Efficient Blind Source Separation Method for fMRI Using Autoencoder and Spatiotemporal Sparsity Constraints

Diversity measures exploited by blind source separation (BSS) methods are usually based on either statistical attributes/geometrical structures or sparse/overcomplete (underdetermined) representations of the signals. This leads to some inefficient BSS methods that are derived from either a mixing matrix (mm), sparse weight vectors (sw), or sparse code (sc). In contrast, the proposed efficient method, sparse spatiotemporal BSS (ssBSS), avoids computational complications associated with lag sets, deflation strategy, and repeated error matrix computation using the whole dataset. It solves the spatiotemporal data reconstruction model (STEM) with
$l_{1}$
-norm penalization and
$l_{0}$
-norm constraints using Neumann’s alternating projection lemma and block coordinate descent approach to yield the desired bases. Its specific solution allows incorporating a three-step autoencoder and univariate soft thresholding for a block update of the source/mixing matrices. Due to the utilization of both spatial and temporal information, it can better distinguish between the sources and yield interpretable results. These steps also make ssBSS unique because, to the best of my knowledge, no mixing matrix based BSS method incorporates sparsity of both features and a multilayer network structure. The proposed method is validated using synthetic and various functional magnetic resonance imaging (fMRI) datasets. Results reveal the superior performance of the proposed ssBSS method compared to the existing methods based on mmBSS and swBSS. Specifically, overall, a 14% increase in the mean correlation value and 91% reduction in computation time over the ssICA algorithm was discovered.