Weak plate mechanical models in Bayesian reconstruction for emission tomography

Bayesian reconstruction methods for emission tomography allow the introduction of prior information in the form of spatial smoothness constraints on the underlying object. The authors extend these priors to model the type of smoothness that favors piecewise linear regions. Empirical evidence that this extension is useful is found in animal autoradiographs that show regions of radionuclide density whose structure is far from piecewise flat. The extension uses a “weak plate” prior (A. Blake and A. Zisserman, 1987) that allows for piecewise-ramplike regions in the reconstruction. Here, discontinuities include creases-discontinuities in the object gradient rather than in the object itself. To incorporate their new prior in a MAP approach, the authors model the prior as a Gibbs distribution and use a GEM formulation for the optimization. They use mathematical phantoms and a phantom derived from an autoradiograph to illustrate the efficacy of the weak plate prior as compared to more conventional priors