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Compressed-Sensing MRI Based on Adaptive Tight Frame in Gradient Domain

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Abstract

Compressed-sensing magnetic resonance imaging (CSMRI) aims to reconstruct the magnetic resonance (MR) image from highly undersampled K-space data. In order to improve the reconstruction quality of the MR image, this paper proposes a new gradient-based tight frame (TFG) learning algorithm (TFG-MRI) for CSMRI. TFG-MRI effectively integrates the tight frame learning technique and total variation into the same framework. In TFG-MRI, the inherent gradient sparsity of the MR image in gradient domain is utilized to represent the sparse prior knowledge, and the sparse priors in the horizontal and vertical gradient directions are exploited to learn adaptive tight frames for reconstructing the desired images. Particularly, we employ the l0-norm to promote the sparsity of the gradient image. The sparse representations of TFG are adapted for the horizontal and vertical gradient information of MR images. TFG-MRI can effectively help to capture edge contour structures in the gradient images, and to preserve more detail information of MR images. The experimental results demonstrate that the proposed TFG-MRI can reconstruct MR images more clearly in various sampling schemes. Compared with the existing MR image reconstruction algorithms, TFG-MRI can achieve higher accurate image reconstruction quality and better robustness to noises.

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References

  1. S. Ravishankar, Y. Bresler, I.E.E.E. Trans. Med. Imaging 30(5), 1028–1041 (2011)

    Article  Google Scholar 

  2. D.L. Donoho, I.E.E.E. Trans. Inf. Theory 52(4), 1289–1306 (2006)

    Article  Google Scholar 

  3. E. Candes, J. Roberg, T. Tao, I.E.E.E. Trans. Inf. Theory 52(2), 489–509 (2006)

    Article  Google Scholar 

  4. Y. Liu, J.F. Cai, Z. Zhan, D. Guo, J. Ye, Z. Chen, X. Qu, PLoS One 10(4), e0119584 (2015)

    Article  Google Scholar 

  5. J. Huang, L. Guo, Q. Feng, W. Chen, Y. Feng, Phys. Med. Biol. 60(14), 5359–5380 (2015)

    Article  Google Scholar 

  6. Y. Zhang, J. Yang, J. Yang, A. Liu, P. Sun, Int. J. Biomed. Imaging 2016(3), 9416435 (2016)

    Google Scholar 

  7. Y. Han, H. Du, X. Gao, W. Mei, IET Image Process. 11(3), 155–163 (2017)

    Article  Google Scholar 

  8. J.P. Huang, L.K. Zhu, L.H. Wang, W.L. Song, Appl. Magn. Reson. 48(8), 749–760 (2017)

    Article  Google Scholar 

  9. M. Lustig, D. Donoho, J. Pauly, Magn. Reson. Med. 58(6), 1182–1195 (2007)

    Article  Google Scholar 

  10. S. Ma, W. Yin, Y. Zhang, A. Chakraborty, in 2008 IEEE Computer Society Conference on Computer Vision and Pattern Recognition  (CVPR, Anchorage, Alaska, 2008), pp. 1–8

  11. J. Huang, S. Zhang, D. Metaxas, Med. Image Anal. 15(5), 670–679 (2011)

    Article  Google Scholar 

  12. J.P. Huang, W.Y. Liu, L.H. Wang, Y.M. Zhu, in 2014 IEEE 11th International Symposium on Biomedical Imaging (ISBI, Beijing, China, 2014) pp. 1063–1066

  13. S. Ravishankar, Y. Bresler, in 2013 IEEE 10th International Symposium on Biomedical Imaging: From Nano to Macro (ISBI, San Francisco, CA, 2013), pp. 17–20

  14. Q. Liu, S. Wang, L. Ying, X. Peng, Y. Zhu, D. Liang, I.E.E.E. Trans. Image Process. 22(12), 4652–4663 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  15. J. Liu, S. Wang, X. Peng, D. Liang, Comput. Math. Method. M. 2015(1), 424087 (2015)

    Google Scholar 

  16. Y. Liu, Z. Zhan, J.F. Cai, D. Guo, Z. Chen, X. Qu, I.E.E.E. Trans. Med. Imaging 35(9), 2130–2140 (2016)

    Article  Google Scholar 

  17. S. Ramani, J.A. Fessler, I.E.E.E. Trans. Med. Imaging 30(3), 694–706 (2011)

    Article  Google Scholar 

  18. H. Liu, B. Song, H. Qin, Z. Qiu, IEEE Signal Process. Lett. 20(4), 315–318 (2013)

    Article  ADS  Google Scholar 

  19. J.F. Cai, H. Ji, Z. Shen, G.B. Ye, Appl. Comput. Harmon. A. 37(1), 89–105 (2014)

    Article  Google Scholar 

  20. S. Ravishankar, Y. Bresler, SIAM J. Imaging Sci. 8(4), 2519–2557 (2015)

    Article  MathSciNet  Google Scholar 

  21. Z. Xu, Q. Shi, IET Image Process. 10(12), 962–970 (2017)

    Article  Google Scholar 

Download references

Acknowledgements

We will sincerely acknowledge the anonymous reviewers for their hard work on this paper. This project was partly supported by China NSFC 61471313, and China Hebei NSFC F2014203076, and the Anhui Science and Technology University Foundation AKZDXK2015C02, and the Open Fund Project of CETC Key Laboratory of Aerospace Information Applications under Grant EX166290016. We gratefully acknowledge the financial support.

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Authors and Affiliations

  1. School of Information Science and Engineering, Yanshan University, Qinhuangdao, 066004, China

    Fan Xiaoyu, Lian Qiusheng & Shi Baoshun

  2. School of Electrical and Electronic Engineering, Anhui Science and Technology University, Chuzhou, 233100, China

    Fan Xiaoyu

  3. CETC Key Laboratory of Aerospace Information Applications, Shijiazhuang, 050081, China

    Shi Baoshun

Authors
  1. Fan Xiaoyu
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  2. Lian Qiusheng
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  3. Shi Baoshun
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Correspondence to Lian Qiusheng.

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Fan, X., Lian, Q. & Shi, B. Compressed-Sensing MRI Based on Adaptive Tight Frame in Gradient Domain. Appl Magn Reson 49, 465–477 (2018). https://doi.org/10.1007/s00723-018-0988-z

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  • DOI: https://doi.org/10.1007/s00723-018-0988-z

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