Rician Noise Removal by Non-Local Means Filtering for Low Signal-to-Noise Ratio MRI: Applications to DT-MRI

  • Nicolas Wiest-Daesslé
  • Sylvain Prima
  • Pierrick Coupé
  • Sean Patrick Morrissey
  • Christian Barillot
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5242)


Diffusion-Weighted MRI (DW-MRI) is subject to random noise yielding measures that are different from their real values, and thus biasing the subsequently estimated tensors. The Non-Local Means (NLMeans) filter has recently been proposed to denoise MRI with high signal-to-noise ratio (SNR). This filter has been shown to allow the best restoration of image intensities for the estimation of diffusion tensors (DT) compared to state-of-the-art methods. However, for DW-MR images with high b-values (and thus low SNR), the noise, which is strictly Rician-distributed, can no longer be approximated as additive white Gaussian, as implicitly assumed in the classical formulation of the NLMeans. High b-values are typically used in high angular resolution diffusion imaging (HARDI) or q-space imaging (QSI), for which an optimal restoration is critical. In this paper, we propose to adapt the NLMeans filter to Rician noise corrupted data. Validation is performed on synthetic data and on real data for both conventional MR images and DT images. Our adaptation outperforms the original NLMeans filter in terms of peak-signal-to-noise ratio (PSNR) for DW-MRI.


Fractional Anisotropy Noise Variance Rician Noise Optimal Restoration Rician Noise Removal 
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.
    Coupé, P., Yger, P., Prima, S., Hellier, P., Kervrann, C., Barillot, C.: An Optimized Blockwise Non Local Means Denoising Filter for 3D Magnetic Resonance Images. Transactions on Medical Imaging 27, 425–441 (2008)CrossRefGoogle Scholar
  2. 2.
    Wiest-Daesslé, N., Prima, S., Coupé, P., Morrissey, S.P., Barillot, C.: Non-local means variants for denoising of diffusion-weighted and diffusion tensor MRI. In: Ayache, N., Ourselin, S., Maeder, A. (eds.) MICCAI 2007, Part II. LNCS, vol. 4792, pp. 344–351. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  3. 3.
    Sijbers, J., den Dekker, A.J.: Maximum likelihood estimation of signal amplitude and noise variance from MR data. Magn. Reson. Med. 51, 586–594 (2004)CrossRefGoogle Scholar
  4. 4.
    Koay, C.G., Chang, L.C., Carew, J.D., Pierpaoli, C., Basser, P.J.: A unifying theoretical and algorithmic framework for least squares methods of estimation in diffusion tensor imaging. J. Magn. Reson. 182, 115–125 (2006)CrossRefGoogle Scholar
  5. 5.
    Chang, L.C., Jones, D.K., Pierpaoli, C.: RESTORE: robust estimation of tensors by outlier rejection. Magn. Reson. Med. 53, 1088–1095 (2005)CrossRefGoogle Scholar
  6. 6.
    Tschumperlé, D., Deriche, R.: Variational frameworks for DT-MRI estimation, regularization and visualization. In: ICCV 2003, pp. 116–121 (2003)Google Scholar
  7. 7.
    Coulon, O., Alexander, D.C., Arridge, S.: Diffusion tensor magnetic resonance image regularization. Med. Image Anal. 8, 47–67 (2004)CrossRefGoogle Scholar
  8. 8.
    Chefd’hotel, C., Tschumperlé, D., Deriche, R., Faugeras, O.: Regularizing flows for constrained matrix-valued images. Journal of Mathematical Imaging and Vision 20, 147–162 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Pennec, X., Fillard, P., Ayache, N.: A Riemannian framework for tensor computing. International Journal of Computer Vision 66, 41–66 (2006)CrossRefzbMATHGoogle Scholar
  10. 10.
    Castaño-Moraga, C., Lenglet, C., Deriche, R., Ruiz-Alzola, J.: A Riemannian approach to anisotropic filtering of tensor fields. Signal Processing 87, 263–276 (2007)CrossRefzbMATHGoogle Scholar
  11. 11.
    Fillard, P., Pennec, X., Arsigny, V., Ayache, N.: Clinical DT-MRI estimation, smoothing, and fiber tracking with log-Euclidean metrics. IEEE TMI 26, 1472–1482 (2007)Google Scholar
  12. 12.
    Landman, B., Bazin, P.L., Prince, J.: Diffusion Tensor Estimation by Maximizing Rician Likelihood. In: Lew, M., Sebe, N., Huang, T., Bakker, E. (eds.) ICCV 2007, Rio de Janeiro, Brazil, pp. 1–8 (2007)Google Scholar
  13. 13.
    Basu, S., Fletcher, P.T., Whitaker, R.T.: Rician Noise Removal in Diffusion Tensor MRI. In: Larsen, R., Nielsen, M., Sporring, J. (eds.) MICCAI 2006. LNCS, vol. 4190, pp. 117–125. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  14. 14.
    Buades, A., Coll, B., Morel, J.M.: A review of image denoising algorithms, with a new one. Multiscale Modeling & Simulation 4, 490–530 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Kervrann, C., Boulanger, J., Coupé, P. (eds.): Bayesian non-local means filter, image redundancy and adaptive dictionaries for noise removal, pp. 520–532. Springer, Heidelberg (2007)Google Scholar
  16. 16.
    Gasser, T., Sroka, L., Steinmetz, C.: Residual variance and residual pattern in non linear regression. Biometrika 73, 625–633 (1986)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Stejskal, E.O., Tanner, J.E.: Spin Diffusion Measurements: Spin Echoes in the Presence of a Time-Dependent Field Gradient. The Journal of Chemical Physics 42, 288–292 (1965)CrossRefGoogle Scholar
  18. 18.
    Arsigny, V., Fillard, P., Pennec, X., Ayache, N.: Fast and simple calculus on tensors in the Log-Euclidean framework. In: Duncan, J.S., Gerig, G. (eds.) MICCAI 2005. LNCS, vol. 3749, pp. 115–122. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  19. 19.
    Manjón, J.V., Carbonell-Caballero, J., Lull, J.J., García-Martí, G., Martí-Bonmatí, L., Robles, M.: MRI denoising using Non-Local Means. Medical Image Analysis (in Press, Corrected Proof 2008)Google Scholar
  20. 20.
    Keiko, T., Satomi, K., Masahiro, I., Sadao, S., Yutaka, A., Kunihiko, F.: Usefulness of high-b-value diffusion-weighted imaging in acute cerebral infarction. European Radiology 17, 1212–1220 (2007)CrossRefGoogle Scholar
  21. 21.
    Yoshiura, T., Mihara, F., Tanaka, A., Ogomori, K., Ohyagi, Y., Taniwaki, T., Yamada, T., Yamasaki, T., Ichimiya, A., Kinukawa, N., Kuwabara, Y., Honda, H.: High b value diffusion-weighted imaging is more sensitive to white matter degeneration in Alzheimer’s disease. NeuroImage 20, 413–419 (2003)CrossRefGoogle Scholar
  22. 22.
    Descoteaux, M., Wiest-Daesslé, N., Prima, S., Barillot, C., Deriche, R.: Impact of Rician Adapted Non-Local Means Filtering on HARDI. In: Metaxas, D., et al. (eds.) MICCAI 2008, Part II. LNCS, vol. 5242, pp. 122–130. Springer, Heidelberg (2008)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Nicolas Wiest-Daesslé
    • 1
    • 2
    • 3
  • Sylvain Prima
    • 1
    • 2
    • 3
  • Pierrick Coupé
    • 1
    • 2
    • 3
  • Sean Patrick Morrissey
    • 1
    • 2
    • 3
    • 4
  • Christian Barillot
    • 1
    • 2
    • 3
  1. 1.INRIA, VisAGeS Project-TeamRennesFrance
  2. 2.INSERM, U746RennesFrance
  3. 3.University of Rennes I, CNRS, UMR 6074, IRISARennesFrance
  4. 4.CHUUniversity Hospital of RennesRennesFrance

Personalised recommendations