Recovering Missing Connections in Diffusion Weighted MRI Using Matrix Completion

  • Chendi Wang
  • Bernard Ng
  • Alborz Amir-Khalili
  • Rafeef Abugharbieh
Conference paper
Part of the Mathematics and Visualization book series (MATHVISUAL)

Abstract

Diffusion weighted magnetic resonance imaging (dwMRI) has become the dominant neuroimaging modality for estimating anatomical connectivity (AC). However, such AC estimation is prone to error due to missing connections resulting from crossing fibers and fiber endpoint uncertainty because of insufficient spatial resolution. Endeavors tackling this problem include improving fiber orientation estimation , applying heuristics to extrapolate fiber endpoints, and increasing spatial resolution. Refining fiber orientation estimation and tractography algorithms can only improve AC estimation to a certain extent, since the attainable improvement is constrained by the current limit on spatial resolution. We thus instead propose using matrix completion (MC) to recover missing connections. The underlying assumption is that the missing connections are intrinsically related to the observed entries of the AC matrix. A critical parameter that governs MC performance is the matrix rank. For this, we present a robust strategy that bypasses selection of a specific rank. Further, standard MC algorithms do not constrain the recovered entries to be non-negative, but this condition is necessary for fiber counts. We thus devise a method to interpolate negative entries based on neighborhood information. On synthetic data, our approach is able to accurately recover deleted AC matrix entries. On real data, AC estimated with our approach achieves higher IQ prediction accuracy than the original AC estimates, fiber endpoint extrapolation, and median filtering.

References

  1. 1.
    Assemlal, H.E., Tschumperlé, D., Brun, L., Siddiqi, K.: Recent advances in diffusion MRI modeling: angular and radial reconstruction. Med. Image Anal. 15(4), 369–396 (2011)CrossRefGoogle Scholar
  2. 2.
    Jbabdi, S., Johansen-Berg, H.: Tractography: where do we go from here? Brain Connect. 1(3), 169–183 (2011)CrossRefGoogle Scholar
  3. 3.
    Descoteaux, M., Deriche, R., Knosche, T.R., Anwander, A.: Deterministic and probabilistic tractography based on complex fibre orientation distributions. IEEE Trans. Med. Imaging 28(2), 269–286 (2009)CrossRefGoogle Scholar
  4. 4.
    Neher, P.F., Stieltjes, B., Reisert, M., Reicht, I., Meinzer, H.P., Fritzsche, K.H.: MITK global tractography. In: SPIE Medical Imaging, International Society for Optics and Photonics, 83144D (2012)Google Scholar
  5. 5.
    Behrens, T.E., Berg, H.J., Jbabdi, S., Rushworth, M., Woolrich, M.: Probabilistic diffusion tractography with multiple fibre orientations: what can we gain? NeuroImage 34(1), 144–155 (2007)CrossRefGoogle Scholar
  6. 6.
    Ng, B., Varoquaux, G., Poline, J.B., Thirion, B.: Implications of inconsistencies between fMRI and dMRI on multimodal connectivity estimation. In: International Conference on Medical Image Computing and Computer-Assisted Intervention, pp. 652–659. Springer, Berlin (2013)Google Scholar
  7. 7.
    Van Essen, D.C., Smith, S.M., Barch, D.M., Behrens, T.E., Yacoub, E., Ugurbil, K., Consortium, W.M.H., et al.: The wu-minn human connectome project: an overview. NeuroImage 80, 62–79 (2013)CrossRefGoogle Scholar
  8. 8.
    Ning, L., Setsompop, K., Michailovich, O., 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
  9. 9.
    Candes, E.J., Recht, B.: Exact low-rank matrix completion via convex optimization. In: 46th Annual Allerton Conference on Communication, Control, and Computing, pp. 806–812. IEEE, New York (2008)Google Scholar
  10. 10.
    Keshavan, R.H., Montanari, A., Oh, S.: Matrix completion from a few entries. IEEE Trans. Inf. Theory 56(6), 2980–2998 (2010)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Xu, Y., Yin, W., Wen, Z., Zhang, Y.: An alternating direction algorithm for matrix completion with nonnegative factors. Front. Math. China 7(2), 365–384 (2012)MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Wen, Z., Yin, W., Zhang, Y.: Solving a low-rank factorization model for matrix completion by a nonlinear successive over-relaxation algorithm. Math. Program. Comput. 4(4), 333–361 (2012)MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Desikan, R.S., Ségonne, F., Fischl, B., Quinn, B.T., Dickerson, B.C., Blacker, D., Buckner, R.L., Dale, A.M., Maguire, R.P., Hyman, B.T., et al.: An automated labeling system for subdividing the human cerebral cortex on MRI scans into gyral based regions of interest. NeuroImage 31(3), 968–980 (2006)CrossRefGoogle Scholar
  14. 14.
    Shirer, W., Ryali, S., Rykhlevskaia, E., Menon, V., Greicius, M.: Decoding subject-driven cognitive states with whole-brain connectivity patterns. Cereb. Cortex 22(1), 158–165 (2012)CrossRefGoogle Scholar
  15. 15.
    Li, Y., Liu, Y., Li, J., Qin, W., Li, K., Yu, C., Jiang, T.: Brain anatomical network and intelligence. PLoS Comput. Biol. 5(5), e1000395 (2009)CrossRefGoogle Scholar
  16. 16.
    Balzano, L., Nowak, R., Recht, B.: Online identification and tracking of subspaces from highly incomplete information. In: 48th Annual Allerton Conference on Communication, Control, and Computing (Allerton), pp. 704–711. IEEE, New York (2010)Google Scholar
  17. 17.
    Fan, R.E., Chang, K.W., Hsieh, C.J., Wang, X.R., Lin, C.J.: Liblinear: a library for large linear classification. J. Mach. Learn. Res. 9, 1871–1874 (2008)MATHGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Chendi Wang
    • 1
  • Bernard Ng
    • 2
    • 3
  • Alborz Amir-Khalili
    • 1
  • Rafeef Abugharbieh
    • 1
  1. 1.Biomedical Signal and Image Computing LabUniversity of British ColumbiaVancouverCanada
  2. 2.Department of StatisticsUniversity of British ColumbiaVancouverCanada
  3. 3.Department of Medical GeneticsUniversity of British ColumbiaVancouverCanada

Personalised recommendations