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Pure Partial Volume Parameters

For some spatial transformations, $ T$, a shape of interest (or a parameter of no interest) can overlap the field of view by less than single voxel. This leads to a column in $ G$ which has a single non-zero value and a very low norm. These parameters are called pure partial volume parameters here, $ \alpha_{pv}$, and require special care in the integration, especially in the case of flat priors, where some simplifying assumptions breakdown.