Analysis of unknown-location signal detectability for regularized tomographic image reconstruction

Our goal is to optimize regularized image reconstruction methods for emission tomography with respect to the task of detecting small lesions of unknown location in the reconstructed images. We consider model observers whose decisions are based on finding the maximum value of a local test statistic over all possible lesion locations. We use tail probability approximations by Adler (AAP 2000) and Siegmund and Worsley (AS 1995) to evaluate the probabilities of false alarm and detection respectively for the observers of interest. We illustrate how these analytical tools can be used to optimize regularization with respect to the performance (at low probability of false alarm operating points) of a maximum channelized non-prewhitening observer