Projected Iterative Soft-Thresholding Algorithm for Tight Frames in Compressed Sensing Magnetic Resonance Imaging

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 (p...

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Bibliographic Details
Published in:IEEE transactions on medical imaging 2016-09, Vol.35 (9), p.2130-2140
Main Authors: Liu, Yunsong, Zhan, Zhifang, Cai, Jian-Feng, Guo, Di, Chen, Zhong, Qu, Xiaobo
Format: Article
Language:English
Subjects:
Algorithm design and analysis
Algorithms
Analytical models
Brain
Compressed sensing
Data Compression
Dictionaries
Frames
Image Processing, Computer-Assisted
Image reconstruction
Iterative methods
iterative thresholding
Magnetic Resonance Imaging
Mathematical model
Mathematical models
MRI
NMR
Nuclear magnetic resonance
Parameters
Pista
Reconstruction
sparse models
Sparsity
tight frames
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Summary: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.
ISSN:0278-0062
1558-254X
DOI:10.1109/TMI.2016.2550080