M/EEG source localization with multi-scale time-frequency dictionaries

Abstract : —Magnetoencephalography (MEG) and electroen-cephalography (EEG) source localization is a challenging ill-posed problem. To identify an appropriate solution out of an infinite set of possible candidates, the problem requires setting certain constraints depending on the assumptions or a priori knowledge about the source distribution. Different constraints have been proposed so far, including those that impose sparsity on the source reconstruction in both standard and time-frequency domains. Source localization in the time-frequency domain has already been investigated using Gabor dictionary in both a convex (TF-MxNE) and non-convex way (Iterative Reweighted TF-MxNE). The iterative reweighted (ir)TF-MxNE solver has been shown to outperform TF-MxNE in both source recovery and amplitude bias. However, the choice of an optimal dictionary remains unsolved. Due to a mixture of signals, i.e. short transient signals (right after the stimulus onset) and slower brain waves, the choice of a single dictionary explaining simultaneously both signals types in a sparse way is difficult. In this work, we introduce a method to improve the source estimation relying on a multi-scale dictionary, i.e. multiple dictionaries with different scales concatenated to fit short transients and slow waves at the same time. We compare our results with irTF-MxNE on realistic simulation, then we use somatosensory data to demonstrate the benefits of the approach in terms of reduced leakage (time courses mixture), temporal smoothness and detection of both signals types. keywords— Inverse problem; MEEG; iterative reweighted optimization algorithm; multi-scale dictionary; Gabor transform. I. INTRODUCTION Magneto-/electroencephalography (M/EEG) allow for non-invasive analysis of functional brain imaging with high temporal and good spatial resolution. Various approaches to tackle the source localization problem from M/EEG data have been proposed in the literature. The distributed-source approach models the brain activity with a fixed number of candidate dipoles distributed over the brain, and estimates their amplitudes and orientations. As the number of candidate dipoles that can explain the measured data is much larger than the number of sensors, source localization is an ill-posed problem. This implies that there is not a unique solution. Literature shows that adding supplementary constraints such as sparse regularization of priors to the neural activation helps to tackle the problem. Those approaches are based on Bayesian modeling [1]–[4], or regularized regression [5]–[7]. These methods implicitly assume stationarity of the source activation. In contrast, the Time-Frequency Mixed Norm Estimate (TF-MxNE) [8], Spatio-Temporal Unifying Tomography (STOUT) [9] and the iterative reweighted TF-MxNE (irTF-MxNE) [10] improve reconstruction of transient and non-stationary sources
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6th International Workshop on Pattern Recognition in Neuroimaging (PRNI), Jun 2016, Trento, Italy. 2016, <http://prni2016.wix.com/prni2016>. <10.1109/PRNI.2016.7552337>
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Yousra Bekhti, Daniel Strohmeier, Mainak Jas, Roland Badeau, Alexandre Gramfort. M/EEG source localization with multi-scale time-frequency dictionaries. 6th International Workshop on Pattern Recognition in Neuroimaging (PRNI), Jun 2016, Trento, Italy. 2016, <http://prni2016.wix.com/prni2016>. <10.1109/PRNI.2016.7552337>. <hal-01313567v2>

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