Abstract
Parallel magnetic resonance imaging (pMRI) is a technique to accelerate the magnetic resonance imaging process. The problem of reconstructing an image from the collected pMRI data is ill-posed. Regularization is needed to make the problem well-posed. In this paper, we first construct a twodimensional tight framelet system whose filters have the same support as the orthogonal Haar filters and are able to detect edges of an image in the horizontal, vertical, and ±45° directions. This system is referred to as directional Haar framelet (DHF). We then propose a pMRI reconstruction model whose regularization term is formed by the DHF. This model is solved by a fast proximal algorithm with low computational complexity. The regularization parameters are updated adaptively and determined automatically during the iteration of the algorithm. Numerical experiments for in-silico and in-vivo data sets are provided to demonstrate the superiority of the DHF-based model and the efficiency of our proposed algorithm for pMRI reconstruction.
Original language | English |
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Pages (from-to) | 794-821 |
Number of pages | 28 |
Journal | SIAM Journal on Imaging Sciences |
Volume | 9 |
Issue number | 2 |
DOIs | |
Publication status | Published - Jan 2016 |
Externally published | Yes |
Bibliographical note
Publisher Copyright:© 2016 Society for Industrial and Applied Mathematics.
Funding
The research of this author was partially supported by the National Science Foundation of China (NSFC 61303102, 61332012, U1301251) and Shenzhen R&D Program (GJHZ20140418191518323). The research of this author was partially supported by HKRGC GRF grant CUHK400412, CUHK300614, CRF grant CUHK2/CRF/11G, AoE grant AoE/M-05/12, CUHK DAG 4053007, and FIS grant 1907303.
Keywords
- Haar wavelet system
- Parallel MRI
- Proximity operator
- Tight frame
- Total variation