Image Restoration Research Based On Regularization And Least-squares And Fourth-order Partial Differential Equations

Image restoration which refers to removing or reducing image degradation resulted from the process to access digital images, is an important research direction in the field of digital image processing. The degradation reasons include in blurred images caused by the optical system, sports, etc., as well as noise brought by circuit and device. In fact, the problem is mathematically inverse and ill-posed problem.Regularization method is a common method to solve the inverse problem of image restoration. Image restoration technology based regularization method and other methods have aroused general concern at present. The constrain conditions of the regularization method are image smoothing, however, it causes to blur the edges of restored images. Therefore, the method with image de-noising algorithm is the direction of the development.Therefore, the research based on regularization method and fourth-order partial differential equations is adopted in this paper. The main contents of the research are as follows:An improved regularization method is adopted to restore images. This method starts from least-squares algorithm, adopting steepest descent method to improve the convergence of the restoration algorithm, using regularization method to overcome the ill-pose problem. Adaptive regularization parameter is adopted in this method, in order to correct it to the optimal value parallel and automatically with iterative computing of image restoration. The specific restoration algorithm is given.An improved method based on fourth-order partial different equations is adopted to de-noise images. Because fourth-order partial different equations method doesn't have the ability to remove the salt-pepper noise, we adopt the equation with an improved diffusion of the original equation. It is a pre-processing algorithm for image restoration, which doesn't only remove salt-pepper, but also maintain the de-noising ability of the original equation. The specific de-noising algorithm of improved equations is designed.Based on the above improved fourth-order partial differential equations and regularization and least-squares method, we construct an improved regularization and least-squares method. It adopts improved fourth-order partial differential equations to remove noise and regularization and least-squares method to restore images.The experimental results show that the algorithm in this method can effectively restore images. The objective evaluating criterions and subjective visual effects of the algorithm in this paper significantly improve.