Dictionary Learning Methods for Brain Activity Mapping with MEG Data.

A central goal in many brain studies is the identification of those brain regions that are activated during an observation window that may correspond to a motor task, a stimulus, or simply a resting state. While functional MRI is currently the most commonly employed modality for such task, methods based on the electromagnetic activity of the brain are valuable alternatives because of their excellent time resolution and of the fact that the measured signals are directly related to brain activation and not to a secondary effect such as the hemodynamic response. In this work we focus on the MEG modality, investigating the performance of a recently proposed Bayesian dictionary learning (BDL) algorithm for brain region identification. The partitioning of the source space into the 148 regions of interest (ROI) corresponding to parcellation of the Destrieux atlas provides a natural determination of the subdictionaries necessary for the BDL algorithm. We design a simulation protocol where a small randomly selected patch in each ROI is activated, the MEG signal is computed and the inverse problem of active brain region identification is solved using the BDL algorithm. The BDL algorithm consists of two phases, the first one comprising dictionary compression and Bayesian compression error analysis, and the second one performing dictionary coding with a deflated dictionary built on the output of the first phase, both steps relying on Bayesian sparsity promoting computations. For assessing the performance, we give a probabilistic interpretation of the confusion matrix, and consider different impurity measures for a multi-class classifier.Key words: Sparse coding, Bayesian approximation error, Matrix factorization, Impurity index, Bayesian hierarchical models.