Skip to main content

Fast Dual-Tree Wavelet Composite Splitting Algorithms for Compressed Sensing MRI

  • Conference paper
  • First Online:
Neural Information Processing (ICONIP 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9947))

Included in the following conference series:

Abstract

We presented new reconstruction algorithms for compressed sensing magnetic resonance imaging (CS-MRI) based on the combination of the fast composite splitting algorithm (FCSA) and complex dual-tree wavelet transform (DT-CWT) and on the combination of FCSA and double density dual-tree wavelet transform (DDDT-DWT), respectively. We applied the bivariate thresholding to these two combinations. The proposed methods not only inherit the effectiveness and fast convergence of FCSA but also improve the sparse representation of both point-like and curve-like features. Experimental results validate the effectiveness and efficiency of the proposed methods.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Donoho, D.: Compressed sensing. IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  2. Tsaig, Y., Donoho, D.L.: Extensions of compressed sensing. Sig. Process. 86(3), 549–571 (2006)

    Article  MATH  Google Scholar 

  3. Lustig, M., Donoho, D., Pauly, J.M.: Sparse MRI: the application of compressed sensing for rapid MR imaging. Magn. Reson. Med. 58(6), 1182–1195 (2007)

    Article  Google Scholar 

  4. Lustig, M., Donoho, D.L., Santos, J.M., Pauly, J.M.: Compressed sensing MRI. IEEE Signal Process. Mag. 25(2), 72–82 (2008)

    Article  Google Scholar 

  5. Kingsbury, N.: Complex wavelets for shift invariant analysis and filtering of signals. Appl. Comput. Harmonic Anal. 10(3), 234–253 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  6. Kingsbury, N.: Image processing with complex wavelets. Philos. Trans. R. Soc. A 357, 2543–2560 (1999)

    Article  MATH  Google Scholar 

  7. Kim, Y., Altbach, M., Trouard, T., Bilgin, A.: Compressed sensing using dual-tree complex wavelet transform. In: Proceedings of the International Society for Magnetic Resonance in Medicine, vol. 17, p. 2814 (2009)

    Google Scholar 

  8. Zhu, Z., Wahid, K., Babyn, P., Yang, R.: Compressed sensing-based MRI reconstruction using complex double-density dual-tree DWT. Int. J. Biomed. Imaging 2013, 1–12 (2013)

    Article  Google Scholar 

  9. Do, M.N., Vetterli, M.: The contourlet transform: an efficient directional multiresolution image representation. IEEE Trans. Image Process. 14(12), 2091–2106 (2005)

    Article  Google Scholar 

  10. Qu, X., Zhang, W., Guo, D., Cai, C., Cai, S., Chen, Z.: Iterative thresholding compressed sensing MRI based on contourlet transform. Inverse Prob. Sci. Eng. 18, 737–758 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  11. Selesnick, I.W.: The double-density dual-tree DWT. IEEE Trans. Sig. Process. 52(5), 1304–1314 (2004)

    Article  MathSciNet  Google Scholar 

  12. Bioucas-Dias, J., Figueiredo, M.: A new TwIST: two step iterative shrinkage/thresholding algorithms for image restoration. IEEE Trans. Image Process. 16(12), 2992–3004 (2007)

    Article  MathSciNet  Google Scholar 

  13. Beck, A., Teboulle, M.: A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM J. Imaging Sci. 2(1), 183–202 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  14. Huang, J., Zhang, S., Metaxas, D.: Efficient MR image reconstruction for compressed MR imaging. Med. Image Anal. 15(5), 670–679 (2011)

    Article  Google Scholar 

  15. Hao, W., Li, J., Qu, X., Dong, Z.: Fast iterative contourlet thresholding for compressed sensing MRI. Electron. Lett. 49(19), 1206–1208 (2013)

    Article  Google Scholar 

  16. Donoho, D.L.: De-noising by soft-thresholding. IEEE Trans. Inf. Theory 41(3), 613–627 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  17. Chang, S.G., Yu, B., Vetterli, M.: Adaptive wavelet thresholding for image denoising and compression. IEEE Trans. Image Process. 9(9), 1532–1546 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  18. Sendur, L., Selesnick, I.W.: Bivariate shrinkage functions for wavelet-based denoising exploiting interscale dependency. IEEE Trans. Sig. Process. 50(11), 2744–2756 (2002)

    Article  Google Scholar 

  19. http://eeweb.poly.edu/iselesni/WaveletSoftware/index.html

  20. http://eeweb.poly.edu/iselesni/DoubleSoftware/index.html

Download references

Acknowledgement

This work is supported by the National Natural Science Foundation of China (No. 61271374).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jianwu Li .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing AG

About this paper

Cite this paper

Li, J., Zhou, J., Tu, Q., Ikram, J., Dong, Z. (2016). Fast Dual-Tree Wavelet Composite Splitting Algorithms for Compressed Sensing MRI. In: Hirose, A., Ozawa, S., Doya, K., Ikeda, K., Lee, M., Liu, D. (eds) Neural Information Processing. ICONIP 2016. Lecture Notes in Computer Science(), vol 9947. Springer, Cham. https://doi.org/10.1007/978-3-319-46687-3_57

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-46687-3_57

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-46686-6

  • Online ISBN: 978-3-319-46687-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics