Magnetic Resonance Imaging
Volume 28, Issue 2 , Pages 200-211 , February 2010

Efficient anisotropic filtering of diffusion tensor images

  • Qing Xu

      Affiliations

    • Vanderbilt University Institute of Imaging Science, Vanderbilt University, Nashville, TN 37232, USA
    • Department of Electrical Engineering and Computer Science, Vanderbilt University, Nashville, TN 37232, USA
  • ,
  • Adam W. Anderson

      Affiliations

    • Vanderbilt University Institute of Imaging Science, Vanderbilt University, Nashville, TN 37232, USA
    • Department of Biomedical Engineering, Vanderbilt University, Nashville, TN 37232, USA
  • ,
  • John C. Gore

      Affiliations

    • Vanderbilt University Institute of Imaging Science, Vanderbilt University, Nashville, TN 37232, USA
    • Department of Biomedical Engineering, Vanderbilt University, Nashville, TN 37232, USA
  • ,
  • Zhaohua Ding

      Affiliations

    • Vanderbilt University Institute of Imaging Science, Vanderbilt University, Nashville, TN 37232, USA
    • Department of Electrical Engineering and Computer Science, Vanderbilt University, Nashville, TN 37232, USA
    • Department of Biomedical Engineering, Vanderbilt University, Nashville, TN 37232, USA
    • Corresponding Author InformationCorresponding author. Vanderbilt University Institute of Imaging Science, Nashville, TN 37232-2310, USA. Tel.: +1 615 322 7889; fax: +1 615 322 0734.

Received 5 August 2009 ,Accepted 12 October 2009.

References 

  1. Basser PJ, Mattiello J, Le Bihan D. MR diffusion tensor spectroscopy and imaging. Biophys J. 1994;66(1):259–267
  2. Le Bihan D, Mangin JF, Poupon C, Clark CA, Pappata S, Molko N, et al. Diffusion tensor imaging: concepts and applications. J Magn Reson Imaging. 2001;13:534–546
  3. Le Bihan D. Looking into the functional architecture of the brain with diffusion MRI. Nat Rev Neurosci. 2003;4(6):469–480
  4. Basser PJ, Pajevic S. Statistical artifacts in diffusion tensor MRI (DT-MRI) caused by background noise. Magn Reson Med. 2000;44:41–50
  5. Anderson AW. Theoretical analysis of the effects of noise on diffusion tensor imaging. Magn Reson Med. 2001;46:1174–1188
  6. Lazar M, Alexander AL. White matter tractography algorithms error analysis. NeuroImage. 2003;20:1140–1153
  7. Parker GJ, Schnabel JA, Symms MR, Werring DJ, Barker GJ. Nonlinear smoothing for reduction of systematic and random errors in diffusion tensor imaging. J Magn Reson Imaging. 2000;11:702–710
  8. Chen B, Hsu E. Noise removal in magnetic resonance diffusion tensor imaging. Magn Reson Med. 2005;54:393–407
  9. Pajevic S, Aldroubi A, Basser PJA. continuous tensor field approximation of discrete DT-MRI data for extracting microstructural and architectural features of tissue. J Magn Reson. 2002;154:85–100
  10. Poupon C, Clark CA, Frouin V, Regis J, Bloch I, LeBihan D, et al. Regularization of diffusion-based direction maps for the tracking of brain white matter fascicles. Neuroimage. 2000;12:184–195
  11. Tench CR, Morgan PS, Blumhardt LD, Constantinescu C. Improved white matter fiber tracking using stochastic labeling. Magn Reson Med. 2002;48:677–683
  12. Coulon O, Alexander DC, Arridge SA. A regularization scheme for diffusion tensor magnetic resonance images. In: Proceedings of 17th IPMI. 2001;p. 92–105
  13. Wang Z, Vemuri BC, Chen Y, Mareci TH. A constrained variational principle for direct estimation and smoothing of the diffusion tensor field from complex DWI. IEEE TMI. 2004;23(8):930–939
  14. Tschumperle D, Deriche R. Constrained and unconstrained PDEs for vector image restoration. In: Proceedings of 12th Scandinavian Conference on Image Analysis. 2001;p. 153–160
  15. Arsigny V, Fillard P, Pennec X, Ayache N. Log-Euclidean metrics for fast and simple calculus on diffusion tensors. Magn Reson Med. 2006;56:411–421
  16. Pennec X, Fillard P, Ayache NA. riemannian framework for tensor computing. Int J Comput Vision. 2006;66(1):41–66
  17. Zhang F, Hancock ER. Riemannian graph diffusion for DT-MRI regularization. MICCAI. 2006;234–242
  18. Basu S, Fletcher PT, Whitaker R. Rician noise removal in diffusion tensor MRI. MICCAI. 2006;117–125
  19. Ding Z, Anderson AW, Gore JC. Reduction of noise in diffusion tensor images using anisotropic smoothing. Magn Reson Med. 2005;49:485–490
  20. Strikwerda JC. Finite difference schemes and partial differential equations. 2nd ed. Philadelphia: SIAM; 2004;
  21. Weickert J, Ter Haar Romeny BM, Viergever MA. Efficient and reliable schemes for nonlinear diffusion filtering. IEEE TIP. 1998;7:398–410
  22. Barash D, Kimmel R. An accurate operator splitting scheme for nonlinear diffusion Filtering. LNCS. 2000;2106:281–289
  23. Craig IJD, Sneyd AD. An alternating direction implicit scheme for parabolic systems of partial differential equations. Comput Math Appl. 1990;20:53–62
  24. Gerig G, Kubler O, Kikinis R, Jolesz FA. Nonlinear anisotropic filtering of MRI data. IEEE TMI. 1992;11(2):221–231
  25. Mrazek P, Navara M. Selection of optimal stopping time for nonlinear diffusion filtering. IJCV. 2003;52(2-3):189–203
  26. Hasan KM, Basser PJ, Parker DL, Alexander AL. Analytical computation of the eigenvalues and eigenvectors in DT-MRI. J Magn Reson. 2001;152(1):41–47

PII: S0730-725X(09)00279-3

doi: 10.1016/j.mri.2009.10.001

Magnetic Resonance Imaging
Volume 28, Issue 2 , Pages 200-211 , February 2010