Image properties of list-mode likelihood reconstruction for a rectangular positron emission mammograph with DOI measurements

A positron emission mammography scanner is under development at our laboratory. The tomograph has a rectangular geometry consisting of four banks of detector modules. For each detector, the system can measure the depth of interaction information inside the crystal. The rectangular geometry leads to irregular radial and angular sampling and spatially variant sensitivity that are different from conventional positron emission tomography (PET) systems. We adapted the theoretical analysis that we had developed for conventional PET systems to the list-mode likelihood reconstruction for this tomograph. The local impulse response and covariance of the reconstruction can be easily computed using the fast Fourier transform. These theoretical results are also used with computer observer models to compute the signal-to-noise ratio for lesion detection. The analysis reveals the spatially variant resolution and noise properties of the list-mode likelihood reconstruction. The theoretical predictions are in good agreement with Monte Carlo results.