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Mathematical Problems in Engineering
Volume 2016, Article ID 4162194, 12 pages
Research Article

Combined Similarity to Reference Image with Joint Sparsifying Transform for Longitudinal Compressive Sensing MRI

1School of Science, Beijing Jiaotong University, Beijing 100044, China
2Beijing Center for Mathematics and Information Interdisciplinary Sciences, Beijing 100048, China
3College of Information Engineering, Xiangtan University, Xiangtan 411105, China
4Yan’an City People’s Hospital MRI, CT Diagnosis Branch, Baota District, Shaanxi 716000, China

Received 8 April 2016; Revised 8 August 2016; Accepted 10 August 2016

Academic Editor: Raffaele Solimene

Copyright © 2016 Ruirui Kang 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.


It is challenging to save acquisition time and reconstruct a medical magnetic resonance (MR) image with important details and features from its compressive measurements. In this paper, a novel method is proposed for longitudinal compressive sensing (LCS) MR imaging (MRI), where the similarity between reference and acquired image is combined with joint sparsifying transform. Furthermore, the joint sparsifying transform with the wavelet and the Contourlet can efficiently represent both isotropic and anisotropic features and the objective function is solved by extended smooth-based monotone version of the fast iterative shrinkage thresholding algorithm (SFISTA). The experiment results demonstrate that the existing regularization model obtains better performance with less acquisition time and recovers both edges and fine details of MR images, much better than the existing regularization model based on the similarity and the wavelet transform for LCS-MRI.