M/EEG source reconstruction based on Gabor thresholding in the source space

International audienceThanks to their high temporal resolution, source reconstruction based on Magnetoencephalography (MEG) and/or Electroencephalography (EEG) is an important tool for noninvasive functional brain imaging. Since the MEG/EEG inverse problem is ill-posed, inverse solvers employ priors on the sources. While priors are generally applied in the time domain, the time-frequency (TF) characteristics of brain signals are rarely employed as a spatio-temporal prior. In this work, we present an inverse solver which employs a structured sparse prior formed by the sum of $\ell_{21}$ and $\ell_{1}$ norms on the coefficients of the Gabor TF decomposition of the source activations. The resulting convex optimization problem is solved using a first-order scheme based on proximal operators. We provide empirical evidence based on EEG simulations that the proposed method is able to recover neural activations that are spatially sparse, temporally smooth and non-stationary. We compare our approach to alternative solvers based also on convex sparse priors, and demonstrate the benefit of promoting sparse Gabor decompositions via a mathematically principled iterative thresholding procedure

Tensor Analysis and Fusion of Multimodal Brain Images

Current high-throughput data acquisition technologies probe dynamical systems with different imaging modalities, generating massive data sets at different spatial and temporal resolutions posing challenging problems in multimodal data fusion. A case in point is the attempt to parse out the brain structures and networks that underpin human cognitive processes by analysis of different neuroimaging modalities (functional MRI, EEG, NIRS etc.). We emphasize that the multimodal, multi-scale nature of neuroimaging data is well reflected by a multi-way (tensor) structure where the underlying processes can be summarized by a relatively small number of components or "atoms". We introduce Markov-Penrose diagrams - an integration of Bayesian DAG and tensor network notation in order to analyze these models. These diagrams not only clarify matrix and tensor EEG and fMRI time/frequency analysis and inverse problems, but also help understand multimodal fusion via Multiway Partial Least Squares and Coupled Matrix-Tensor Factorization. We show here, for the first time, that Granger causal analysis of brain networks is a tensor regression problem, thus allowing the atomic decomposition of brain networks. Analysis of EEG and fMRI recordings shows the potential of the methods and suggests their use in other scientific domains.Comment: 23 pages, 15 figures, submitted to Proceedings of the IEE