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Computational and Mathematical Methods in Medicine
Volume 2014 (2014), Article ID 546814, 12 pages
Research Article

Energy Preserved Sampling for Compressed Sensing MRI

1School of Computer Science and Technology, Nanjing Normal University, Nanjing, Jiangsu 210023, China
2Brain Imaging Laboratory, Department of Psychiatry, Columbia University, New York, NY 10032, USA
3MRI Unit, New York State Psychiatric Institute, New York, NY 10032, USA

Received 1 November 2013; Revised 3 March 2014; Accepted 6 March 2014; Published 26 May 2014

Academic Editor: William Crum

Copyright © 2014 Yudong Zhang 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.


The sampling patterns, cost functions, and reconstruction algorithms play important roles in optimizing compressed sensing magnetic resonance imaging (CS-MRI). Simple random sampling patterns did not take into account the energy distribution in -space and resulted in suboptimal reconstruction of MR images. Therefore, a variety of variable density (VD) based samplings patterns had been developed. To further improve it, we propose a novel energy preserving sampling (ePRESS) method. Besides, we improve the cost function by introducing phase correction and region of support matrix, and we propose iterative thresholding algorithm (ITA) to solve the improved cost function. We evaluate the proposed ePRESS sampling method, improved cost function, and ITA reconstruction algorithm by 2D digital phantom and 2D in vivo MR brains of healthy volunteers. These assessments demonstrate that the proposed ePRESS method performs better than VD, POWER, and BKO; the improved cost function can achieve better reconstruction quality than conventional cost function; and the ITA is faster than SISTA and is competitive with FISTA in terms of computation time.