Emission Computed Tomography (ECT) is widely applied in medical diagnostic imaging. 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 method for ECT image reconstruction based on a Taylor series quadratic approximation to the usual Poisson log-likelihood function. The quadratic approximation yields simplification in understanding and manipulating models for emission tomographic imagery. We introduce an algorithm similar to global Newton methods which updates the point of expansion a limited number of times and we give quantitative measures of the accuracy of the reconstruction. The results show little difference in quality from those obtained with the Poisson model, thus being greatly improved relative to the conventional filtered back-projection method.
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