Hierarchical prior for Bayesian deconvolution of radioactive sources with Poisson statistics

Guillaume Stawinski; Patrick Duvaut

doi:10.1117/12.323809

22 September 1998 Hierarchical prior for Bayesian deconvolution of radioactive sources with Poisson statistics

Guillaume Stawinski, Patrick Duvaut

Proceedings Volume 3459, Bayesian Inference for Inverse Problems; (1998) https://doi.org/10.1117/12.323809
Event: SPIE's International Symposium on Optical Science, Engineering, and Instrumentation, 1998, San Diego, CA, United States

Abstract

The problem of deconvolution is a classical problem in Gamma imaging. Using the conventional statistical model introduced by Shepp and Verdi (1982), many authors have adopted a Bayesian approach to address this problem and to estimate the different numbers of Gamma rays emitted A = (As)SET at each pixel s. As prior on A to regularize the picture, one uses a Gauss Markov random Field. However, this approach has one major drawback: the choice of the regularization parameter 3. If3 is too high, the discontinuities are oversmoothed, and if /3is too low, the picture is not regularized enough. In this paper, we introduce a new hierarchical prior model for A , inwhich 3 is not constant over the picture. This hierarchical prior model uses a Markov random field to describe spatial variation of the logarithm of the smoothing parameter log /3= (log3s)sET fl a second random field which describes the spatial variation in A. The coupled Markov random fields are used as prior distributions. Similar ideas have occurred in Aykroyd (1996), but our prior model is quite different.Our new hierarchical prior model is applied for the problem of deconvolution of radioactive sources in Gamma imaging.The estimation of A and i3 is based on their joint posterior density, following a Bayesian framework. This estimation is performed using a new SAGE EM algorithm (Hero and Fessler,1995), where the parameters A and 3 are updated sequentially. Our new prior model is tested on synthetic and real data and compared to the conventional Gauss Markov random field prior model : our algorithm increases significantly the results obtained by using a classical prior model.

keywords : adaptive smoothing, Compound Gauss-Markov random Fields, Doubly stochastic random fields, SAGE EM algorithms.

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Guillaume Stawinski and Patrick Duvaut "Hierarchical prior for Bayesian deconvolution of radioactive sources with Poisson statistics", Proc. SPIE 3459, Bayesian Inference for Inverse Problems, (22 September 1998); https://doi.org/10.1117/12.323809

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KEYWORDS

Expectation maximization algorithms

Algorithm development

Deconvolution

Reconstruction algorithms

Signal to noise ratio

Argon

Cameras

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