A 3-D spatio-temporal deconvolution approach for MR perfusion in the brain

[Display omitted] •We propose a theoretically grounded spatio-temporal model for the PWI deconvolution problem.•We provide a globally convergent algorithm to solve the associated optimization problem.•We show that our approach outperforms the standard (temporal-only) deconvolution methods using both synthetic and real data.•The validation of the proposed approach was carried out at each step of the PWI processing pipeline. We propose an original spatio-temporal deconvolution approach for perfusion-weighted MRI applied to cerebral ischemia. The regularization of the underlying inverse problem is achieved with spatio-temporal priors and the resulting optimization problem is solved by half-quadratic minimization. Our approach offers strong convergence guarantees, including when the spatial priors are non-convex. Moreover, experiments on synthetic data and on real data collected from subjects with ischemic stroke show significant performance improvements over the standard approaches—namely, temporal deconvolution based on either truncated singular-value decomposition or ℓ2-regularization—in terms of various performance measures.