25 June 1999 Approximate Poisson likelihoods for simple optimization in MAP tomographic estimation
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Emission Computed Tomography (ECT) is widely applied in medical diagnostic imaging, especially to determine physiological function. The available set of measurements is,however, often incomplete and corrupted, and the quality of image reconstruction is enhanced by the computation of a statistically optimal estimate. We present here a numerical method of ECT image reconstruction based on a Taylor series quadratic approximation to the usual Poison log-likelihood function. The quadratic approximation yields simplification in understanding and manipulating Poisson models. We introduce an algorithm similar to global Newton methods which updates the point of expansion a limited number of time sand we give quantitative measures of the accuracy of the reconstruction. The result show little difference in quality from those obtained with the exact Poisson model.
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Jean-Baptiste Thibault, Ken D. Sauer, Charles A. Bouman, "Approximate Poisson likelihoods for simple optimization in MAP tomographic estimation", Proc. SPIE 3816, Mathematical Modeling, Bayesian Estimation, and Inverse Problems, (25 June 1999); doi: 10.1117/12.351311; https://doi.org/10.1117/12.351311

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