| Blind image restoration is a process of deconvolution while the point spread function is unknown, and it is a severe ill-posed problem. This problem can be effectively transformed to a well-posed problem by using regularization method. Based on the traditional total variation blind image restoration method, this article proposes a nonconvex higher-order total variation blind image restoration method. This method uses the higher-order total variation which can produce piecewise- linear solutions and brings in image sparse prior to form the cost function. Then we exploit a reweighted minimization scheme to obtain the approximate solution of this cost function, which achieves the goal of image restoration. The main research works carried out in this article are as follows:①The article made a survey of blind image restoration technology development status, and summarized the basic theory and difficulties. We studied the ill-posed property of blind image deblurring, and the solution of reguralization method.② The article made an in-depth study of traditional total variation regularization blind image restoration method, and analyzed the advantage of preserving edges and disadvantage of producing staircass effect in total variation. Then we studied how to use the higher-order total variation to overcome this shortcoming. We also studied a fast solution for image restoration in which the nonconvex nonsmooth regularization is utilized, and made an analysis and summarization of its excellent edge preserving property.③ The article adopted higher-order total variation instead of the traditional total variation to form the blind image restoration cost function model, and based on the in-depth study of the sparse prior about the natural image statistics, we brought this prior which can improve the edge recovery effect into this model. Consequently, we proposed a new nonconvex higher-order total variation cost function model, and made a discretized setting of this model in detail for the convenience of numerical computation.④ Based on the traditional total variation blind deblurring method, the article exploited a binary iteration algorithm of reweighted minimization approximation scheme which incorporates a weight update in outer iteration and a split Bregman method in inner iteration to obtain the solution of the nonconvex higher-order total variation cost function. In the inner iterative process of this algorithm, we imposed nonnegative constraints on the image, normalized and dynamic threshold constraints on the point spread function to improve the accuracy of the deblurring result. At last, we gave a theoretical analysis of the convergence of the proposed algorithm.⑤ The proposed nonconvex higher-order total variation blind restoration method was tested on synthetic and real- life degradations with multiple blurring types. Comparisons were also conducted with some existing image restoration methods recently published in the literature. The superior performance of the algorithm was verified in terms of both visual evaluation and objective evaluation. |
