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Neighborhood Matching for Curved Domains with Application to Denoising in Diffusion MRI

  • Geng Chen
  • Bin Dong
  • Yong Zhang
  • Dinggang Shen
  • Pew-Thian YapEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10433)

Abstract

In this paper, we introduce a strategy for performing neighborhood matching on general non-Euclidean and non-flat domains. Essentially, this involves representing the domain as a graph and then extending the concept of convolution from regular grids to graphs. Acknowledging the fact that convolutions are features of local neighborhoods, neighborhood matching is carried out using the outcome of multiple convolutions at multiple scales. All these concepts are encapsulated in a sound mathematical framework, called graph framelet transforms (GFTs), which allows signals residing on non-flat domains to be decomposed according to multiple frequency subbands for rich characterization of signal patterns. We apply GFTs to the problem of denoising of diffusion MRI data, which can reside on domains defined in very different ways, such as on a shell, on multiple shells, or on a Cartesian grid. Our non-local formulation of the problem allows information of diffusion signal profiles of drastically different orientations to be borrowed for effective denoising.

References

  1. 1.
    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
  2. 2.
    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. on Med. Imaging 27(4), 425–441 (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.
    Dong, B., Shen, Z.: MRA-based wavelet frames and applications. In: IAS Lecture Notes Series, Summer Program on The Mathematics of Image Processing, Park City Mathematics Institute (2010)Google Scholar
  5. 5.
    Dong, B.: Sparse representation on graphs by tight wavelet frames and applications. Appl. Comput. Harmonic Anal. 42(3), 452–479 (2017)MathSciNetCrossRefGoogle Scholar
  6. 6.
    St-Jean, S., Coupé, P., Descoteaux, M.: Non local spatial and angular matching: enabling higher spatial resolution diffusion MRI datasets through adaptive denoising. Med. Image Anal. 32, 115–130 (2016)CrossRefGoogle Scholar
  7. 7.
    Chen, G., Wu, Y., Shen, D., Yap, P.-T.: XQ-NLM: denoising diffusion mri data via x-q space non-local patch matching. In: Ourselin, S., Joskowicz, L., Sabuncu, M.R., Unal, G., Wells, W. (eds.) MICCAI 2016. LNCS, vol. 9902, pp. 587–595. Springer, Cham (2016). doi: 10.1007/978-3-319-46726-9_68CrossRefGoogle Scholar
  8. 8.
    Henaff, M., Bruna, J., LeCun, Y.: Deep convolutional networks on graph-structured data. arXiv preprint (2015). arXiv:1506.05163
  9. 9.
    Yap, P.-T., Dong, B., Zhang, Y., Shen, D.: Tight graph framelets for sparse diffusion MRI q-space representation. In: Ourselin, S., Joskowicz, L., Sabuncu, M.R., Unal, G., Wells, W. (eds.) MICCAI 2016. LNCS, vol. 9902, pp. 561–569. Springer, Cham (2016). doi: 10.1007/978-3-319-46726-9_65CrossRefGoogle Scholar
  10. 10.
    Caruyer, E., Daducci, A., Descoteaux, M., Houde, J.C., Thiran, J.P., Verma, R.: Phantomas: a flexible software library to simulate diffusion MR phantoms. In: ISMRM (2014)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Geng Chen
    • 1
  • Bin Dong
    • 2
  • Yong Zhang
    • 3
  • Dinggang Shen
    • 1
  • Pew-Thian Yap
    • 1
    Email author
  1. 1.Department of Radiology and BRICUniversity of North CarolinaChapel HillUSA
  2. 2.Beijing International Center for Mathematical ResearchPeking UniversityBeijingChina
  3. 3.Colin Artificial Intelligence LabRichmondCanada

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