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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.
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Accuracy, limits, and approximation
Accuracy is defined as the closeness of the measured value to the true or actual value. In engineering mechanics, repeated measurements are taken during theoretical or experimental analyses to ensure that the result is precise and accurate.
The accuracy of any solution is based on the...

