Arterial Spin Labeling (ASL) permits the non-invasive assessment of cerebral perfusion, by magnetically labeling all the blood flowing into the brain. Vessel encoded (VE) ASL extends this concept by introducing spatial modulations of the labeling procedure, resulting in different patterns of label applied to the blood from different vessels. Here a Bayesian inference solution to the analysis of VE-ASL is presented based on a description of the relative locations of labeled vessels and a probabilistic classification of brain tissue to vessel source. In simulation and on real data the method is shown to reliably determine vascular territories in the brain, including the case where the number of vessels exceeds the number of independent measurements.
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