Wavelet thresholding on independent subspace factorizations of spatially indexed wide functional data for robust estimation of cortical activity

Abstract

We address the mathematical and statistical formalism that underpins optimal estimation of brain activity in artifact-corrupted electroencephalographic (EEG) signals. We argue the reconstruction of artifacts relates to approximating a function in a Hilbert basis that is a realization of a spatio-temporal random variable taking values in a Hilbert space. A model for sparse optimization based on a fixed-point iteration over the spatial domain and posterior enhancement in the temporal domain via wavelet thresholding is discussed under the paradigm of “wide functional data”. Two criteria are introduced for selecting wavelet expansion coefficients in scenarios where noise lacks a precise parametric specification: one based on multiplicative scaling and the other on the entropic NID (ENID), as introduced in Bruni et al. (2020). Through comprehensive numerical simulations and real data analyses of EEG data, we showcase the effectiveness of the proposed methods.