Maximum Entropy and Bayesian Methods, in press, 1996 MECHANICAL MODELS AS PRIORS IN BAYESIAN TOMOGRAPHIC RECONSTRUCTION

We introduce a new prior|the weak plate|to Bayesian tomographic reconstruction. The weak plate captures the piecewise ramplike spatial structure evident in primate autoradiograph source distributions. The weak plate is a part of a family of \mechanical" models|weak membrane (1st order), weak plate (2nd order), and weak quadric (3rd order)|in which a class of smoothness constraints derived from properties of ideal physical materials are used as models in the associated reconstruction problem. Since \weak" priors generate local minima in MAP estimation, we have designed novel Generalized Expectation{Maximization deter-ministic annealing algorithms to alleviate this problem. Our simulation studies qualitatively demonstrate the improvements over the weak membrane and maximum likelihood reconstructions.