On the validity of hypothesis testing for feasibility of image reconstructions

Feasible images have been defined as those images that could have generated the original data by the statistical process that governs the measurement. In the case of emission tomography, the statistical process of emission is Poisson and it is known that feasible images resulting from the maximum likelihood estimator (MLE) and Bayesian methods with entropy priors can be of high quality. Tests for feasibility have been described that are based on one critical assumption: the image that is being tested is independent of the data, even though the reconstruction algorithm has used those data in order to obtain the image. This fact could render the procedure unacceptable unless it is shown that its effects on the results of the tests are negligible. Experimental evidence is presented showing that images reconstructed by the MLE and stopped before convergence do indeed behave as if independent of the data. The results justify the use of hypothesis testing in practice, although they leave the problem of analytical proof still open.