Functional MRI deconvolution algorithms are gaining popularity to study the dynamicss of functional brain activity and connectivity at short timescales. This work sheds light on our understanding of two state-of-the-art approaches based on L1-norm regularized estimators: Paradigm Free Mapping (synthesis model) and Total Activation (analysis model). Through simulations with varying signal-to-noise ratios, and an experimental motor task dataset, we demonstrate that both formulations produce identical estimates of the innovation and activity-inducing signals underlying BOLD events when identical hemodynamic response and regularization parameters are used. These observations open up the possibility for future developments without questioning their core formulation and performance.
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