A remedy for nonstationarity in background transition regions for real time hyperspectral detection

Real-time hyperspectral systems rely on a variety of statistical detection methods that all require the adaptive estimation of first- and second-order background statistics. Inadequate adaptation can occur when an airborne sensor encounters a physical transition area (e.g. forest to meadow), resulting both in excessive false detections, and in the failure to detect targets that have been strategically positioned in boundary areas. Here we describe a two-component statistical mixture model that gracefully grows the capabilities of deployed systems to adapt to abrupt transitions. First, the parameters of a bi-modal Gaussian model are found with a modified expectation maximization technique. Next, the detection phase of processing tests for hypotheses that allow mixtures of these background components, with unknown mixing fraction estimated as part of a generalized likelihood ratio test (GLRT). A straightforward application of existing real time spectral whitening modules allows the simultaneous diagonalization of the estimated covariance matrices of both primary mixture components. This generates, for both anomaly- and signature-based detection, only a small additional computational burden, consisting of a standard Newton-Raphson algorithm applied to a polynomial function