Abstract
To relate diffusion-weighted MRI-signal to the underlying tissue structure remains one of the major challenges in interpreting experimental data, in particular for reconstruction of the structural connectivity in the human brain. Various ideas to tackle this problem are around, either model-based or model-free. We proceed on a third way by proposing a method that automatically determines the basis components of diffusion-weighted MRI signal without any usage of prior knowledge. The resulted components can be well associated with white matter, gray matter and cerebrospinal fluid, respectively. The performance of our method is demonstrated on two DSI datasets and one multi-shell acquisition.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bilgic, B., Setsompop, K., Cohen-Adad, J., Yendiki, A., Wald, L.L., Adalsteinsson, E.: Accelerated diffusion spectrum imaging with compressed sensing using adaptive dictionaries. Magn. Reson. Med. 68(6), 1747–1754 (2012)
Callaghan, P.T.: Principles of nuclear magnetic resonance microscopy. Oxford University Press, New York (1991)
Fieremans, E., Jensen, J.H., Helpern, J.A.: White matter characterization with diffusional kurtosis imaging. Neuroimage 58(1), 177–188 (2011)
Frank, L.R.: Characterization of anisotropy in high angular resolution diffusion-weighted mri. Magn. Reson. Med. 47(6), 1083–1099 (2002). 22106772 0740-3194 Journal Article
Gramfort, A., Poupon, C., Descoteaux, M.: Sparse dsi: learning dsi structure for denoising and fast imaging. In: Medical Image Computing and Computer-Assisted Intervention – MICCAI 2012, Nice, pp. 288–296 (2012)
Jones, D.K. (ed.) Diffusion MRI: Theory, Methods and Applications. Oxford University Press, New York (2010)
Kiselev, V.G.: The cumulant expansion: an overarching mathematical framework for understanding diffusion NMR. In: Jones, D.K. (ed.) Diffusion MRI: Theory, Methods and Applications, Chapter 10. Oxford University Press, New York (2010)
Mairal, J., Bach, F, Ponce, J., Sapiro, G.: Online learning for matrix factorization and sparse coding. J. Mach. Learn. Res. 11, 19–60 (2010)
Merlet, S., Caruyer, E., Deriche, R.: Parametric dictionary learning for modeling eap and odf in diffusion MRI. In: Medical Image Computing and Computer-Assisted Intervention–MICCAI 2012, Nice, pp. 10–17 (2012)
Novikov, D.S., Fieremans, E., Jensen, J.H., Helpern, J.A.: Random walk with barriers. Nat. Phys. 7(6), 508–514 (2011)
Panagiotaki, E., Schneider, T., Siow, B., Hall, M.G., Lythgoe, M.F., Alexander, D.C.: Compartment models of the diffusion MR signal in brain white matter: a taxonomy and comparison. Neuroimage 59(3), 2241–2254 (2012)
Acknowledgements
We want to thank Alessandro Daducci from the Ecole Polytechnique Federale de Lausanne for kindly providing the QSI measurements. The work of Marco Reisert is supported by the DFG (Deutsche Forschungsgemeinschaft) grant RE 32-86/2-1.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Reisert, M., Skibbe, H., Kiselev, V.G. (2014). The Diffusion Dictionary in the Human Brain Is Short: Rotation Invariant Learning of Basis Functions. In: Schultz, T., Nedjati-Gilani, G., Venkataraman, A., O'Donnell, L., Panagiotaki, E. (eds) Computational Diffusion MRI and Brain Connectivity. Mathematics and Visualization. Springer, Cham. https://doi.org/10.1007/978-3-319-02475-2_5
Download citation
DOI: https://doi.org/10.1007/978-3-319-02475-2_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-02474-5
Online ISBN: 978-3-319-02475-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)