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.

Publications

• Junzhou Huang, Shaoting Zhang and Dimitris Metaxas. "Efficient MR Image Reconstruction for Compressed MR Imaging", In Proc. of the 13th Annual International Conf. on Medical Image Computing and Computer Assisted Intervention, MICCAI’2010, Beijing, China, 2010. Oral presentation.
• Junzhou Huang, Shaoting Zhang and Dimitris Metaxas. "Fast Optimization for Mixture Prior Models", In Proc. of the 11th European Conference on Computer Vision, ECCV'2010.

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