Parallel and distributed computation: numerical methods
Parallel and distributed computation: numerical methods
Nonlinear total variation based noise removal algorithms
Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
Mathematical Programming: Series A and B
Iterative methods for total variation denoising
SIAM Journal on Scientific Computing - Special issue on iterative methods in numerical linear algebra; selected papers from the Colorado conference
Gradient Method with Retards and Generalizations
SIAM Journal on Numerical Analysis
A Nonlinear Primal-Dual Method for Total Variation-Based Image Restoration
SIAM Journal on Scientific Computing
An Algorithm for Total Variation Minimization and Applications
Journal of Mathematical Imaging and Vision
A New Class of Alternating Proximal Minimization Algorithms with Costs-to-Move
SIAM Journal on Optimization
The Split Bregman Method for L1-Regularized Problems
SIAM Journal on Imaging Sciences
A Fast Algorithm for Edge-Preserving Variational Multichannel Image Restoration
SIAM Journal on Imaging Sciences
A New Alternating Minimization Algorithm for Total Variation Image Reconstruction
SIAM Journal on Imaging Sciences
Duality-based algorithms for total-variation-regularized image restoration
Computational Optimization and Applications
A Unified Primal-Dual Algorithm Framework Based on Bregman Iteration
Journal of Scientific Computing
Bregmanized Nonlocal Regularization for Deconvolution and Sparse Reconstruction
SIAM Journal on Imaging Sciences
SIAM Journal on Imaging Sciences
IEEE Transactions on Information Theory
Efficient Total Variation Minimization Methods for Color Image Restoration
IEEE Transactions on Image Processing
An Efficient Algorithm for l0 Minimization in Wavelet Frame Based Image Restoration
Journal of Scientific Computing
Bregman operator splitting with variable stepsize for total variation image reconstruction
Computational Optimization and Applications
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This paper presents two fast algorithms for total variation-based image reconstruction in a magnetic resonance imaging technique known as partially parallel imaging (PPI), where the inversion matrix is large and ill-conditioned. These algorithms utilize variable splitting techniques to decouple the original problem into more easily solved subproblems. The first method reduces the image reconstruction problem to an unconstrained minimization problem, which is solved by an alternating proximal minimization algorithm. One phase of the algorithm solves a total variation (TV) denoising problem, and the second phase solves an ill-conditioned linear system. Linear and sublinear convergence results are given, and an implementation based on a primal-dual hybrid gradient (PDHG) scheme for the TV problem and on a Barzilai-Borwein scheme for the linear inversion is proposed. The second algorithm exploits the special structure of the PPI reconstruction problem by decomposing it into one subproblem involving Fourier transforms and another subproblem that can be treated by the PDHG scheme. Numerical results and comparisons with recently developed methods indicate the efficiency of the proposed algorithms.