Blind Image Restoration Based On Split Bregman Method

As the rapid development of multimedia technology and computer technology, digital image processing has been developed widely. Image restoration is an important branch of image processing, and blind image restoration is a crucial issue of image restoration study. Blind image restoration studies how to restore the original image from the degraded observed image directly when the precise prior information of degradation process is unknown. In addition, blind image restoration has strong background in mathematics, such as computational methods for inverse problems, linear algebra, stochastic processes, numerical analysis and partial differential equation and so on. The process of solving blind restoration can be divided into two phases general:establishing the corresponding mathematical model of the degradation processes first, and then solving the inverse problem to get a reasonable estimation of the original image.In this article, since the blind restoration problem is a kind of typical ill-posed problem, some regularization methods will be introduced to avoid the shortcomings of ill-posed problems effectively. Split Bregman method has significant stability and fast convergence advantages, and it is not simple but effective when using Split Bregman technique to solve TV (total variation) problem. We propose two blind image restoration algorithms which are all based on Split Bregman method. Algorithml(TV-SB):it includes two cases, there are to use the Split Bregman method for solving blind restoration problems based on isotropic TV regularization and anisotropic TV regularization, respectively. Algorithm2(NTRF-SB):we also apply Split Bregman method to solve blind restoration problems based on the combination of anisotropic regularization with the new Tikhonov regularization, using L2norm as the fidelity term. Numerical experiments implemented with MATLAB demonstrate that our proposed blind algorithms improve the quality of image evidently under the cases of different blurs types and different noise levels, meanwhile, get promising ISNR values.