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BioMed Research International
Volume 2016 (2016), Article ID 2860643, 7 pages
http://dx.doi.org/10.1155/2016/2860643
Research Article

Two-Layer Tight Frame Sparsifying Model for Compressed Sensing Magnetic Resonance Imaging

1Paul C. Lauterbur Research Center for Biomedical Imaging, Shenzhen Institutes of Advanced Technology, Shenzhen, Guangdong 518055, China
2The Beijing Center for Mathematics and Information Interdisciplinary Sciences, Beijing 100048, China
3Biomedical and Multimedia Information Technology (BMIT) Research Group, School of Information Technologies, The University of Sydney, Sydney, NSW 2006, Australia
4Nanchang University, Nanchang, Jiangxi, China

Received 20 April 2016; Revised 5 August 2016; Accepted 18 August 2016

Academic Editor: Andrey Krylov

Copyright © 2016 Shanshan Wang 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.

Linked References

  1. M. Lustig, D. Donoho, and J. M. Pauly, “Sparse MRI: the application of compressed sensing for rapid MR imaging,” Magnetic Resonance in Medicine, vol. 58, no. 6, pp. 1182–1195, 2007. View at Publisher · View at Google Scholar · View at Scopus
  2. J. Trzasko and A. Manduca, “Highly undersampled magnetic resonance image reconstruction via homotopic l0-minimization,” IEEE Transactions on Medical Imaging, vol. 28, no. 1, pp. 106–121, 2009. View at Publisher · View at Google Scholar · View at Scopus
  3. Q. Liu, S. Wang, K. Yang, J. Luo, Y. Zhu, and D. Liang, “Highly undersampled magnetic resonance image reconstruction using two-level Bregman method with dictionary updating,” IEEE Transactions on Medical Imaging, vol. 32, no. 7, pp. 1290–1301, 2013. View at Publisher · View at Google Scholar · View at Scopus
  4. X. Qu, Y. Hou, F. Lam, D. Guo, J. Zhong, and Z. Chen, “Magnetic resonance image reconstruction from undersampled measurements using a patch-based nonlocal operator,” Medical Image Analysis, vol. 18, no. 6, pp. 843–856, 2014. View at Publisher · View at Google Scholar · View at Scopus
  5. D. Liang, H. Wang, Y. Chang, and L. Ying, “Sensitivity encoding reconstruction with nonlocal total variation regularization,” Magnetic Resonance in Medicine, vol. 65, no. 5, pp. 1384–1392, 2011. View at Publisher · View at Google Scholar · View at Scopus
  6. X. Qu, D. Guo, B. Ning et al., “Undersampled MRI reconstruction with patch-based directional wavelets,” Magnetic Resonance Imaging, vol. 30, no. 7, pp. 964–977, 2012. View at Publisher · View at Google Scholar · View at Scopus
  7. C. Chen and J. Huang, “The benefit of tree sparsity in accelerated MRI,” Medical Image Analysis, vol. 18, no. 6, pp. 834–842, 2014. View at Publisher · View at Google Scholar · View at Scopus
  8. J. Liu, S. Wang, X. Peng, and D. Liang, “Undersampled MR image reconstruction with data-driven tight frame,” Computational and Mathematical Methods in Medicine, vol. 2015, Article ID 424087, 10 pages, 2015. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. S. Ravishankar and Y. Bresler, “MR image reconstruction from highly undersampled k-space data by dictionary learning,” IEEE Transactions on Medical Imaging, vol. 30, no. 5, pp. 1028–1041, 2011. View at Publisher · View at Google Scholar · View at Scopus
  10. Y. Huang, J. Paisley, Q. Lin, X. Ding, X. Fu, and X.-P. Zhang, “Bayesian nonparametric dictionary learning for compressed sensing MRI,” IEEE Transactions on Image Processing, vol. 23, no. 12, pp. 5007–5019, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. Y. Liu, J.-F. Cai, Z. Zhan et al., “Balanced sparse model for tight frames in compressed sensing magnetic resonance imaging,” PLoS ONE, vol. 10, no. 4, Article ID e0119584, 2015. View at Publisher · View at Google Scholar · View at Scopus
  12. B. Ophir, M. Lustig, and M. Elad, “Multi-scale dictionary learning using wavelets,” IEEE Journal on Selected Topics in Signal Processing, vol. 5, no. 5, pp. 1014–1024, 2011. View at Publisher · View at Google Scholar · View at Scopus
  13. Q. Liu, S. Wang, L. Ying, X. Peng, Y. Zhu, and D. Liang, “Adaptive dictionary learning in sparse gradient domain for image recovery,” IEEE Transactions on Image Processing, vol. 22, no. 12, pp. 4652–4663, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. R. Rubinstein, M. Zibulevsky, and M. Elad, “Double sparsity: learning sparse dictionaries for sparse signal approximation,” IEEE Transactions on Signal Processing, vol. 58, no. 3, part 2, pp. 1553–1564, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. S. Ravishankar and Y. Bresler, “Learning doubly sparse transforms for images,” IEEE Transactions on Image Processing, vol. 22, no. 12, pp. 4598–4612, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  16. J.-F. Cai, H. Ji, Z. Shen, and G.-B. Ye, “Data-driven tight frame construction and image denoising,” Applied and Computational Harmonic Analysis, vol. 37, no. 1, pp. 89–105, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  17. X. Peng and D. Liang, “MR image reconstruction with convolutional characteristic constraint (CoCCo),” IEEE Signal Processing Letters, vol. 22, no. 8, pp. 1184–1188, 2015. View at Publisher · View at Google Scholar · View at Scopus
  18. Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Transactions on Image Processing, vol. 13, no. 4, pp. 600–612, 2004. View at Publisher · View at Google Scholar · View at Scopus