image, by making use of the idea of learning image structure features and training to obtain the learning basis has been widely used to image denoising, rehabilitation, and other image processing branch. The BM3D method is the most representative approach of this kind, whether in the recovery effect or running time, all display superiority compare with other methods. The principle of HOSVD method is similar to BM3D. The former utilizes the singular value decomposition and the thresholding shrinkage to 3D matrix which is made of patches in order to filter the noisy image. The denoising result makes a significantly improvement compare to non-local SVD decomposition. Similar to the former methods we proposed, the LASSC method and the WNNM method all use the self-similar principle, but the two are low-order methods. The HOSVD method and the BM3D method filters noises in two steps. In the framework of iterative regularization, the LASSC method and the WNNM method firstly use the Bayes Shrinkage threshold estimation method to estimate the thresholding, and then use self-adaptive thresholding method for adaptive filtering the coefficient matrix. The two methods both have higher PSNR value, but both of them need too much CPU time, which makes them hard to large-scale matrices.To further enhance the effect and decrease the running time, we propose a two-step group-based adaptive soft-thresholding algorithm to image denoising. Through the numerical experiments, we can see that the recovery effect of the method proposed in this paper is more superior on the whole performance compare with other high-order and low-order methods. In fact, our method saves a lot of time and cheaper than several similar methods mentioned in this article expect for BM3D method.