(k, q)-Compressed Sensing for dMRI with Joint Spatial-Angular Sparsity Prior

Conference paper
Part of the Mathematics and Visualization book series (MATHVISUAL)

Abstract

Advanced diffusion magnetic resonance imaging (dMRI) techniques, like diffusion spectrum imaging (DSI) and high angular resolution diffusion imaging (HARDI), remain underutilized compared to diffusion tensor imaging because the scan times needed to produce accurate estimations of fiber orientation are significantly longer. To accelerate DSI and HARDI, recent methods from compressed sensing (CS) exploit a sparse underlying representation of the data in the spatial and angular domains to undersample in the respective k- and q-spaces. State-of-the-art frameworks, however, impose sparsity in the spatial and angular domains separately and involve the sum of the corresponding sparse regularizers. In contrast, we propose a unified (k, q)-CS formulation which imposes sparsity jointly in the spatial-angular domain to further increase sparsity of dMRI signals and reduce the required subsampling rate. To efficiently solve this large-scale global reconstruction problem, we introduce a novel adaptation of the FISTA algorithm that exploits dictionary separability. We show on phantom and real HARDI data that our approach achieves significantly more accurate signal reconstructions than the state of the art while sampling only 2–4% of the (k, q)-space, allowing for the potential of new levels of dMRI acceleration.

Notes

Acknowledgements

This work was supported by JHU start-up funds.

References

  1. 1.
    Beck, A., Teboulle, M.: A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM J. Imag. Sci. 2(1), 183–202 (2009)Google Scholar
  2. 2.
    Candès, E.: Compressive sampling. In: Proceedings of the International Congress of Mathematics (2006)Google Scholar
  3. 3.
    Candès, E., Eldar, Y.C., Needell, D., Randall, P.: Compressed sensing with coherent and redundant dictionaries. Appl. Comput. Harmonic Anal. 31(1), 59–73 (2011)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Cheng, J., Shen, D., Basser, P.J., Yap, P.T.: Joint 6D kq space compressed sensing for accelerated high angular resolution diffusion MRI. In: Information Processing in Medical Imaging, pp. 782–793. Springer, New York (2015)Google Scholar
  5. 5.
    Goldstein, T., Osher, S.: The split Bregman method for L1-regularized problems. SIAM J. Imag. Sci. 2(2), 323–343 (2009)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    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)CrossRefGoogle Scholar
  7. 7.
    Mani, M., Jacob, M., Guidon, A., Magnotta, V., Zhong, J.: Acceleration of high angular and spatial resolution diffusion imaging using compressed sensing with multichannel spiral data. Magn. Reson. Med. 73(1), 126–138 (2015)CrossRefGoogle Scholar
  8. 8.
    Ning, L., et al.: Sparse reconstruction challenge for diffusion MRI: validation on a physical phantom to determine which acquisition scheme and analysis method to use? Med. Image Anal. 26(1), 316–331 (2015)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Ning, L., Setsompop, K., Michailovich, O.V., Makris, N., Shenton, M.E., Westin, C.-F., Rathi, Y.: A joint compressed-sensing and super-resolution approach for very high-resolution diffusion imaging. NeuroImage 125, 386–400 (2016)CrossRefGoogle Scholar
  10. 10.
    Schwab, E., Vidal, R., Charon, N.: Spatial-angular sparse coding for HARDI. In: Medical Image Computing and Computer Assisted Intervention, pp. 475–483. Springer, New York (2016)Google Scholar
  11. 11.
    Schwab, E., Vidal, R., Charon, N.: Efficient global spatial-angular sparse coding for diffusion MRI with separable dictionaries (2017). arXivGoogle Scholar
  12. 12.
    Sun, J., Sakhaee, E., Entezari, A., Vemuri, B.C.: Leveraging EAP-sparsity for compressed sensing of MS-HARDI in (k,q)-space. In: Information Processing in Medical Imaging, pp. 375–386. Springer, New York (2015)Google Scholar
  13. 13.
    Tan, Z., Eldar, Y.C., Beck, A., Nehorai, A.: Smoothing and decomposition for analysis sparse recovery. IEEE Trans. Signal Process. 62(7), 1762–1774 (2014)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Tristán-Vega, A., Westin, C.-F.: Probabilistic ODF estimation from reduced HARDI data with sparse regularization. In: Medical Image Computing and Computer Assisted Intervention, pp. 182–190. Springer, New York (2011)Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Center for Imaging ScienceJohns Hopkins UniversityBaltimoreUSA

Personalised recommendations