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Computational and Mathematical Methods in Medicine
Volume 2014, Article ID 134058, 11 pages
Research Article

Sparse-Representation-Based Direct Minimum -Norm Algorithm for MRI Phase Unwrapping

1Department of Biomedical Engineering, Zhejiang University, Hangzhou 310027, China
2School of Information Technology and Electrical Engineering, The University of Queensland, Brisbane, QLD 4072, Australia

Received 6 December 2013; Revised 8 February 2014; Accepted 12 February 2014; Published 26 March 2014

Academic Editor: Xiaobo Qu

Copyright © 2014 Wei He et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A sparse-representation-based direct minimum -norm algorithm is proposed for a two-dimensional MRI phase unwrapping. First, the algorithm converts the weighted- -norm-minimization-based phase unwrapping problem into a linear system problem whose system (coefficient) matrix is a large, symmetric one. Then, the coefficient-matrix is represented in the sparse structure. Finally, standard direct solvers are employed to solve this linear system. Several wrapped phase datasets, including simulated and MR data, were used to evaluate this algorithm’s performance. The results demonstrated that the proposed algorithm for unwrapping MRI phase data is reliable and robust.