Geometric methods for covariance-based neural decoding

Abstract

Neuroimaging tasks present significant challenges in signal processing and analysis due to factors such as low signal-to-noise ratios, high non-stationarity, and limited dataset sizes. Furthermore, understanding brain dynamics is complicated by the coupling mechanisms across various neuroimaging modalities. To address these challenges, my study introduces an alternative approach by formulating covariance-based neuroimaging data on symmetric positive definite manifolds. I integrate various geometric methods to model this data and develop geometric deep learning frameworks for multiple neuroimaging tasks, including EEG-based motor imagery classification and the multimodal fusion of simultaneous EEG-fMRI data.