Reliable Detection of Dynamic Anomalies with Application to Extracting Faint Space Object Streaks from Digital Frames

We consider a problem of reliable detection of dynamic anomalies in observed data. The problem is of importance for many applications, e.g., for signal and image processing where dynamic anomalies (corresponding to changes in distributions of observed processes) take place when signals appear and disappear at unknown points in time or space. We assume that the duration of the change may be finite and unknown and focus on Bayesian and maximin optimality criteria of maximizing the probability of detection in a prespecified time interval under constraints imposed on the rate of false positives. Using optimal stopping theory we find optimal Bayesian and maximin detection procedures. We then compare operating characteristics of the optimal procedures with the popular Finite Moving Average (FMA) rule, using Monte Carlo simulations, which show that typically the FMA procedure has almost the same performance as the optimal ones. The FMA rule is applied to the extraction of faint streaks of satellites from digital frames captured with telescopes.