Projected Surrogate Constrain Method For Linear Split Feasibility Problems And The Application In Image Reconstruction Problem

In recent years, the Image processing problems have been made great attention, coming with the development of so many new methods, and new algorithms. Image reconstruction problem is one of the image processing technology. In a technology, it is mainly interested in the image of the target detection and measurement, to obtain objective information so as to establish the image and objectives of the description. The approach of Image reconstruction problem is often transformed into two major categories. Based on this paper, we compared and improved some algorithms, and increased noise in the image reconstruction problem, using new methods in order to reduce the experimental error.A modified projected surrogate constraint (MPSC) method for solving the linear split feasibility problem (LSFP) is proposed in this paper. Each step in this method consists of finding two orthogonal projections onto both a surrogate hyper-plane and a relaxed half-space, and hence is easily implemented. Furthermore, our method is proven to be full convergent to a solution of the solvable LSFP, and is demonstrated to be effective by numerical experiments. Even if for the infeasible system of linear inequalities in real-world image reconstruction, the testing results are also satisfactory.