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International Journal of Biomedical Imaging
Volume 2017 (2017), Article ID 9604178, 13 pages
Research Article

Fast Compressed Sensing MRI Based on Complex Double-Density Dual-Tree Discrete Wavelet Transform

1Centers for Biomedical Engineering, University of Science and Technology of China, Hefei, Anhui 230027, China
2School of Computer Science, University of Lincoln, Brayford Pool, Lincoln LN6 7TS, UK

Correspondence should be addressed to Hongwei Du

Received 6 November 2016; Accepted 7 February 2017; Published 9 April 2017

Academic Editor: Itamar Ronen

Copyright © 2017 Shanshan Chen 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) has been applied to accelerate magnetic resonance imaging (MRI) for many years. Due to the lack of translation invariance of the wavelet basis, undersampled MRI reconstruction based on discrete wavelet transform may result in serious artifacts. In this paper, we propose a CS-based reconstruction scheme, which combines complex double-density dual-tree discrete wavelet transform (CDDDT-DWT) with fast iterative shrinkage/soft thresholding algorithm (FISTA) to efficiently reduce such visual artifacts. The CDDDT-DWT has the characteristics of shift invariance, high degree, and a good directional selectivity. In addition, FISTA has an excellent convergence rate, and the design of FISTA is simple. Compared with conventional CS-based reconstruction methods, the experimental results demonstrate that this novel approach achieves higher peak signal-to-noise ratio (PSNR), larger signal-to-noise ratio (SNR), better structural similarity index (SSIM), and lower relative error.