Dictionary learning methods for brain activity mapping with MEG data

TL;DR

This paper tackles the problem of identifying active brain regions from MEG data by formulating it as a Bayesian dictionary learning with group sparsity across ROI-based subdictionaries defined by the Destrieux atlas. It introduces a two-phase classifier: first compresses the dictionary and performs Bayesian compression-error aware matching, then deflates the dictionary to refine sparse coding and improve ROI identification, leveraging the IAS MAP framework. Through simulations using realistic MEG forward models, the method demonstrates improved accuracy and interpretability, including ROI-wise recall and uncertainty representations via posterior variances. The approach offers robust MEG-based region identification and highlights the potential to shift atlas design toward electromagnetic activity patterns, with avenues for uncertainty quantification and alternative inference strategies.

Abstract

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.

Figures (11)

• Figure 1: Heatmaps of the confusion matrices after the first phase using reduced dictionaries and winner-takes-all classification principle (left) and second phase based on the deflated model (right).
• Figure 2: Scatter plots of the misclassification errors of each brain region (left) and the Gini indices (right). The horizontal axes correspond to the classification based on the reduced dictionaries, and the vertical plot to the deflated dictionaries. Observe that decreases of the impurity in Phase 2 is indicated by the marker for brain region to be below the red diagonal line.
• Figure 3: The recalls $s_j = 1-MCR_j$ of the brain regions of the left hemisphere in decreasing order. Here, both phases of the classifier algorithm was applied.
• Figure 4: Visualization of entries $({\mathsf P}_{ij})_{i=1}^N$, $j$ of the $j$th vector, interpreted as probabilities, corresponding to vertical ramus of the anterior segment of the lateral fissure, the brain region with the highest recall value of 0.91.
• Figure 5: Visualization of the probabilities of the regions to be identified as left precuneus, with recall value 0.65. Observe that due to the proximity of the left precuneus to the longitudinal fissure separating the hemispheres, the misclassification includes some brain regions on the right hemisphere.