Whitening Pre-Filters with Circular Symmetry for Anomaly Detection in Hyperspectral Imagery

The Reed-Xiaoli anomaly-detector assumes that spectral samples are distributed as a multivariate Gaussian, which is rarely the case for real data. In this paper it is shown that a spatial pre-filter, with stop- and pass-bands that are tuned to the expected texture in the scene and the scale of the target (respectively), may be used to support this approximation, by decorrelating structured background and attenuating noise. For this purpose, a novel procedure for the design of two-dimensional (2-D) spatial filters, with a finite impulse response (FIR), is proposed. Expressing the optimal spatial filter as a linear combination of a few annular basis-functions with circular symmetry, instead of many shifted unit impulses, degrades the integral-squared error (ISE) of the least-squares solution because there are fewer degrees of freedom but improves the isotropy (ISO) of the filter response. Simulation is used to show that optimal filters with a near-zero ISE and near-unity ISO (i.e. with circular symmetry) have the potential to increase the power of hyperspectral anomaly detectors, by reducing the background variance in each channel.