On The Applicability Of The Maximum Likelihood Estimator Algorithm For Image Recovery In Accelerated Positron Emitter Beam Injection

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Abstract
The Maximum Likelihood Estimator (MLE) algorithm for tomographic image reconstruction is being investigated in substantial detail by a number of research groups, as it appears to promise images with very low noise and increased sharpness when compared with filtered backprojection techniques. Recently, however, it has been found that the reconstruction of data from uniform activity distributions exhibits strong peaks and valleys when the number of iterations increases toward a maximum in the likelihood function. This problem has now been investigated with our Positron Emitter Beam Analyzer (PEBA) camera, which, because of its small size and favorable geometry, has allowed an analysis with enough detail to find the origin of that apparent instability. The findings can be summarized as follows: 1) The very low noise of the MLE reconstructions comes about by the ability of the Poisson-based MLE algorithm to generate an image which favors the matching of experimental data (detector pairs) containing few counts. 2) The image instability at a high number of iterations is a direct consequence of the above characteristic. 3) The matrix of probability elements needed for the MLE reconstruction provides the link between the two above observed phenomena. It appears that, by proper system design, it is possible to obtain the favorable low noise characteristic without the instability. The applicability of the above findings to true tomography (PEBA does not carry out a true tomographic reconstruction) seems direct, but confirmation should be obtained by further research on the question.© (1986) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

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