Abstract
Magnetoencephalography (MEG) and electroencephalography (EEG) are non-invasive modalities that measure the weak electromagnetic fields generated by neural activity. Inferring the location of the current sources that generated these magnetic fields is an ill-posed inverse problem known as source imaging. When considering a group study, a baseline approach consists in carrying out the estimation of these sources independently for each subject. The ill-posedness of each problem is typically addressed using sparsity promoting regularizations. A straightforward way to define a common pattern for these sources is then to average them. A more advanced alternative relies on a joint localization of sources for all subjects taken together, by enforcing some similarity across all estimated sources. An important advantage of this approach is that it consists in a single estimation in which all measurements are pooled together, making the inverse problem better posed. Such a joint estimation poses however a few challenges, notably the selection of a valid regularizer that can quantify such spatial similarities. We propose in this work a new procedure that can do so while taking into account the geometrical structure of the cortex. We call this procedure Minimum Wasserstein Estimates (MWE). The benefits of this model are twofold. First, joint inference allows to pool together the data of different brain geometries, accumulating more spatial information. Second, MWE are defined through Optimal Transport (OT) metrics which provide a tool to model spatial proximity between cortical sources of different subjects, hence not enforcing identical source location in the group. These benefits allow MWE to be more accurate than standard MEG source localization techniques. To support these claims, we perform source localization on realistic MEG simulations based on forward operators derived from MRI scans. On a visual task dataset, we demonstrate how MWE infer neural patterns similar to functional Magnetic Resonance Imaging (fMRI) maps.
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Ahlfors, S.P., Ilmoniemi, R.J., Hämäläinen, M.S.: Estimates of visually evoked cortical currents. Electroencephalogr. Clin. Neurophysiol. 82(3), 225–236 (1992/2018)
Argyriou, A., Evgeniou, T., Pontil, M.: Multi-task feature learning. In: NIPS (2007)
Benamou, J., Carlier, G., Cuturi, M., Nenna, L., Peyré, G.: Iterative Bregman Projections For Regularized Transportation Problems. Society for Industrial and Applied Mathematics (2015)
Chizat, L., Peyré, G., Schmitzer, B., Vialard, F.X.: Scaling Algorithms for Unbalanced Transport Problems. arXiv:1607.05816 [math.OC] (2017)
Cuturi, M.: Sinkhorn distances: lightspeed computation of optimal transport. In: NIPS (2013)
Dale, A.M., et al.: Dynamic statistical parametric mapping. Neuron 26(1), 55–67 (2000)
Fercoq, O., Richtárik, P.: Accelerated, parallel and proximal coordinate descent. SIAM J. Optim. 25, 1997–2023 (2015)
Fischl, B., Sereno, M.I., Dale, A.M.: Cortical surface-based analysis: II: inflation, flattening, and a surface-based coordinate system. NeuroImage 9, 195–207 (1999). Mathematics in Brain Imaging
Gramfort, A., et al.: MNE software for processing MEG and EEG data. NeuroImage 86, 446–460 (2013)
Gramfort, A., Strohmeier, D., Haueisen, J., Hämäläinen, M., Kowalski, M.: Time-frequency mixed-norm estimates: sparse M/EEG imaging with non-stationary source activations. NeuroImage 70, 410–422 (2013)
Hämäläinen, M.S., Ilmoniemi, R.J.: Interpreting magnetic fields of the brain: minimum norm estimates. Med. Biol. Eng. Comput. 32(1), 35–42 (1994)
Hämäläinen, M.S., Sarvas, J.: Feasibility of the homogeneous head model in the interpretation of neuromagnetic fields. Phys. Med. Biol. 32(1), 91 (1987)
Henson, R.N., Wakeman, D.G., Litvak, V., Friston, K.J.: A parametric empirical Bayesian framework for the EEG/MEG inverse problem: generative models for multi-subject and multi-modal integration. Front. Hum. Neurosci. 5, 76 (2011)
Jalali, A., Ravikumar, P., Sanghavi, S., Ruan, C.: A dirty model for multi-task learning. In: NIPS (2010)
Janati, H., Cuturi, M., Gramfort, A.: Wasserstein regularization for sparse multi-task regression (2018)
Kantorovic, L.: On the translocation of masses. C.R. Acad. Sci. URSS (1942)
Kanwisher, N., McDermott, J., Chun, M.M.: The fusiform face area: a module in human extrastriate cortex specialized for face perception. J. Neurosci. 17(11), 4302–4311 (1997)
Knopp, P., Sinkhorn, R.: Concerning nonnegative matrices and doubly stochastic matrices. Pac. J. Math. 1(2), 343–348 (1967)
Kozunov, V.V., Ossadtchi, A.: Gala: group analysis leads to accuracy, a novel approach for solving the inverse problem in exploratory analysis of group MEG recordings. Front. Neurosci. 9, 107 (2015)
Larson, E., Maddox, R.K., Lee, A.K.C.: Improving spatial localization in MEG inverse imaging by leveraging intersubject anatomical differences. Front. Neurosci. 8, 330 (2014)
Lim, M., Ales, J., Cottereau, B.M., Hastie, T., Norcia, A.M.: Sparse EEG/MEG source estimation via a group lasso. PLOS (2017)
Lozano, A., Swirszcz, G.: Multi-level lasso for sparse multi-task regression. In: ICML (2012)
Mainini, E.: A description of transport cost for signed measures. J. Math. Sci. 181(6), 837–855 (2012)
Massias, M., Fercoq, O., Gramfort, A., Salmon, J.: Generalized concomitant multi-task lasso for sparse multimodal regression. In: Proceedings of Machine Learning Research, vol. 84, pp. 998–1007. PMLR, 09–11 April 2018
Ndiaye, E., Fercoq, O., Gramfort, A., Leclère, V., Salmon, J.: Efficient smoothed concomitant lasso estimation for high dimensional regression. J. Phys.: Conf. Ser. 904(1), 012006 (2017)
Okada, Y.: Empirical bases for constraints in current-imaging algorithms. Brain Topogr. 5, 373–377 (1993)
Owen, A.B.: A robust hybrid of lasso and ridge regression. Contemp. Math. 443, 59–72 (2007)
Pascual-Marqui, R.: Standardized low-resolution brain electromagnetic tomography (sLORETA): technical details. Methods Find Exp. Clin. Pharmacol. 24, D:5–D:12 (2002)
Profeta, A., Sturm, K.T.: Heat flow with dirichlet boundary conditions via optimal transport and gluing of metric measure spaces (2018)
Strohmeier, D., Bekhti, Y., Haueisen, J., Gramfort, A.: The iterative reweighted mixed-norm estimate for spatio-temporal MEG/EEG source reconstruction. IEEE Trans. Med. Imaging 35(10), 2218–2228 (2016)
Sun, T., Zhang, C.H.: Scaled sparse linear regression. Biometrika 99, 879–898 (2012)
Tibshirani, R.: Regression shrinkage and selection via the lasso. J. R. Stat. Soc. 58(1), 267–288 (1996)
Tseng, P.: Convergence of a block coordinate descent method for nondifferentiable minimization. J. Optim. Theory Appl. 109(3), 475–494 (2001)
Uutela, K., Hämäläinen, M.S., Somersalo, E.: Visualization of magnetoencephalographic data using minimum current estimates. NeuroImage 10(2), 173–180 (1999)
Varoquaux, G., Gramfort, A., Pedregosa, F., Michel, V., Thirion, B.: Multi-subject dictionary learning to segment an atlas of brain spontaneous activity. In: Székely, G., Hahn, H.K. (eds.) IPMI 2011. LNCS, vol. 6801, pp. 562–573. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-22092-0_46
Wakeman, D., Henson, R.: A multi-subject, multi-modal human neuroimaging dataset. Sci. Data 2(150001) (2015)
Yuan, M., Lin, Y.: Model selection and estimation in regression with grouped variables. J. R. Stat. Soc. 68(1), 49–67 (2006)
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Janati, H., Bazeille, T., Thirion, B., Cuturi, M., Gramfort, A. (2019). Group Level MEG/EEG Source Imaging via Optimal Transport: Minimum Wasserstein Estimates. In: Chung, A., Gee, J., Yushkevich, P., Bao, S. (eds) Information Processing in Medical Imaging. IPMI 2019. Lecture Notes in Computer Science(), vol 11492. Springer, Cham. https://doi.org/10.1007/978-3-030-20351-1_58
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