One of the hallmarks of the Bayesian approach to modeling is the posterior probability, which summarizes all uncertainties regarding the analysis. Using a Markov Chain Monte Carlo (MCMC) technique, it is possible to generate a sequence of objects that represent random samples drawn from the posterior distribution. We demonstrate this technique for a reconstruction of a two-dimensional object from two orthogonal noisy projections. The reconstructed object is modeled in terms of a deformable geometrically-defined boundary with a constant interior density yielding a nonlinear reconstruction problem. We show how an MCMC sequence can be used to estimate uncertainties in the location of the edge of the reconstructed object.
Keywords: > uncertainty estimation, Bayesian estimation, Markov Chain Monte Carlo, deformable geometric model, tomographic reconstruction
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