Skip to main content

Part of the book series: Springer Series on Bio- and Neurosystems ((SSBN,volume 9))

  • 942 Accesses

Abstract

Compressed sensing MRI (CS-MRI) seeks good quality MR image reconstruction from relatively less number of measurements than the traditional Nyquist sampling theorem. This in return increases the computational effort for reconstruction which may be dealt with some efficient solvers based on convex optimization. To reconstruct MR image from undersampled Fourier data, an underdetermined system of equations is needed to be solved with some additional information as regularization priors, like, compressibility of MR images in the spatial as well as wavelet domains.

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 109.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 139.99
Price excludes VAT (USA)
  • Durable hardcover 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. Candes, E.J., Romberg, J.K., Tao, T.: Stable signal recovery from incomplete and inaccurate measurements. Commun. Pure Appl. Math. 59(8), 1207–1223 (2006)

    Article  MathSciNet  Google Scholar 

  2. Candes, E., Wakin, M., Boyd, S.: Enhancing sparsity by reweighted L1 minimization. J. Fourier Anal. Appl. 14(5), 877–905 (2008)

    Article  MathSciNet  Google Scholar 

  3. Chen, S.S., Donoho, D.L., Saunders, M.A.: Atomic decomposition by basis pursuit. SIAM J. Sci. Comput. 20, 33–61 (1998)

    Article  MathSciNet  Google Scholar 

  4. Davis, G., Mallat, S., Avellaneda, M.: Adaptive greedy approximations. Constr. Approx. 13(1), 57–98 (1997)

    Article  MathSciNet  Google Scholar 

  5. Deka, B., Datta, S.: High throughput MR image reconstruction using compressed sensing. In: Proceedings of the 2014 Indian Conference on Computer Vision Graphics and Image Processing, ICVGIP14, pp. 89:1–89:6. ACM, Bangalore, India (2014)

    Google Scholar 

  6. Donoho, D.L., Tsaig, Y., Drori, I., Starck, J.L.: Sparse solution of underdetermined systems of linear equations by stagewise orthogonal matching pursuit. IEEE Trans. Inf. Theory 58(2), 1094–1121 (2012)

    Article  MathSciNet  Google Scholar 

  7. Efron, B., Hastie, T., Johnstone, I., Tibshirani, R.: Least angle regression. Ann. Stat. 32(2), 407–451 (2004)

    Google Scholar 

  8. Eldar, Y.C., Kuppinger, P., Bolcskei, H.: Block-sparse signals: uncertainty relations and efficient recovery. IEEE Trans. Signal Process. 58(6), 3042–3054 (2010)

    Article  MathSciNet  Google Scholar 

  9. Gamper, U., Boesiger, P., Kozerke, S.: Compressed sensing in dynamic MRI. Magn. Reson. Med. 59(2), 365–373 (2008)

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  12. Ma, S., Yin, W., Zhang, Y., Chakraborty, A.: An efficient algorithm for compressed MR imaging using total variation and wavelets. In: IEEE Conference on Computer Vision and Pattern Recognition (CVPR 2008), pp. 1–8. Anchorage, AK (2008)

    Google Scholar 

  13. Majumdar, A.: Compressed Sensing for Magnetic Resonance Image Reconstruction. Cambridge University Press, Delhi (2015)

    Google Scholar 

  14. Majumdar, A., Ward, R.K.: Fast group sparse classification. Can. J. Electr. Comput. Eng. 34(4), 136–144 (2009)

    Article  Google Scholar 

  15. Mallat, S., Zhang, Z.: Matching pursuits with time-frequency dictionaries. IEEE Trans. Signal Process. 41, 3397–3415 (1993)

    Article  Google Scholar 

  16. Murphey, M., Keutzer, K., Vasanawala, S., Lustig, M.: Clinically feasible reconstruction time for \(L_1\)-SPIRiT parallel imaging and compressed sensing MRI. In: Proceedings of the International Society for Magnetic Resonance in Medicine, pp. 48–54 (2010)

    Google Scholar 

  17. Murphey, M., Alley, M., Demmel, J., Keutzer, K., Vasanawala, S., Lustig, M.: Fast \(L_1\)-SPIRiT compressed sensing parralel imaging MRI: scalable parallel implementation and clinically feasible runtime. IEEE Trans. Med. Imaging 31(6), 1250–1262 (2012)

    Article  Google Scholar 

  18. Needell, D., Tropp, J.: CoSaMP: iterative signal recovery from incomplete and inaccurate samples. Appl. Comput. Harmon. Anal. 26(3), 301–321 (2009)

    Article  MathSciNet  Google Scholar 

  19. Needell, D., Vershynin, R.: Signal recovery from incomplete and inaccurate measurements via regularized orthogonal matching pursuit. IEEE J. Sel. Top. Signal Process. 4(2), 310–316 (2010)

    Article  Google Scholar 

  20. Pati, Y.C., Rezaiifar, R., Rezaiifar, Y.C.P.R., Krishnaprasad, P.S.: Orthogonal matching pursuit: recursive function approximation with applications to wavelet decomposition. In: Proceedings of the 27th Annual Asilomar Conference on Signals, Systems, and Computers, pp. 40–44 (1993)

    Google Scholar 

  21. Rudin, L.I., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Phys. D 60, 259–268 (1992)

    Article  MathSciNet  Google Scholar 

  22. Tropp, J.A., Gilbert, A.C., Strauss, M.J.: Algorithms for simultaneous sparse approximation. part i. Signal Process. 86(3), 572–588 (2006)

    Google Scholar 

  23. Usman, M., Prieto, C., Odille, F., Atkinson, D., Schaeffter, T., Batchelor, P.G.: A computationally efficient OMP-based compressed sensing reconstruction for dynamic MRI. Phys. Med. Biol. 56(7), N99–N114 (2011)

    Article  Google Scholar 

  24. Vasanawala, S., Murphy, M., Alley, M., Lai, P., Keutzer, K., Pauly, J., Lustig, M.: Practical parallel imaging compressed sensing MRI: summary of two years of experience in accelerating body MRI of pediatric patients. In: IEEE International Symposium on Biomedical Imaging: From Nano to Macro 2011, pp. 1039-1043. Chicago, IL (2011)

    Google Scholar 

  25. Vasanawala, S., Alley, M., Hargreaves, B., Barth, R., Pauly, J., Lustig, M.: Improved pediatric MR imaging with compressed sensing. Radiology 256(2), 607–616 (2010)

    Article  Google Scholar 

  26. Wang, J., Kwon, S., Shim, B.: Generalized orthogonal matching pursuit. IEEE Trans. Signal Process. 60(12), 6202–6216 (2012)

    Article  MathSciNet  Google Scholar 

  27. Yang, A.Y., Ganesh, A., Zhou, Z., Sastry, S., Ma, Y.: A review of fast \(L_1\)-minimization algorithms for robust face recognition (2010) CoRR arXiv:abs/1007.3753

  28. Yang, J., Zhang, Y., Yin, W.: A fast alternating direction method for TV\(L_1\)-\(L_2\) signal reconstruction from partial Fourier data. IEEE J. Sel. Top. Signal Process. 4(2), 288–297 (2010)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Bhabesh Deka .

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Singapore Pte Ltd.

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Deka, B., Datta, S. (2019). CS-MRI Reconstruction Problem. In: Compressed Sensing Magnetic Resonance Image Reconstruction Algorithms. Springer Series on Bio- and Neurosystems, vol 9. Springer, Singapore. https://doi.org/10.1007/978-981-13-3597-6_2

Download citation

  • DOI: https://doi.org/10.1007/978-981-13-3597-6_2

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-13-3596-9

  • Online ISBN: 978-981-13-3597-6

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics