Advertisement

From Expected Propagator Distribution to Optimal Q-space Sample Metric

  • Hans Knutsson
  • Carl-Fredrik Westin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8675)

Abstract

We present a novel approach to determine a local q-space metric that is optimal from an information theoretic perspective with respect to the expected signal statistics. It should be noted that the approach does not attempt to optimize the quality of a pre-defined mathematical representation, the estimator. In contrast, our suggestion aims at obtaining the maximum amount of information without enforcing a particular feature representation.

Results for three significantly different average propagator distributions are presented. The results show that the optimal q-space metric has a strong dependence on the assumed distribution in the targeted tissue. In many practical cases educated guesses can be made regarding the average propagator distribution present. In such cases the presented analysis can produce a metric that is optimal with respect to this distribution. The metric will be different at different q-space locations and is defined by the amount of additional information that is obtained when adding a second sample at a given offset from a first sample. The intention is to use the obtained metric as a guide for the generation of specific efficient q-space sample distributions for the targeted tissue.

Keywords

Information Gain Axis Ratio Angular Direction Propagator Distribution Information Theoretic Perspective 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Jones, D.K., Simmons, A., Williams, S.C.R., Horsfield, M.A.: Non-invasive assessment of axonal fiber connectivity in the human brain via diffusion tensor MRI. Magn. Reson. Med. 42, 37–41 (1999)CrossRefGoogle Scholar
  2. 2.
    Assaf, Y., Freidlin, R.Z., Rohde, G.K., Basser, P.J.: New modeling and experimental framework to characterize hindered and restricted water diffusion in brain white matter. Magn. Reson. Med. 52(5), 965–978 (2004)CrossRefGoogle Scholar
  3. 3.
    Wu, Y.C., Alexander, A.: Hybrid diffusion imaging. Neuroimage 36(3), 617–629 (2007)CrossRefGoogle Scholar
  4. 4.
    Alexander, D.C.: A general framework for experiment design in diffusion MRI and its application in measuring direct tissue-microstructure features. Magn. Reson. Med. 60(2), 439–448 (2008)CrossRefGoogle Scholar
  5. 5.
    Merlet, S., Caruyer, E., Deriche, R.: Impact of radial and angular sampling on multiple shells acquisition in diffusion MRI. Med. Image Comput. Comput. Assist. Interv. 14(Pt. 2), 116–123 (2011); Eds: T. Peters, G. Fichtinger, A. MartelGoogle Scholar
  6. 6.
    Caruyer, E., Cheng, J., Lenglet, C., Sapiro, G., Jiang, T., Deriche, R.: Optimal Design of Multiple Q-shells experiments for Diffusion MRI. In: MICCAI Workshop CDMRI 2011 (2011)Google Scholar
  7. 7.
    Ye, W., Portnoy, S., Entezari, A., Blackband, S.J., Vemuri, B.C.: An Efficient Interlaced Multi-shell Sampling Scheme for Reconstruction of Diffusion Propagators. IEEE Trans. Med. Imaging 31(5), 1043–1050 (2012)CrossRefGoogle Scholar
  8. 8.
    Westin, C.F., Pasternak, O., Knutsson, H.: Rotationally invariant gradient schemes for diffusion MRI. In: Proc. of the ISMRM Annual Meeting (ISMRM 2012), p. 3537 (2012)Google Scholar
  9. 9.
    Scherrer, B., Warfield, S.K.: Parametric Representation of Multiple White Matter Fascicles from Cube and Sphere Diffusion MRI. PLoS One 7(11), 1–20 (2012)Google Scholar
  10. 10.
    Knutsson, H., Westin, C.-F.: Charged Containers for Optimal 3D Q-space Sampling. In: ISMRM 2013 (2013)Google Scholar
  11. 11.
    Shannon, C.: Communication in the Presence of Noise. Proceedings of the IRE 37(1), 10–21 (1949)CrossRefMathSciNetGoogle Scholar
  12. 12.
    Rao, C.R.: Bull. Calcutta Math. Soc. 37 (1945)Google Scholar
  13. 13.
    Pires, C.A.L., Perdigo, R.A.P.: Minimum Mutual Information and Non-Gaussianity Through the Maximum Entropy Method: Theory and Properties. Entropy 14, 1103–1126 (2012); Ed: K. H. Knuth Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Hans Knutsson
    • 1
  • Carl-Fredrik Westin
    • 2
  1. 1.Linköping UniversitySweden
  2. 2.Harvard Medical SchoolUSA

Personalised recommendations