Efficient projective methods for the split feasibility problem and its applications to compressed sensing and image debluring

In this paper, new projective algorithms using linesearch technique are proposed to solve the split feasibility problem. Weak convergence theorems are established, under suitable conditions, in a real Hilbert space. Some numerical experiments in compressed sensing and image debluring are also provided to show its implementation and efficiency. The main results improve the corresponding results in the literature.