In this dissertation we present a new approach to estimate the volume of ischermic stroke lesions using magnetic resonance imagery (MRI). The approach is hierarchical, regularized, and guided by statistical theory, resulting in a confidence map for the lesion itself and a confidence interval for the lesion volume. We test the procedure on synthetic data and real MRI, with estimates to within 6% of the volumes from physicians' hand segmentations. These results compare favorably to those from other Bayesian-based methods. Also, we present a formulation of the free induction decay signal for several MR pulse sequences, which allow for the classification of distinct tissue types in MRI.