Ing. Vojtěch Cvrček

Matched filter is an exceedingly popular method in many fields. In optical astronomy, the common application includes matching streak templates of various lengths and orientations (shape hypothesis). We present a matched filter modification suitable for shorter streaks (less than ca. 100 px) that is faster than current state-of-the-art approaches.

Fast-moving celestial objects, like near-Earth objects (NEOs), orbiting space debris, or meteors, appear as streaks superimposed over the star background in images taken by an optical telescope at long exposures. As the apparent magnitude of the object increases (the object becomes fainter), its detection becomes progressively harder. We discuss a statistical procedure that makes a binary decision on the presence/absence of a streak in the image which is called streak certification. The certification is based purely on a single input image and a public star catalog, using a minimalistic statistical model. Certification accuracy greater than 90% for streaks of arbitrary orientation, longer than 500 pixels, and the signal-to-background log-ratio is better than −10dB is achieved on the same dataset as in an earlier similar method, whose performance is thus exceeded, especially for close-to-horizontal streaks. We also show that the certification decision indicates detection failure well.

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 approximately 0.97, which means that the Bayesian detection certificate is wrong in just 3% of cases.