Figure. Brain MR image reconstruction from 20% sampling (a) Original image; (b), (c), (d) (e) and (f) are the reconstructed images by the CG , TVCMRI , RecPF , CSA and FCSA. Their SNR are 8.71, 12.12, 12.40, 18.68 and 20.35 (db). Their CPU time are 2.75, 3.03, 3.00, 2.22 and 2.20 (s).
We consider the minimization of a smooth convex function regularized by the composite prior models. This problem is generally difficult to solve even each subproblem regularized by one prior model is convex and easy. In this paper, we present two algorithms to effectively solve it. First, the original problem is decomposed into multiple simpler subproblems. Then, these subproblems are efficiently solved by existing techniques in parallel. Finally, the result of the original problem is obtained from the weighted average of solutions of subproblems in an iterative framework. The proposed composite splitting algorithms are applied to the compressed MR image reconstruction and low-rank tensor completion respectively. Numerous experiments demonstrate the superior performance of the proposed algorithm in terms of both the accuracy and computation complexity.