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

• Published in: IEEE transactions on medical imaging Vol. 35; no. 9; pp. 2130 - 2140
• Main Authors: Liu, Yunsong, Zhan, Zhifang, Cai, Jian-Feng, Guo, Di, Chen, Zhong, Qu, Xiaobo
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.09.2016; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• 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
• ISSN: 0278-0062; 1558-254X; 1558-254X
• DOI: 10.1109/TMI.2016.2550080

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.