Composite splitting algorithms for convex optimization

We consider the minimization of a smooth convex function regularized by the composite prior models. This problem is generally difficult to solve even if each subproblem regularized by one prior model is convex and simple. 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 by averaging 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. Numerous experiments demonstrate the superior performance of the proposed algorithms in terms of both accuracy and computation complexity.

► We propose a general scheme (FCSA) to solve the composite regularization problem.
► The FCSA can be used to reconstruct compressed MR images and outperform the state-of-the-art methods.
► The FCSA can be applied to low rank tensor completion and outperform other classic methods.
► Future work will study how to adapt step sizes in the CSD or FCSA.