title: Asymptotics of Bayesian error probability and source super-localization in three dimensions.
abstract: We present an asymptotic analysis of the minimum probability of error (MPE) in inferring the correct hypothesis in a Bayesian multi-hypothesis testing (MHT) formalism using many pixels of data that are corrupted by signal dependent shot noise, sensor read noise, and background illumination. We perform our analysis for a variety of combined noise and background statistics, including a pseudo-Gaussian distribution that can be employed to treat approximately the photon-counting statistics of signal and background as well as purely Gaussian sensor read-out noise and more general, exponentially peaked distributions. We subsequently evaluate both the exact and asymptotic MPE expressions for the problem of three-dimensional (3D) point source localization. We focus specifically on a recently proposed rotating-PSF imager and compare, using the MPE metric, its 3D localization performance with that of conventional and astigmatic imagers in the presence of background and sensor-noise fluctuations.
authors: S
authors: S
authors: Prasad