Object-oriented methods in Bayesian 3-D tomographic reconstruction from radiographs

Abstract

Maximum a posteriori probability (MAP) estimation is the method of choice in many sparse data problems in reconstruction from projections. But with low signal-to-noise ratios, MAP tends to yield very conservative estimates, necessitating adjustment of the parameters which are to describe random fields regardless of noise levels in data. We propose a nonstationary Markov random field model, with the local variations in parameters due to the presence of objects, whose precise form and size are random. The problem is formulated as maximum-likelihood estimation, with the locations of the objects as parameters. The random field is then Markov, conditioned on the parameters set by object detection, allowing MAP reconstruction of the most likely field. With the estimated locations of the objects, the MAP reconstruction, conditioned on their presence, yields estimates of improved accuracy, without noise-dependent adjustment of the Markov model. >