A Novel Spatial-Angular Domain Regularisation Approach for Restoration of Diffusion MRI

  • Alessandro MellaEmail author
  • Alessandro Daducci
  • Giandomenico Orlandi
  • Jean-Philippe Thiran
  • Maria Deprez
  • Merixtell Bach Cuadra
Conference paper
Part of the Mathematics and Visualization book series (MATHVISUAL)


In this paper we tackle the problem of regularisation for inverse problems in single shell diffusion weighted image restoration. Our aim is to recover a high-resolution and denoised DWI signal, prior to any model fitting. The main contribution of our method is the combination of two regularization terms, one using the information arising from the spatial domain, hence analysing the single image, while the other uses information coming from the angular domain, thus using the relationships between the values along different directions within a single voxel. We show that our novel regularization method outperforms widely used and recent DWI denoising algorithms. Additionally we demonstrate that the proposed regularisation technique can be successfully applied to the super-resolution reconstruction of high-resolution volume from thick-slice data. Both scenarios are tested on simulated phantom and real DWI data.



This work was supported by the CIBM of the Unil, the Swiss Federal Institute of Technology Lausanne, the University of Geneva, the CHUV, the Hôpitaux Universitaires de Genève, the Leenaards and Jeantet Foundations. This work was also supported by the Swiss National Science Foundation grant SNSF-IZK0Z2_170894.


  1. 1.
    Aura Rasclosa, A.: Sparse inverse problems for Fourier imaging applications to Optical Interferometry and Diffusion Magnetic Resonance Imaging. Ph.D. thesis, Lausanne (2017)Google Scholar
  2. 2.
    Chambolle, A., Pock, T.: A first-order primal-dual algorithm for convex problems with applications to imaging. J. Math. Imag. Vis. 40(1), 120–145 (2011)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Chen, Y., Dai, Y.H., Han, D.: Fiber orientation distribution estimation using a Peaceman-Rachford splitting method. SIAM J. Imag. Sci. 9(2), 573–604 (2016)MathSciNetCrossRefGoogle Scholar
  4. 4.
    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. Imag. 27(4), 425–441 (2008)CrossRefGoogle Scholar
  5. 5.
    Coupé, P., Manjón, J.V., Chamberland, M., Descoteaux, M., Hiba, B.: Collaborative patch-based super-resolution for diffusion-weighted images. NeuroImage 83, 245–261 (2013)CrossRefGoogle Scholar
  6. 6.
    Descoteaux, M., Angelino, E., Fitzgibbons, S., Deriche, R.: Regularized, fast, and robust analytical q-ball imaging. Mag. Res. Med. 58(3), 497–510 (2007)CrossRefGoogle Scholar
  7. 7.
    Diffusion Imaging in PYthon (DIPY).
  8. 8.
    HARDI Reconstruction Challenge, ISBI 2013.
  9. 9.
    Jiang, S., Xue, H., Glover, A., Rutherford, M., Rueckert, D., Hajnal, J.V.: MRI of moving subjects using multislice snapshot images with volume reconstruction (SVR): application to fetal, neonatal, and adult brain studies. IEEE Trans. Med. Imag. 26(7), 967–980 (2007)CrossRefGoogle Scholar
  10. 10.
    Kuklisova-Murgasova, M., Quaghebeur, G., Rutherford, M.A., Hajnal, J.V., Schnabel, J.A.: Reconstruction of fetal brain MRI with intensity matching and complete outlier removal. Med. Image Anal. 16(8), 1550–1564 (2012)CrossRefGoogle Scholar
  11. 11.
    Liu, R.W., Shi, L., Huang, W., Xu, J., Yu, S.C.H., Wang, D.: Generalized total variation-based MRI Rician denoising model with spatially adaptive regularization parameters. Magn. Reson. Imag. 32(6), 702–720 (2014)CrossRefGoogle Scholar
  12. 12.
  13. 13.
    Ouyang, Y., Chen, Y., Wu, Y., Zhou, H.: Total variation and wavelet regularization of orientation distribution functions in diffusion MRI. Inv. Prob. Imag. 7, 565–583 (2013)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Scherrer, B., Gholipour, A., Warfield, S.: Super-resolution in diffusion-weighted imaging. In: MICCAI 2011, pp. 124–132 (2011)Google Scholar
  15. 15.
    Scherrer, B., Gholipour, A., Warfield, S.K.: Super-resolution reconstruction to increase the spatial resolution of diffusion weighted images from orthogonal anisotropic acquisitions. Med. Image Anal. 16(7), 1465–1476 (2012)CrossRefGoogle Scholar
  16. 16.
    Tobisch, A., Neher, P.F., Rowe, M.C., Maier-Hein, K.H., Zhang, H.: Model-based super-resolution of diffusion MRI. In: Computational Diffusion MRI and Brain Connectivity, pp. 25–34. Springer, Cham (2014)Google Scholar
  17. 17.
    Tournier, J.D., Calamante, F., Gadian, D.G., Connelly, A.: Direct estimation of the fiber orientation density function from diffusion-weighted MRI data using spherical deconvolution. NeuroImage 23(3), 1176–1185 (2004)CrossRefGoogle Scholar
  18. 18.
    Tourbier, S., Bresson, X., Hagmann, P., Thiran, J.P., Meuli, R., Cuadra, M.B.: An efficient total variation algorithm for super-resolution in fetal brain MRI with adaptive regularization. NeuroImage 118, 584–597 (2015)CrossRefGoogle Scholar
  19. 19.
    Van Essen, D.C., Smith, S.M., Barch, D.M., Behrens, T.E., Yacoub, E., Ugurbil, K., Consortium, W.M.H., et al.: The WU-Minn human connectome project: an overview. Neuroimage 80, 62–79 (2013)CrossRefGoogle Scholar
  20. 20.
    Veraart, J., Fieremans, E., Novikov, D.S.: Diffusion MRI noise mapping using random matrix theory. Magn. Reson. Med. (2016)Google Scholar
  21. 21.
    Veraart, J., Novikov, D.S., Christiaens, D., Ades-Aron, B., Sijbers, J., Fieremans, E.: Denoising of diffusion MRI using random matrix theory. NeuroImage 142, 394–406 (2016)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Alessandro Mella
    • 1
    Email author
  • Alessandro Daducci
    • 2
  • Giandomenico Orlandi
    • 2
  • Jean-Philippe Thiran
    • 3
    • 4
  • Maria Deprez
    • 5
  • Merixtell Bach Cuadra
    • 3
    • 4
  1. 1.University of Bologna, MathematicsBolognaItaly
  2. 2.Computer Science DepartmentUniversity of VeronaVeronaItaly
  3. 3.Radiology DepartmentLausanne University Hospital; Center for Biomedical Imaging (CIBM), Lausanne UniversityLausanneSwitzerland
  4. 4.EPFL, Signal Processing Laboratory 5 (LTS5)LausanneSwitzerland
  5. 5.Department of Biomedical EngineeringKing’s College LondonLondonUK

Personalised recommendations