Mechanical Models as Priors in Bayesian Tomographic Reconstruction
نویسنده
چکیده
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.
منابع مشابه
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 ...
متن کاملSpline-based sparse tomographic reconstruction with Besov priors
Tomographic reconstruction from limited X-ray data is an ill-posed inverse problem. A common Bayesian approach is to search for the maximum a posteriori (MAP) estimate of the unknowns that integrates the prior knowledge, about the nature of biomedical images, into the reconstruction process. Recent results on the Bayesian inversion have shown the advantages of Besov priors for the convergence o...
متن کاملFlexible Prior Models in Bayesian Image Analysis
A new class of prior models is proposed for Bayesian image analysis. This class of priors provides an inherent geometrical flexibility, which is achieved through a transformation of the coordinate system of the prior distribution or model into that of the object under analysis. Thus prior morphological information about the object being reconstructed may be adapted to various degrees to match t...
متن کاملBayesian Sample size Determination for Longitudinal Studies with Continuous Response using Marginal Models
Introduction Longitudinal study designs are common in a lot of scientific researches, especially in medical, social and economic sciences. The reason is that longitudinal studies allow researchers to measure changes of each individual over time and often have higher statistical power than cross-sectional studies. Choosing an appropriate sample size is a crucial step in a successful study. A st...
متن کاملLocation Reparameterization and Default Priors for Statistical Analysis
This paper develops default priors for Bayesian analysis that reproduce familiar frequentist and Bayesian analyses for models that are exponential or location. For the vector parameter case there is an information adjustment that avoids the Bayesian marginalization paradoxes and properly targets the prior on the parameter of interest thus adjusting for any complicating nonlinearity the details ...
متن کامل