We develop anomaly detectors, i.e., detectors that do not presuppose a signature model of one or more dimensions, for three clutter models: the local normal model, the global normal mixture model, and the global linear mixture model. The local normal model treats the neighborhood of a pixel as having a normal probability distribution. The normal mixture model considers the observation from each pixel as arising from one of several possible classes such that each class has a normal probability distribution. The linear mixture model considers each observation to be a linear combination of fixed spectra, known as endmembers, that are, or may be, associated with materials in the scene, and the coefficients, interpreted as fractional abundance, are constrained to be nonnegative and sum to one. We show how the generalized likelihood ratio test (GLRT) may be used to derive anomaly detectors for the local normal and global normal mixture models. The anomaly detector applied with the linear mixture approach proceeds by identifying target like endmembers based on properties of the histogram of the abundance estimates and employing a matched filter in the space of abundance estimates. To overcome the limitations of the individual models, we develop a joint decision logic, based on a maximum entropy probability model and the GLRT, that utilizes multiple decision statistics, and we apply this approach using the detection statistics derived from the three clutter models. Examples demonstrate that the joint decision logic can improve detection performance in comparison with the individual anomaly detectors. We also describe the application of linear prediction filters to repeated images of the same area to detect changes that occur within the scene over time.