Advertisement

Non-negative Spherical Deconvolution (NNSD) for Fiber Orientation Distribution Function Estimation

  • Jian ChengEmail author
  • Rachid Deriche
  • Tianzi Jiang
  • Dinggang Shen
  • Pew-Thian YapEmail author
Conference paper
Part of the Mathematics and Visualization book series (MATHVISUAL)

Abstract

In diffusion Magnetic Resonance Imaging (dMRI), Spherical Deconvolution (SD) is a commonly used approach for estimating the fiber Orientation Distribution Function (fODF). As a Probability Density Function (PDF) that characterizes the distribution of fiber orientations, the fODF is expected to be non-negative and to integrate to unity on the continuous unit sphere \({\mathbb{S}}^{2}\). However, many existing approaches, despite using continuous representation such as Spherical Harmonics (SH), impose non-negativity only on discretized points of \({\mathbb{S}}^{2}\). Therefore, non-negativity is not guaranteed on the whole \({\mathbb{S}}^{2}\). Existing approaches are also known to exhibit false positive fODF peaks, especially in regions with low anisotropy, causing an over-estimation of the number of fascicles that traverse each voxel. This paper proposes a novel approach, called Non-Negative SD (NNSD), to overcome the above limitations. NNSD offers the following advantages. First, NNSD is the first SH based method that guarantees non-negativity of the fODF throughout the unit sphere. Second, unlike approaches such as Maximum Entropy SD (MESD), Cartesian Tensor Fiber Orientation Distribution (CT-FOD), and discrete representation based SD (DR-SD) techniques, the SH representation allows closed form of spherical integration, efficient computation in a low dimensional space resided by the SH coefficients, and accurate peak detection on the continuous domain defined by the unit sphere. Third, NNSD is significantly less susceptible to producing false positive peaks in regions with low anisotropy. Evaluations of NNSD in comparison with Constrained SD (CSD), MESD, and DR-SD (implemented using L1-regularized least-squares with non-negative constraint), indicate that NNSD yields improved performance for both synthetic and real data. The performance gain is especially prominent for high resolution \({(1.25\,\text{mm})}^{3}\) data.

Keywords

Diffusion Tensor Image Spherical Harmonics Success Ratio Spherical Harmonics Coefficient Spurious Peak 
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.
    Alexander, D.: Maximum entropy spherical deconvolution for diffusion MRI. In: Christensen, G.E., Sonka, M. (eds.) Information Processing in Medical Imaging, pp. 27–57. Springer, Berlin/New York (2005)Google Scholar
  2. 2.
    Cheng, J., Ghosh, A., Jiang, T., Deriche, R.: A Riemannian framework for orientation distribution function computing. In: Medical Image Computing and Computer-Assisted Intervention – MICCAI, London, vol. 5761, pp. 911–918 (2009)Google Scholar
  3. 3.
    Cheng, J., Ghosh, A., Jiang, T., Deriche, R.: Diffeomorphism invariant Riemannian framework for ensemble average propagator computing. In: Medical Image Computing and Computer-Assisted Intervention – MICCAI, Toronto. LNCS, vol. 6892, pp. 98–106. Springer, Berlin/Heidelberg (2011)Google Scholar
  4. 4.
    Cheng, J., Jiang, T., Deriche, R.: Nonnegative definite EAP and ODF estimation via a unified multi-shell HARDI reconstruction. In: Medical Image Computing and Computer-Assisted Intervention – MICCAI, Nice. LNCS, vol. 6892, pp. 98–106. Springer, Berlin/Heidelberg (2012)Google Scholar
  5. 5.
    Cheng, J., Deriche, R., Jiang, T., Shen, D., Yap, P.T.: Non-local non-negative spherical deconvolution for single and multiple shell diffusion MRI. In: HARDI Reconstruction Challenge, International Symposium on Biomedical Imaging (ISBI), San Francisco (2013)Google Scholar
  6. 6.
    Dell’Acqua, F., Rizzo, G., Scifo, P., Clarke, R.A., Scotti, G., Fazio, F.: A model-based deconvolution approach to solve fiber crossing in diffusion-weighted MR imaging. IEEE Trans. Biomed. Eng. 54(3), 462–472 (2007)CrossRefGoogle Scholar
  7. 7.
    Descoteaux, M., Angelino, E., Fitzgibbons, S., Deriche, R.: Regularized, fast and robust analytical Q-ball imaging. Magn. Reson. Med. 58, 497–510 (2007)CrossRefGoogle Scholar
  8. 8.
    Descoteaux, M., Wiest-Daessle, N., Prima, S., Barillot, C., Deriche, R.: Impact of Rician adapted non-local means filtering on HARDI. In: Proceedings of the MICCAI, New York (2008)Google Scholar
  9. 9.
    Jian, B., Vemuri, B.C.: A unified computational framework for deconvolution to reconstruct multiple fibers from diffusion weighted MRI. IEEE Trans. Med. Imaging 26, 1464–1471 (2007)CrossRefGoogle Scholar
  10. 10.
    Johansen-Berg, H., Behrens, T.E.: Diffusion MRI: From Quantitative Measurement to In Vivo Neuroanatomy. Elsevier, Amsterdam (2009)Google Scholar
  11. 11.
    Landman, B., Bogovic, J., Wan, H., El Zahraa, E., Bazin, P., Prince, J.: Resolution of crossing fibers with constrained compressed sensing using diffusion tensor MRI. NeuroImage 59(3), 2175 (2012)CrossRefGoogle Scholar
  12. 12.
    Tournier, J.D., Calamante, F., Gadian, D., Connelly, A.: Direct estimation of the fiber orientation density function from diffusion-weighted MRI data using spherical deconvolution. NeuroImage 23, 1176–1185 (2004)CrossRefGoogle Scholar
  13. 13.
    Tournier, J., Calamante, F., Connelly, A.: Robust determination of the fibre orientation distribution in diffusion MRI: non-negativity constrained super-resolved spherical deconvolution. NeuroImage 35(4), 1459–1472 (2007)CrossRefGoogle Scholar
  14. 14.
    Tuch, D.S.: Q-ball imaging. Magn. Reson. Med. 52, 1358–1372 (2004)Google Scholar
  15. 15.
    Wedeen, V.J., Hagmann, P., Tseng, W.Y.I., Reese, T.G., Weisskoff, R.M.: Mapping complex tissue architecture with diffusion spectrum magnetic resonance imaging. Magn. Reson. Med. 54, 1377–1386 (2005)CrossRefGoogle Scholar
  16. 16.
    Weldeselassie, Y., Barmpoutis, A., Atkins, M.: Symmetric positive-definite Cartesian tensor orientation distribution functions (CT-ODF). In: Medical Image Computing and Computer-Assisted Intervention – MICCAI 2010, Beijing (2010)Google Scholar
  17. 17.
    Weldeselassie, Y.T., Barmpoutis, A., Stella Atkins, M.: Symmetric positive semi-definite Cartesian tensor fiber orientation distributions (CT-FOD). Med. Image Anal. 16, 1121–1129 (2012)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.University of North Carolina at Chapel HillChapel HillUSA
  2. 2.INRIA Sophia AntipolisValbonneFrance
  3. 3.Institute of AutomationChinese Academy of SciencesBeijingChina

Personalised recommendations