Applied Magnetic Resonance

, Volume 50, Issue 1–3, pp 243–261 | Cite as

Accelerating Parallel Magnetic Resonance Imaging Using p-Thresholding Based Compressed-Sensing

  • Irfan Ullah
  • Omair InamEmail author
  • Ibtisam Aslam
  • Hammad Omer
Original Paper


Conjugate gradient-based SENSE (CG-SENSE) and compressed-sensing (CS) are well-established techniques to accelerate magnetic resonance imaging (MRI) data acquisition. CG-SENSE is an iterative parallel MRI (pMRI) technique, used for the reconstruction of unaliased MR images from the under-sampled arbitrary k-space trajectories (Cartesian and non-Cartesian). Whereas CS is a promising technique that requires fewer random samples in the k-space to speed up the data acquisition process for MR image reconstruction. In the recent past, further acceleration in MR data acquisitions has been achieved using pMRI and CS jointly. In this paper, a novel method is proposed which sequentially combines CG-SENSE with p-thresholding based CS to achieve higher acceleration factors without compromising the quality of image reconstruction. In the proposed method, CG-SENSE and p-thresholding based CS reconstructions are sequentially combined to recover aliased free images from highly under-sampled k-space data. The performance of the proposed method is evaluated for arbitrary k-space Cartesian and radial trajectories. The reconstruction results are compared with conventional methods, e.g., CG-SENSE and \(\ell_{1}\)-SPIR-iT. Several experiments are performed using simulated phantom and in vivo datasets. The reconstruction quality of the proposed method is evaluated in terms of artifact power (AP), peak signal-to-noise ratio (PSNR) and root mean square error (RMSE). The experimental results show that the proposed method outperforms the CG-SENSE and \(\ell_{1}\)-SPIR-iT by achieving superior image reconstruction quality.

Supplementary material

723_2018_1062_MOESM1_ESM.docx (18 kb)
Supplementary material 1 (DOCX 18 kb)


  1. 1.
    D.W. McRobbie, E.A. Moore, M.J. Graves, M.R. Prince, MRI from Picture to Proton (Cambridge University Press, Cambridge, 2007)Google Scholar
  2. 2.
    A.G. van der Kolk, J. Hendrikse, J.J. Zwanenburg, F. Visser, P.R. Luijten, Eur. J. Radiol. 82, 708–718 (2013)CrossRefGoogle Scholar
  3. 3.
    M.A. Bernstein, K.F. King, X.J. Zhou, Handbook of MRI Pulse Sequences (Elsevier, New York, 2004)Google Scholar
  4. 4.
    R.J. Stafford, in Proceedings of the 46th Annual Meeting of American Association of Physicists in Medicine AAPM (Pittsburgh, Pensnsylvania, 25–29 July 2004), p. 1836Google Scholar
  5. 5.
    S.O. Schoenberg, A. Baert, O. Dietrich, M.F. Reiser, Parallel Imaging in Clinical MR Applications (Springer, Berlin, 2007)CrossRefGoogle Scholar
  6. 6.
    A. Deshmane, V. Gulani, M.A. Griswold, N. Seiberlich, J. Magn. Reson. Imaging 36, 55–72 (2012)CrossRefGoogle Scholar
  7. 7.
    I. Ullah, H. Nisar, H. Raza, M. Qasim, O. Inam, H. Omer, Comput. Biol. Med. 95, 1–12 (2018)CrossRefGoogle Scholar
  8. 8.
    M. Lustig, J.M. Pauly, Magn. Reson. Med. 64, 457–471 (2010)Google Scholar
  9. 9.
    M.A. Griswold, P.M. Jakob, R.M. Heidemann, M. Nittka, V. Jellus, J. Wang, B. Kiefer, A. Haase, Magn. Reson. Med. 47, 1202–1210 (2002)CrossRefGoogle Scholar
  10. 10.
    O. Inam, M. Qureshi, S.A. Malik, H. Omer, BioMed Res. Int. 2017, 3872783 (2017)CrossRefGoogle Scholar
  11. 11.
    A. Tolouee, J. Alirezaie, P. Babyn, J. Magn. Reson. 260, 10–19 (2015)ADSCrossRefGoogle Scholar
  12. 12.
    G. Glover, J. Pauly, Magn. Reson. Med. 28, 275–289 (1992)CrossRefGoogle Scholar
  13. 13.
    J.G. Pipe, Magn. Reson. Med. 42, 963–969 (1999)CrossRefGoogle Scholar
  14. 14.
    K.L. Wright, J.I. Hamilton, M.A. Griswold, V. Gulani, N. Seiberlich, J. Magn. Reson. Imaging 40, 1022–1040 (2014)CrossRefGoogle Scholar
  15. 15.
    M.A. Griswold, R.M. Heidemann, P.M. Jakob, in Proceedings of the 11th Annual Meeting of the International Society for Magnetic Resonance in Medicine (ISMRM) (Toronto, Ontario, Canada, 10–16 July 2003), vol. 2349Google Scholar
  16. 16.
    K.P. Pruessmann, M. Weiger, P. Börnert, P. Boesiger, Magn. Reson. Med. 46, 638–651 (2001)CrossRefGoogle Scholar
  17. 17.
    M. Khan, T. Aslam, H. Shahzad, H. Omer, Appl. Magn. Reson. 48, 227–240 (2017)CrossRefGoogle Scholar
  18. 18.
    I. Aslam, F. Najeeb, H. Omer, Appl. Magn. Reson. 49, 107–124 (2018)CrossRefGoogle Scholar
  19. 19.
    N. Seiberlich, F. Breuer, R. Heidemann, M. Blaimer, M. Griswold, P. Jakob, Magn. Reson. Med. 59, 1127–1137 (2008)CrossRefGoogle Scholar
  20. 20.
    M. Lustig, D. Donoho, J.M. Pauly, Magn. Reson. Med. 58, 1182–1195 (2007)CrossRefGoogle Scholar
  21. 21.
    J. Shah, I. Qureshi, J. Proano, Y. Deng, Appl. Magn. Reson. 46, 837–851 (2015)CrossRefGoogle Scholar
  22. 22.
    M. Kaleem, M. Qureshi, H. Omer, Appl. Magn. Reson. 47, 415–428 (2016)CrossRefGoogle Scholar
  23. 23.
    D.S. Weller, J.R. Polimeni, L. Grady, L.L. Wald, E. Adalsteinsson, V.K. Goyal, in Proceedings of the 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) (Prague, Czech Republic, 22–27 May 2011), pp. 553–556Google Scholar
  24. 24.
    B. Wu, R.P. Millane, R. Watts, P.J. Bones, Magn. Reson. Med. 65, 83–95 (2011)CrossRefGoogle Scholar
  25. 25.
    D. Liang, B. Liu, J. Wang, L. Ying, Magn. Reson. Med. 62, 1574–1584 (2009)CrossRefGoogle Scholar
  26. 26.
    M. Lustig, M. Alley, S. Vasanawala, D.L. Donoho, J.M. Pauly, in Proceedings of the 17th Annual ISMRM Scientific Meeting and Exhibition 2009 (Honolulu, Hawaii ,18–24 April 2009), vol. 17, p. 379Google Scholar
  27. 27.
    M. Murphy, M. Alley, J. Demmel, K. Keutzer, S. Vasanawala, M. Lustig, IEEE Trans. Med. Imaging 31, 1250–1262 (2012)CrossRefGoogle Scholar
  28. 28.
    S. Voronin, R. Chartrand, in Proceedings of the 2013 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) (Vancouver, British Columbia, Canada, May 26–31, 2013), pp. 1636–1640Google Scholar
  29. 29.
    I. Daubechies, M. Defrise, C. De Mol, Commun. Pure Appl. Math. 57, 1413–1457 (2004)CrossRefGoogle Scholar
  30. 30.
    S. Elahi, H. Omer, J. Magn. Reson. 286, 91–98 (2018)ADSCrossRefGoogle Scholar
  31. 31.
    X. Zhang, M. Burger, X. Bresson, S. Osher, SIAM Imaging Sci. 3, 253–276 (2010)CrossRefGoogle Scholar
  32. 32.
    M.P. Romaniuk, Ph.D Thesis, Imperial College London, London, UK (2016)Google Scholar
  33. 33.
    S. Xie, W. Huang, Z. Lu, S. Huang, C. Guan, in Proceedings of the 2017 IEEE 2nd International Conference on Signal and Image Processing (ICSIP) (Singapore, August 4–6, 2017), pp. 193–197Google Scholar
  34. 34.
    M. Çetin, W.C. Karl, IEEE Trans. Image Process. 10, 623–631 (2001)ADSCrossRefGoogle Scholar
  35. 35.
    R. Chartrand, IEEE Signal Process. Lett. 14, 707–710 (2007)ADSCrossRefGoogle Scholar
  36. 36.
    R. Chartrand, V. Staneva, Inverse Prob. 24, 035020 (2008)ADSCrossRefGoogle Scholar
  37. 37.
    R. Chartrand, W. Yin, in Proceedings of the 2008 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) (Las Vegas, Nevada, USA, March 30–April 4, 2008), pp. 3869–3872Google Scholar
  38. 38.
    E.J. Candes, M.B. Wakin, S.P. Boyd, J. Fourier Anal. Appl. 14, 877–905 (2008)MathSciNetCrossRefGoogle Scholar
  39. 39.
    Y. She, Electron. J. Stat. 3, 384–415 (2009)MathSciNetCrossRefGoogle Scholar
  40. 40.
    D. Krishnan, R. Fergus, in Proceedings of the 23rd Annual Conference on Neural Information Processing Systems 2009 (Vancouver, British Columbia, Canada, 7–10 December 2009), pp. 1033–1041Google Scholar
  41. 41.
    W. Zuo, D. Meng, L. Zhang, X. Feng, D. Zhang, in Proceedings of the 2013 IEEE International Conference on Computer Vision (ICCV) (Sydney, NSW, Australia, 1–8 December 2013), pp. 217–224Google Scholar
  42. 42.
    O. Inam, M. Qureshi, S.A. Malik, H. Omer, Appl. Magn. Reson. 48, 1055–1074 (2017)CrossRefGoogle Scholar
  43. 43.
    N. Seiberlich, F. Breuer, M. Blaimer, P. Jakob, M. Griswold, Magn. Reson. Med. 59, 930–935 (2008)CrossRefGoogle Scholar
  44. 44.
    J. Petr, J. Kybic, in Proceedings of Medical Imaging 2007: Image Processing (San Diego, California, USA, 18–20 February 2007), vol. 6512, p. 651241Google Scholar
  45. 45.
    S.E. Ghrare, S.M. Shreef, Int Sch Sci Res Innov 6, 641–643 (2012)Google Scholar
  46. 46.
    M. Uecker, F. Ong, J.I. Tamir, D. Bahri, P. Virtue, J.Y. Cheng, T. Zhang, M. Lustig, in Proceedings of the 23rd Annual Meeting of the International Society for Magnetic Resonance in Medicine (ISMRM) (Toronto, Ontario, Canada, 30 May–05 June 2015), vol. 23, p. 2486Google Scholar
  47. 47.
    M.F. Siddiqui, A.W. Reza, A. Shafique, H. Omer, J. Kanesan, Magn. Reson. Imaging 44, 82–91 (2017)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Electrical EngineeringCOMSATS University IslamabadIslamabadPakistan

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