CQ algorithm with inertial and correction terms for split feasibility problems

This paper aims to study a new type of CQ algorithm for split feasibility problems in Hilbert spaces. We introduce a new CQ algorithm by incorporating a step that involves an inertial extrapolation term and correction terms into the basic CQ algorithm. We then obtain weak convergence results under some conditions on the iterative parameters. Furthermore, a linear convergence result is obtained when the split feasibility problem satisfies some bounded linear regularity property. Several results in the literature are recovered as special cases of our method. Our numerical experiments from image deblurring and CT image reconstruction show the superiority of our method over related methods for split feasibility problems in the literature.