Observing and analyzing human brain function is a truly interdisciplinary endeavor combining engineering, neurosciences, and medicine. State-of-the-art technologies such as functional magnetic resonance imaging (fMRI) allow to non-invasively acquire a sequence of whole-brain snapshots that indirectly measure neuronal activity. Recent ``big data'’ initiatives (e.g., Human Connectome Project) provide us with large datasets reflecting the complex structure of human brain activity. Advanced signal processing plays a major role to extract meaningful and interpretable features. Here we present one such example to characterize dynamics of resting-state fMRI. Using state-of-the-art sparsity-driven deconvolution [1,2], we extract innovation-driven co-activation patterns (iCAPs) from resting-state fMRI [3]. The iCAPs' maps are spatially overlapping and their activity-inducing signals temporally overlapping. Decomposing resting-state fMRI in terms of iCAPs reveals the rich spatiotemporal structure of functional components that dynamically assemble known resting-state networks. The temporal overlap between iCAPs is substantial, which confirms crosstalk happening at the fMRI timescale; on average, three to four iCAPs occur simultaneously in specific combinations that are consistent with their behaviour profiles according to BrainMap. Intriguingly, in contrast to conventional connectivity analysis, which suggests a negative correlation between fluctuations in the default-mode network (DMN) and task-positive networks, we instead find evidence for two DMN-related iCAPs consisting the posterior cingulate cortex that differentially interact with the attention network. These findings illustrate how conventional correlational approaches might be misleading in terms of how task-positive and -negative networks interact, and suggest that more detailed, dynamical decompositions can give more accurate descriptions of functional components of spontaneous activity.

Data-driven methods such as independent component analysis (ICA) have proven quite effective for the analysis of functional magnetic resonance (fMRI) data and for discovering associations between fMRI and other medical imaging data types such as electroencephalography (EEG) and structural MRI data. Without imposing strong modeling assumptions, these methods effectively take advantage of the multivariate nature of fMRI data and are particularly attractive for use in cognitive paradigms where detailed a priori models of brain activity are not available.

This talk reviews major data-driven methods that have been successfully applied to fMRI analysis, presents recent examples of their application for studying the brain function, and addresses current challenges and prospects.

Adapting sparse image modeling to the data has been shown to provide improved image reconstruction in several imaging modalities. However, synthesis or analysis dictionary learning involves approximations of NP-hard sparse coding, and expensive learning steps. Recently, sparsifying transform learning (STL) received interest for its cheap and exact closed-form solutions to iteration steps. We describe the evolution of this framework and several variations as applied to biomedical imaging, including online STL for dynamic and big data; learning a union of transforms model for greater representation power; and a filter bank STL that provides more degrees of freedom in modeling by acting on entire images rather than on patches.