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Computational and Mathematical Methods in Medicine
Volume 2014 (2014), Article ID 958671, 11 pages
Research Article

Compressed Sensing MR Image Reconstruction Exploiting TGV and Wavelet Sparsity

School of Information and Electronics, Beijing Institute of Technology, Beijing 100081, China

Received 4 April 2014; Revised 7 September 2014; Accepted 11 September 2014; Published 13 October 2014

Academic Editor: William Crum

Copyright © 2014 Di Zhao 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.


Compressed sensing (CS) based methods make it possible to reconstruct magnetic resonance (MR) images from undersampled measurements, which is known as CS-MRI. The reference-driven CS-MRI reconstruction schemes can further decrease the sampling ratio by exploiting the sparsity of the difference image between the target and the reference MR images in pixel domain. Unfortunately existing methods do not work well given that contrast changes are incorrectly estimated or motion compensation is inaccurate. In this paper, we propose to reconstruct MR images by utilizing the sparsity of the difference image between the target and the motion-compensated reference images in wavelet transform and gradient domains. The idea is attractive because it requires neither the estimation of the contrast changes nor multiple times motion compensations. In addition, we apply total generalized variation (TGV) regularization to eliminate the staircasing artifacts caused by conventional total variation (TV). Fast composite splitting algorithm (FCSA) is used to solve the proposed reconstruction problem in order to improve computational efficiency. Experimental results demonstrate that the proposed method can not only reduce the computational cost but also decrease sampling ratio or improve the reconstruction quality alternatively.