On the CFAR property of the RX algorithm in the presence of signal dependent noise in hyperspectral images

In this paper, we investigate the constant false-alarm rate (CFAR) property of the RX anomaly detector which is widely used for the analysis of hyperspectral data. The RX detector relies on an adaptive scheme where the mean vector and the covariance matrix of the background are locally estimated from the image pixels themselves. First, demeaning is accomplished by removing the estimated local background mean value, and then, the covariance matrix is estimated in a homogeneous neighborhood of each pixel. In principle, if the local mean is perfectly removed and the covariance matrix is estimated from background pixels sharing the same covariance matrix, the RX algorithm has the CFAR property, which is highly desirable in practical applications. The CFAR behavior of the algorithm also requires the spatial stationarity of the random noise affecting the hyperspectral image. In data collected by new-generation sensors, such an assumption is not valid because photon noise contribution, which depends on the spatially varying signal level, is not negligible. This has motivated us to analyze the behavior of the RX algorithm with respect to the CFAR property in data affected by signal-dependent (SD) noise. In this paper, we show both theoretically and experimentally that the SD noise is one of the causes of the non-CFAR behavior of the RX detector that we have experienced in many practical situations. We propose a strategy to enhance the robustness of the anomaly detection scheme with respect to the CFAR property based on an adaptive nonlinear transform aimed at reducing the dependence of the noise on the signal level. Experiments on simulated data and real data collected by a new hyperspectral camera are also presented and discussed.