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In this paper, we apply a deflection-optimal linear-quadratic detector to the detection of buried mines in images formed by a forward-looking ground-penetrating synthetic aperture radar. The detector is a linear-quadratic form that maximizes the output SNR (deflection), and its parameters are estimated from a set of training data. We show that this detector is useful when the signal to be detected is expected to be stochastic, with an unknown distribution, and when only a small set of training data is available to estimate its statistics. The detector structure can be understood in terms of the singular value decomposition; the statistical variations of the target signature are modeled using a compact set of orthogonal "eigenmodes" (or principal components) of the training dataset. Because only the largest eigenvalues and associated eigenvectors contribute, statistical variations that are underrepresented in the training data do not significantly corrupt the detector performance. The resulting detection algorithm is tested on data that are not in the training set, which has been collected at government test sites, and the algorithm performance is reported.