Structurally-Informed Deconvolution of Functional Magnetic Resonance Imaging Data

Neural activity occurs in the shape of spatially organized patterns: networks of brain regions activate in synchrony. Many of these functional networks also happen to be strongly structurally connected. We use this information to revisit the fundamental problem of functional magnetic resonance imaging (fMRI) data deconvolution. Using tools from graph signal processing (GSP), we extend total activation, a spatiotemporal deconvolution technique, to data defined on graph domains. The resulting approach simultaneously cancels out the effect of the haemodynamics, and promotes spatial patterns that are in harmony with predefined structural wirings. More precisely, we minimize a functional involving one data fidelity and two regularization terms. The first regularizer uses the concept of generalized total variation to promote sparsity in the activity transients domain. The second term controls the overall spatial variation over the graph structure. We demonstrate the relevance of this structurally-driven regularization on synthetic and experimental data