Highly effective logistic regression model for signal (anomaly) detection

High signal to noise separation has been a long standing goal in the signal detection community. High in the sense of being able to separate, by orders of magnitude, a signal(s) of interest from its surrounding noise, in order to yield a high signal detection probability at a near zero false-alarm rate. In this paper, I propose to use some of the advances made on the theory of logistic regression models to achieve just that. I discuss a logistic regression model - relatively unknown in our community - based on case-control data, also its maximum likelihood method and asymptotic behavior. An anomaly detector is designed, based on the model's asymptotic behavior, and its performance is compared to performances of alternative anomaly detectors, commonly used with hyperspectral data. The comparison clearly shows the proposed detector's superiority over the others. The overall approach should be of interest to the entire signal processing community.