The Fusion of Quadratic Detection Statistics Applied to Hyperspectral Imagery

A variety of detection statistics have been developed and applied to hyperspectral imagery (HSI). The Reed Xiaoli (RX) algorithm is a generalized likelihood ratio test (GLRT) that uses local estimates of the spectral mean and spectral covariance. It satisfies an optimality criterion if, locally, the spectral data have a multivariate normal probability distribution. Alternatively, the stochastic expectation maximization (SEM) algorithm may be used to estimate the spectral mean values and spectral covariance matrices of a pre-determined number of classes. A detection statistic is computed by identifying each pixel with the class having maximal a posteriori probability and applying the GLRT detection statistic for that class. These algorithms are based on different models and provide different information about the imagery. For example, the RX algorithm seeks to identify local anomalies, and the SEM based detector attempts to discern those pixels that do not belong to one of the model classes. Thus we evaluate the improvement in detection performance that results from developing a joint RX-SEM decision criterion. The joint decision boundaries are obtained by modeling the output distribution of each of the algorithms and selecting a joint distribution that further incorporates the correlation between the RX and SEM detector output. The performance of the resulting fusion statistics are compared with the separate performance of the algorithms and AND/OR fusion rules.