Faint Streak Detection with Certificate by Adaptive Multi-level Bayesian Inference

It is known that detecting straight streaks from fast moving celestial objects in optical images is an easy problem as long as the streaks are sufficiently long and/or their signal-to-background (SBR) is sufficiently high. At low SBR the situation is different. Since the SBR can be arbitrarily small in practice, a good detection procedure has to provide a detection certificate which is a yes/no answer to the question “does the image contain a streak?” In this paper we pose detection with certificate as a Multi-Level Bayesian Inference (MLBI) problem which is based on Bayesian model selection. We describe the algorithm and show an experimental proof of good behavior on synthetic streaks over real image data. A systematic performance evaluation shows that MLBI confirms and partially exceeds results of state-of-the art methods. In particular, in the class of difficult problem instances with SBR of 0 dB to −5 dB and streak length 10 to 500 pixels, we achieved AUC ≈ 0.97, which means that the Bayesian detection certificate is wrong in just 3% of cases.