Performance analysis of the adaptive GMRF anomaly detector for hyperspectral imagery

We have developed an adaptive anomaly detector based on a three-dimensional Gauss-Markov random field model (GMRF) for the background clutter in hyperspectral imagery. We have shown that incorporating the modeling framework into a single-hypothesis detection scheme leads to an efficient and effective algorithm for discriminating manmade objects (the anomalies) in real hyperspectral imagery. A major feature of our GMRF anomaly detector is that it adapts to the local statistics of the clutter through the use of an approximate maximum-likelihood (approximate-ML) estimation scheme. In this paper, we focus on a thorough performance evaluation of our Adaptive GMRF Anomaly detector for hyperspectral imagery. We evaluate the detector along three directions: estimation error performance, computational cost, and detection performance. In terms of estimation error, we derive the Cramer-Rao bounds and carry out Monte Carlo simulation studies that show that the approximate-ML estimation procedure performs quite well when the fields are highly correlated, as often the case with real hyperspectral imagery. Finally we test extensively the adaptive anomaly detector with real hyperspectral imagery from both the HYDICE and SEBASS sensors. The performance of our anomaly detector compares very favorably with that of the RX-algorithm, an alternative maximum-likelihood detector used with multispectral data, while reducing by up to an order of magnitude the associated computational cost.