期刊
IEEE TRANSACTIONS ON MEDICAL IMAGING
卷 35, 期 9, 页码 2130-2140出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TMI.2016.2550080
关键词
Compressed sensing; iterative thresholding; MRI; sparse models; tight frames
类别
资金
- National Natural Science Foundation of China [61571380, 61201045, 61302174, 11375147]
- Natural Science Foundation of Fujian Province of China [2015J01346, 2016J05205]
- Important Joint Research Project on Major Diseases of Xiamen City [3502Z20149032]
- Fundamental Research Funds for the Central Universities [20720150109, 2013SH002]
- NSF [DMS-1418737]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1418737] Funding Source: National Science Foundation
Compressed sensing (CS) has exhibited great potential for accelerating magnetic resonance imaging (MRI). In CS-MRI, we want to reconstruct a high-quality image from very few samples in a short time. In this paper, we propose a fast algorithm, called projected iterative soft-thresholding algorithm (pISTA), and its acceleration pFISTA for CS-MRI image reconstruction. The proposed algorithms exploit sparsity of the magnetic resonance (MR) images under the redundant representation of tight frames. We prove that pISTA and pFISTA converge to a minimizer of a convex function with a balanced tight frame sparsity formulation. The pFISTA introduces only one adjustable parameter, the step size, and we provide an explicit rule to set this parameter. Numerical experiment results demonstrate that pFISTA leads to faster convergence speeds than the state-of-art counterpart does, while achieving comparable reconstruction errors. Moreover, reconstruction errors incurred by pFISTA appear insensitive to the step size.
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