Modified projection method for linear split feasibility problems applied to medical image reconstruction

In this paper, we propose a Modified Surrogate Constraint Projection (MSCP) method for solving the linear split feasibility problem, which can be applied to medical image reconstruction. In our method, each step consists of finding two orthogonal projections onto both a surrogate hyperplane and a relaxed halfspace. We also give the convergence of the MSCP method. It is demonstrated to be effective for the infeasible system of linear inequalities in real-world image reconstruction.