Probabilistic ODF Estimation from Reduced HARDI Data with Sparse Regularization

  • Antonio Tristán-Vega
  • Carl-Fredrik Westin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6892)


High Angular Resolution Diffusion Imaging (HARDI) demands a higher amount of data measurements compared to Diffusion Tensor Imaging (DTI), restricting its use in practice. We propose to represent the probabilistic Orientation Distribution Function (ODF) in the frame of Spherical Wavelets (SW), where it is highly sparse. From a reduced subset of measurements (nearly four times less than the standard for HARDI), we pose the estimation as an inverse problem with sparsity regularization. This allows the fast computation of a positive, unit-mass, probabilistic ODF from 14-16 samples, as we show with both synthetic diffusion signals and real HARDI data with typical parameters.


Diffusion Tensor Image Spherical Harmonics Sparse Representation Compressed Sensing Orientation Distribution Function 
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.


  1. 1.
    Callaghan, P.T.: Principles of Nuclear Magnetic Resonance Microscopy. Clarendon Press, Oxford (1991)Google Scholar
  2. 2.
    Wedeen, V.J., Hagmann, P., Tseng, W.-Y.I., Reese, T.G., Weisskoff, R.M.: Mapping complex tissue architecture with DSI. Mag. Res. Med. 54, 1377–1386 (2005)CrossRefGoogle Scholar
  3. 3.
    Merlet, S., Deriche, R.: Compressed sensing for accelerated EAP recovery in diffusion MRI. In: MICCAI Workshop Comp. Diffusion MRI, Beijing (China) (September 2010)Google Scholar
  4. 4.
    Donoho, D.L.: Compressed sensing. IEEE Trans. Info. Th. 52(4), 1289–1306 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Tuch, D.S.: Q–Ball imaging. Mag. Res. Med. 52, 1358–1372 (2004)CrossRefGoogle Scholar
  6. 6.
    Assemlal, H.-E., Tschumperlé, D., Brun, L., Siddiqui, K.: Recent advances in diffusion MRI modeling: Angular and radial reconstruction. Med. Im. Anal. (2011), doi:10.1016/ Scholar
  7. 7.
    Tristán-Vega, A., Westin, C.-F., Aja-Fernández, S.: A new methodology for the estimation of fiber populations in the white matter of the brain with the Funk-Radon transform. NeuroIm. 49, 1301–1315 (2010)CrossRefGoogle Scholar
  8. 8.
    Michailovich, O., Rathi, Y.: Fast and accurate reconstruction of HARDI data using compressed sensing. In: Jiang, T., Navab, N., Pluim, J.P.W., Viergever, M.A. (eds.) MICCAI 2010. LNCS, vol. 6361, pp. 607–614. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  9. 9.
    Jian, B., Vemuri, B.C.: Multi-fiber reconstruction from diffusion MRI using mixture of wisharts and sparse deconvolution. In: Karssemeijer, N., Lelieveldt, B. (eds.) IPMI 2007. LNCS, vol. 4584, pp. 384–395. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  10. 10.
    Freeden, W., Schreiner, M.: Orthogonal and non-orthogonal multirresolution analysis, scale discrete and exact fully discrete wavelet transform on the sphere. Const. Approx. 14, 493–515 (1998)CrossRefzbMATHGoogle Scholar
  11. 11.
    Lawson, C.L., Hanson, R.J.: Solving Least Squares Problems. Prentice-Hall, Englewood Cliffs (1974)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Antonio Tristán-Vega
    • 1
  • Carl-Fredrik Westin
    • 1
  1. 1.Laboratory of Mathematics in ImagingBrigham and Women’s HospitalBostonUSA

Personalised recommendations