Regularized spatiotemporal deconvolution of fMRI data using gray-matter constrained total variation

摘要

Resting-state fMRI provides challenging data that needs to be analyzed without knowledge about timing or duration of neuronal events. The “total activation” framework is one recent approach that combines temporal and spatial regularization to deconvolve the fMRI signals; i.e., undo them from the influence of the hemodynamic response. The temporal regularization is using generalized total variation that promotes piece-wise constant signals of the deconvolved timecourses. In the original formulation, the spatial regularization is expressing ℓ-smoothness within regions of a predefined brain atlas. In this work, we replace the latter with 3-D total variation that constrained to the gray matter domain. This allows the recovery of activation clusters with sharp boundaries without any bias from the atlas' partitioning. We propose the corresponding variational formulation and optimization problem, together with results that demonstrate the feasibility of the proposed approach for both simulated and real fMRI data.