Any observer performing a detection task on an image produces a single number that represents the observer's confidence that a signal (e.g., a tumor) is present. A linear observer produces this test statistic using a linear template or a linear discriminant. The optimal linear discriminant is well-known to be the Hotelling observer and uses both first- and second-order statistics of the image data. There are many situations where it is advantageous to consider discriminant functions that adapt themselves to some characteristics of the data. In these situations, the linear template is itself a function of the data and, thus, the observer is nonlinear. In this paper, we present an example adaptive Hotelling discriminant and compare the performance of this observer to that of the Hotelling observer and the Bayesian ideal observer. The task is to detect a signal that is imbedded in one of a finite number of possible random backgrounds. Each random background is Gaussian but has different covariance properties. The observer uses the image data to determine which background type is present and then uses the template appropriate for that background. We show that the performance of this particular observer falls between that of Hotelling and ideal observers.