Feasible images and practical stopping rules for iterative algorithms in emission tomography

The discussion of the causes of image deterioration in the maximum-likelihood estimator (MLE) method of tomographic image reconstruction, initiated with the publication of a stopping rule for that iterative process (E. Veklerov and J. Llacer, 1987) is continued. The concept of a feasible image is introduced, which is a result of a reconstruction that, if it were a radiation field, could have generated the initial projection data by the Poisson process that governs radioactive decay. From the premise that the result of a reconstruction should be feasible, the shape and characteristics of the region of feasibility in projection space are examined. With a new rule, reconstructions from real data can be tested for feasibility. Results of the tests and reconstructed images for the Hoffman brain phantom are shown. A comparative examination of the current methods of dealing with MLE image deterioration is included.