We discuss an optimum method for target detection where the input data consist of a time series of images in one or more data channels. Backgrounds are assumed to be complicated by nonstationary Gaussian clutter that is correlated over time and across channels and may be further corrupted by highly localized non-Gaussian interference terms that appear target-like. Because of the nonstationary clutter, methods based on the Fourier transform are impractical. Instead, we use a pixel-based autoregressive (AR) model. To deal with the inhomogeneous clutter, we segment the data into locally stationary regions; each region is then whitened using its estimated AR parameters, and an optimum matched filter is applied to the whitened data. The main contributions are the following. First, we develop a generalized AR model to describe multiple frames of multiple-channel data. Second, we introduce a novel automated method for the detection of small targets in nonstationary background. Third, we discuss some special applications such as the detection of small targets in non-Gaussian background clutter. We describe in detail the implementation of these techniques, and demonstrate their performance using both synthetic data and real data obtained from the Compact Airborne Spectrographic Imager (CASI).