A projection proximal-point algorithm for MR imaging using the hybrid regularization model

In this paper, we present a fast algorithm for MR image reconstruction based on the TV-L1/TGV-L1 model. By utilizing the connection between the cut operator (called projection operator) and the shrink operator, the proposed algorithm adopts a semi-implicit scheme to get a compact iteration sequence so as to reduce computational cost. By combining the proximal point scheme, we can ensure that the system of linear equations to be solved at each iteration is well-conditioned. In addition, we also give convergence analysis of the proposed method. Numerical results with comparison to the split Bregman algorithm are supplied to demonstrate the efficiency of the proposed algorithm.