Abstract
Sparse prior information is introduced to improve the accuracy of (FOD) estimation. Spatial continuity is another important aspect of prior information, but it is difficult to directly consider in sparse FODs estimation. First, we proposed a model based on adaptive group-patch and \(l_1\)-norm regularization. Second, in order to solve the FOD estimation problem of complex spherical deconvolution optimization using alternating directions method of multipliers (ADMM), a deep ADMM network is proposed to learn the optimal model parameters from training data. In order to obtain the qualitative and quantitative evaluation of the proposed method and the state-of-the-art constrained spherical deconvolution (CSD): first, ISBI 2013 phantom with known ground truth will be used to evaluate the local accuracy of the fiber configuration. Second, the global impact of FOD accuracy on real brain datasets was assessed using standard tractography and automatic white matter analysis algorithms. Compared with the comparison method, the proposed method has good consistency in sparse fiber reconstruction and fiber continuity.
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
Similar content being viewed by others
References
Tournier, J.D., Calamante, F., Connelly, A.: Robust determination of the fibre orientation distribution in diffusion MRI: non-negativity constrained super-resolved spherical deconvolution. Neuroimage 35(4), 1459–1472 (2007). https://doi.org/10.1016/j.neuroimage.2007.02.016
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). https://doi.org/10.1016/j.neuroimage.2004.07.037
Jeurissen, B., Tournier, J.D., Dhollander, T., Connelly, A., Sijbers, J.: Multi-tissue constrained spherical deconvolution for improved analysis of multi-shell diffusion MRI data. NeuroImage 103, 411–426 (2014). https://doi.org/10.1016/j.neuroimage.2014.07.061
Landman, B.A., Bogovic, J.A., Wan, H., ElShahaby, F.E.Z., Bazin, P.L., Prince, J.L.: Resolution of crossing fibers with constrained compressed sensing using diffusion tensor MRI. NeuroImage 59(3), 2175–2186 (2012). https://doi.org/10.1016/j.neuroimage.2011.10.011
Daducci, A., Canales-Rodrı, E.J., Descoteaux, M., Garyfallidis, E., Gur, Y., Lin, Y.C., Mani, M., Merlet, S., Paquette, M., Ramirez-Manzanares, A., Reisert, M.: Quantitative comparison of reconstruction methods for intra-voxel fiber recovery from diffusion MRI. IEEE Trans. Med. Imaging 33(2), 384–399 (2013). https://doi.org/10.1109/TMI.2013.2285500
Daducci, A., Van De Ville, D., Thiran, J.P., Wiaux, Y.: Sparse regularization for fiber ODF reconstruction: From the suboptimality of \(\ell 2\) and \(\ell 1\) priors to \(\ell 0\). Med. Image Anal. 18(6), 820–833 (2014). https://doi.org/10.1016/j.media.2014.01.011
Auría, A., Daducci, A., Thiran, J.P., Wiaux, Y.: Structured sparsity for spatially coherent fibre orientation estimation in diffusion MRI. NeuroImage 115, 245–255 (2015). https://doi.org/10.1016/j.neuroimage.2015.04.049
Rathi, Y., Michailovich, O., Laun, F., Setsompop, K., Grant, P.E., Westin, C.F.: Multi-shell diffusion signal recovery from sparse measurements. Med. Image Anal. 18(7), 1143–1156 (2014). https://doi.org/10.1016/j.media.2014.06.003
Lin, Z., Gong, T., Wang, K., Li, Z., He, H., Tong, Q., Yu, F., Zhong, J.: Fast learning of fiber orientation distribution function for MR tractography using convolutional neural network. Med. Phys. (2019). https://doi.org/10.1002/mp.13555
Garyfallidis, E., Brett, M., Amirbekian, B., Rokem, A., Van Der Walt, S., Descoteaux, M., Nimmo-Smith, I.: Dipy, a library for the analysis of diffusion MRI data. Frontiers Neuroinform. 8, 8 (2014). https://doi.org/10.3389/fninf.2014.00008
Zhang, F., Wu, Y., Norton, I., Rigolo, L., Rathi, Y., Makris, N., O’Donnell, L.J.: An anatomically curated fiber clustering white matter atlas for consistent white matter tract parcellation across the lifespan. NeuroImage 179, 429–447 (2018). https://doi.org/10.1016/j.neuroimage.2018.06.027
Wu, Y., Feng, Y., Li, F., Westin, C.F.: Global consistency spatial model for fiber orientation distribution estimation. In: 2015 IEEE 12th International Symposium on Biomedical Imaging (ISBI), pp. 1180–1183. IEEE (2015). https://doi.org/10.1109/ISBI.2015.7164083
Elden, L.: Algorithms for the regularization of ill-conditioned least squares problems. BIT Numer. Math. 17(2), 134–145 (1977). https://doi.org/10.1007/BF01932285
Canales-Rodríguez, E.J., Legarreta, J.H., Pizzolato, M., Rensonnet, G., Girard, G., Rafael-Patino, J., Barakovic, M., Romascano, D., Aleman-Gomez, Y., Radua, J., Pomarol-Clotet, E.: Sparse wars: A survey and comparative study of spherical deconvolution algorithms for diffusion MRI. NeuroImage 184, 140–160 (2019). https://doi.org/10.1016/j.neuroimage.2018.08.071
Kottath, R., Narkhede, P., Kumar, V., Karar, V., Poddar, S.: Multiple model adaptive complementary filter for attitude estimation. Aerosp. Sci. Technol. 69, 574–581 (2017). https://doi.org/10.1016/j.ast.2017.07.011
Acknowledgments
The research is supported by National Natural Science Foundation of China [grant number 61703369, 61976190]. Natural Sciene Foundation of Zhejiang Profince [grant number LQ16F030009, LY13F030007]. Major Science and Technology Projects of Wenzhou [grant number ZS2017007].
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Akbar, R. et al. (2020). Spatial Sparse Estimation of Fiber Orientation Distribution Using Deep Alternating Directions Method of Multipliers Network. In: Bonet-Carne, E., Hutter, J., Palombo, M., Pizzolato, M., Sepehrband, F., Zhang, F. (eds) Computational Diffusion MRI. Mathematics and Visualization. Springer, Cham. https://doi.org/10.1007/978-3-030-52893-5_7
Download citation
DOI: https://doi.org/10.1007/978-3-030-52893-5_7
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-52892-8
Online ISBN: 978-3-030-52893-5
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)