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International Journal of Biomedical Imaging
Volume 2017, Article ID 9604178, 13 pages
https://doi.org/10.1155/2017/9604178
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; nc.ude.ctsu@whud

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.

Linked References

  1. D. G. Nishimura, Principles of Magnetic Resonance Imaging, Stanford University, 1996.
  2. D. L. Donoho, “Compressed sensing,” IEEE Transactions on Information Theory, vol. 52, no. 4, pp. 1289–1306, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  3. M. Lustig, D. L. Donoho, J. M. Santos, and J. M. Pauly, “Compressed sensing MRI,” IEEE Signal Processing Magazine, vol. 25, no. 2, pp. 72–82, 2008. View at Publisher · View at Google Scholar · View at Scopus
  4. E. J. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Transactions on Information Theory, vol. 52, no. 2, pp. 489–509, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. Z. Lai, X. Qu, Y. Liu et al., “Image reconstruction of compressed sensing MRI using graph-based redundant wavelet transform,” Medical Image Analysis, vol. 27, pp. 93–104, 2016. View at Publisher · View at Google Scholar · View at Scopus
  6. C.-M. Tsai and D. G. Nishimura, “Reduced aliasing artifacts using variable-density k-space sampling trajectories,” Magnetic Resonance in Medicine, vol. 43, no. 3, pp. 452–458, 2000. View at Publisher · View at Google Scholar · View at Scopus
  7. Y. Wang and L. Ying, “Compressed sensing dynamic cardiac cine MRI using learned spatiotemporal dictionary,” IEEE Transactions on Biomedical Engineering, vol. 61, no. 4, pp. 1109–1120, 2014. View at Publisher · View at Google Scholar · View at Scopus
  8. 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
  9. Y. Yang, F. Liu, W. Xu, and S. Crozier, “Compressed sensing MRI via two-stage reconstruction,” IEEE Transactions on Biomedical Engineering, vol. 62, no. 1, pp. 110–118, 2015. View at Publisher · View at Google Scholar · View at Scopus
  10. M. V. Afonso, J. M. Bioucas-Dias, and M. A. Figueiredo, “Fast image recovery using variable splitting and constrained optimization,” IEEE Transactions on Image Processing, vol. 19, no. 9, pp. 2345–2356, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. E. J. Candès, J. K. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Communications on Pure and Applied Mathematics, vol. 59, no. 8, pp. 1207–1223, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. D. R. Thedens, P. Irarrazaval, T. S. Sachs, C. H. Meyer, and D. G. Nishimura, “Fast magnetic resonance coronary angiography with a three-dimensional stack of spirals trajectory,” Magnetic Resonance in Medicine, vol. 41, no. 6, pp. 1170–1179, 1999. View at Publisher · View at Google Scholar · View at Scopus
  13. K. T. Block, M. Uecker, and J. Frahm, “Undersampled radial MRI with multiple coils. Iterative image reconstruction using a total variation constraint,” Magnetic Resonance in Medicine, vol. 57, no. 6, pp. 1086–1098, 2007. View at Publisher · View at Google Scholar · View at Scopus
  14. J. P. Haldar, D. Hernando, and Z.-P. Liang, “Compressed-sensing MRI with random encoding,” IEEE Transactions on Medical Imaging, vol. 30, no. 4, pp. 893–903, 2011. View at Publisher · View at Google Scholar · View at Scopus
  15. Z. Zhu, K. Wahid, P. Babyn, and R. Yang, “Compressed sensing-based MRI reconstruction using complex double-density dual-tree DWT,” International Journal of Biomedical Imaging, vol. 2013, Article ID 907501, 12 pages, 2013. View at Publisher · View at Google Scholar · View at Scopus
  16. W. Hao, J. Li, X. Qu, and Z. Dong, “Fast iterative contourlet thresholding for compressed sensing MRI,” Electronics Letters, vol. 49, no. 19, pp. 1206–1208, 2013. View at Publisher · View at Google Scholar · View at Scopus
  17. M. H. Kayvanrad, A. J. McLeod, J. S. H. Baxter, C. A. McKenzie, and T. M. Peters, “Stationary wavelet transform for under-sampled MRI reconstruction,” Magnetic Resonance Imaging, vol. 32, no. 10, pp. 1353–1364, 2014. View at Publisher · View at Google Scholar · View at Scopus
  18. I. W. Selesnick, “The double-density dual-tree DWT,” IEEE Transactions on Signal Processing, vol. 52, no. 5, pp. 1304–1314, 2004. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  19. I. W. Selesnick, “The double density DWT,” in Wavelets in Signal and Image Analysis, vol. 19 of Computational Imaging and Vision, pp. 39–66, Springer, Dordrecht, Netherlands, 2001. View at Publisher · View at Google Scholar
  20. I. Daubechies, M. Defrise, and C. De Mol, “An iterative thresholding algorithm for linear inverse problems with a sparsity constraint,” Communications on Pure and Applied Mathematics, vol. 57, no. 11, pp. 1413–1457, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  21. J. M. Bioucas-Dias and M. A. Figueiredo, “A new TwIST: two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE Transactions on Image Processing, vol. 16, no. 12, pp. 2992–3004, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  22. J. M. Bioucas-Dias and M. A. Figueiredo, “Two-step algorithms for linear inverse problems with non-quadratic regularization,” in Proceedings of the IEEE International Conference on Image Processing (ICIP '07), vol. 1, pp. 105–108, San Antonio, Tex, USA, 2007.
  23. A. Beck and M. Teboulle, “A fast iterative shrinkage-thresholding algorithm for linear inverse problems,” SIAM Journal on Imaging Sciences, vol. 2, no. 1, pp. 183–202, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  24. Y. Nesterov, “A method of solving a convex programming problem with convergence rate O (1/k2),” Soviet Mathematics—Doklady, vol. 27, pp. 372–376, 1983. View at Google Scholar
  25. Y. Kim, M. Altbach, T. Trouard, and A. Bilgin, “Compressed sensing using dual-tree complex wavelet transform,” in Proceedings of the International Society for Magnetic Resonance in Medicine, vol. 17, p. 2814, Honolulu, Hawaii, USA, 2009.
  26. I. W. Selesnick, R. G. Baraniuk, and N. G. Kingsbury, “The dual-tree complex wavelet transform,” IEEE Signal Processing Magazine, vol. 22, no. 6, pp. 123–151, 2005. View at Publisher · View at Google Scholar · View at Scopus
  27. http://eeweb.poly.edu/iselesni/DoubleSoftware/index.html.
  28. J. Bruck, “On the weak convergence of an ergodic iteration for the solution of variational inequalities for monotone operators in Hilbert space,” Journal of Mathematical Analysis and Applications, vol. 61, no. 1, pp. 159–164, 1977. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  29. http://eeweb.poly.edu/iselesni/WaveletSoftware/.
  30. C. Chen and J. Huang, “Exploiting the wavelet structure in compressed sensing MRI,” Magnetic Resonance Imaging, vol. 32, no. 10, pp. 1377–1389, 2014. View at Publisher · View at Google Scholar · View at Scopus