SIAM Journal on Control and Optimization
A Modified Forward-Backward Splitting Method for Maximal Monotone Mappings
SIAM Journal on Control and Optimization
Iterative Algorithms Based on Decoupling of Deblurring and Denoising for Image Restoration
SIAM Journal on Scientific Computing
An accelerated gradient method for trace norm minimization
ICML '09 Proceedings of the 26th Annual International Conference on Machine Learning
Sparse reconstruction by separable approximation
IEEE Transactions on Signal Processing
Fixed-Point Continuation for $\ell_1$-Minimization: Methodology and Convergence
SIAM Journal on Optimization
General Projective Splitting Methods for Sums of Maximal Monotone Operators
SIAM Journal on Control and Optimization
Regularization Methods for Semidefinite Programming
SIAM Journal on Optimization
A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
SIAM Journal on Imaging Sciences
A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
SIAM Journal on Imaging Sciences
A New Alternating Minimization Algorithm for Total Variation Image Reconstruction
SIAM Journal on Imaging Sciences
IEEE Transactions on Image Processing
Fast image recovery using variable splitting and constrained optimization
IEEE Transactions on Image Processing
A Singular Value Thresholding Algorithm for Matrix Completion
SIAM Journal on Optimization
Fixed point and Bregman iterative methods for matrix rank minimization
Mathematical Programming: Series A and B
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
A review of motion analysis methods for human Nonverbal Communication Computing
Image and Vision Computing
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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.