Decoding penalty calculation for a ring Compton camera using uniform Cramer-Rao bound

Compton cameras completely decouple the inverse relationship between spatial resolution and detection sensitivity which compromises the performance of conventional collimated cameras. However, this improvement is usually achieved at the expense of the amount of information conveyed by each detected photon. In this paper, we propose a simple approach to calculate the information loss for a ring Compton camera. We describe this information loss as “decoding penalty”, defined as the ratio of variance of reconstructed intensity for a pixel of interest for a ring Compton camera to a mechanically collimated camera normalized to a per-detected-photon basis. The uniform Cramer-Rao bound, our mathematical tool, provides a lower bound on the variance dependent on the system and data statistics alone rather than the estimator. Results of a decoding penalty calculation suggest that ring Compton cameras outperform conventional cameras at incident photon energies of 364 keV and higher