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.