XQ-NLM: Denoising Diffusion MRI Data via x-q Space Non-local Patch Matching

  • Geng Chen
  • Yafeng Wu
  • Dinggang Shen
  • Pew-Thian YapEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9902)


Noise is a major issue influencing quantitative analysis in diffusion MRI. The effects of noise can be reduced by repeated acquisitions, but this leads to long acquisition times that can be unrealistic in clinical settings. For this reason, post-acquisition denoising methods have been widely used to improve SNR. Among existing methods, non-local means (NLM) has been shown to produce good image quality with edge preservation. However, currently the application of NLM to diffusion MRI has been mostly focused on the spatial space (i.e., the x-space), despite the fact that diffusion data live in a combined space consisting of the x-space and the q-space (i.e., the space of wavevectors). In this paper, we propose to extend NLM to both x-space and q-space. We show how patch-matching, as required in NLM, can be performed concurrently in x-q space with the help of azimuthal equidistant projection and rotation invariant features. Extensive experiments on both synthetic and real data confirm that the proposed x-q space NLM (XQ-NLM) outperforms the classic NLM.


  1. 1.
    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
  2. 2.
    Descoteaux, M., Wiest-Daesslé, N., Prima, S., Barillot, C., Deriche, R.: Impact of rician adapted non-local means filtering on HARDI. In: Metaxas, D., Axel, L., Fichtinger, G., Székely, G. (eds.) MICCAI 2008, Part II. LNCS, vol. 5242, pp. 122–130. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  3. 3.
    Chen, G., Zhang, P., Wu, Y., Shen, D., Yap, P.T.: Denoising magnetic resonance images using collaborative non-local means. Neurocomputing 177, 215–227 (2016)CrossRefGoogle Scholar
  4. 4.
    Buades, A., Coll, B., Morel, J.M.: A review of image denoising algorithms, with a new one. Multiscale Model. Simul. 4(2), 490–530 (2005)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Wessel, P., Smith, W.H.: The generic mapping tools.
  6. 6.
    Yap, P.T., Jiang, X., Kot, A.C.: Two-dimensional polar harmonic transforms for invariant image representation. IEEE Trans. Pattern Anal. Mach. Intell. 32(7), 1259–1270 (2010)CrossRefGoogle Scholar
  7. 7.
    Coupé, P., Yger, P., Prima, S., Hellier, P., Kervrann, C., Barillot, C.: An optimized blockwise nonlocal means denoising filter for 3-D magnetic resonance images. IEEE Trans. Med. Imaging 27(4), 425–441 (2008)CrossRefGoogle Scholar
  8. 8.
    Manjón, J.V., Carbonell-Caballero, J., Lull, J.J., García-Martí, G., Martí-Bonmatí, L., Robles, M.: MRI denoising using non-local means. Med. Image Anal. 12(4), 514–523 (2008)CrossRefGoogle Scholar
  9. 9.
    Koay, C.G., Özarslan, E., Basser, P.J.: A signal transformational framework for breaking the noise floor and its applications in MRI. J. Magn. Reson. 197(2), 108–119 (2009)CrossRefGoogle Scholar

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Authors and Affiliations

  • Geng Chen
    • 1
    • 2
  • Yafeng Wu
    • 1
  • Dinggang Shen
    • 2
  • Pew-Thian Yap
    • 2
    Email author
  1. 1.Data Processing CenterNorthwestern Polytechnical UniversityXi’anChina
  2. 2.Department of Radiology and BRICUniversity of North CarolinaChapel HillUSA

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