List-mode maximum-likelihood reconstruction applied to positron emission mammography (PEM) with irregular sampling

We present a preliminary study of list-mode likelihood reconstruction of images for a rectangular positron emission tomograph (PET) specifically designed to image the human breast. The prospective device consists of small arrays of scintillation crystals for which depth of interaction is estimated. Except in very rare instances, the number of annihilation events detected is expected to be far less than the number of distinguishable events, If one were to histogram the acquired data, most histogram bins would remain vacant. Therefore, it seems natural to investigate the efficacy of processing events one at a time rather than processing the data in histogram format. From a reconstruction perspective, the new tomograph presents a challenge in that the rectangular geometry leads to irregular radial and angular sampling, and the field of view extends completely to the detector faces. Simulations are presented that indicate that the proposed tomograph can detect 8-mm-diameter spherical tumors with a tumor-to-background tracer density ratio of 3 : 1 using realistic image acquisition parameters. Spherical tumors of 4-mm diameter are near the limit of detectability with the image acquisition parameters used. Expressions are presented to estimate the loss of image contrast due to Compton scattering.