Hyperspectral imagery: clutter adaptation in anomaly detection

Abstract

Abstract-Hyperspectral sensors are passive sensors that simultaneously record images for hundreds of contiguous and narrowly spaced regions of the electromagnetic spectrum. Each image corresponds to the same ground scene, thus creating a cube of images that contain both spatial and spectral information about the objects and backgrounds in the scene. In this paper, we present an adaptive anomaly detector designed assuming that the background clutter in the hyperspectral imagery is a three-dimensional Gauss-Markov random field. This model leads to an efficient and effective algorithm for discriminating man-made objects (the anomalies) in real hyperspectral imagery. The major focus of the paper is on the adaptive stage of the detector, i.e., the estimation of the Gauss-Markov random field parameters. We develop three methods: maximum-likelihood; least squares; and approximate maximum-likelihood. We study these approaches along three directions: estimation error performance, computational cost, and detection performance. In terms of estimation error, we derive the Cramér-Rao bounds and carry out Monte Carlo simulation studies that show that the three estimation procedures have similar performance when the fields are highly correlated, as is often the case with real hyperspectral imagery. The approximate maximum-likelihood method has a clear advantage from the computational point of view. Finally, we test extensively with real hyperspectral imagery the adaptive anomaly detector incorporating either the least squares or the approximate maximum-likelihood estimators. Its performance compares very favorably with that of the RX algorithm, an alternative detector commonly used with multispectral data, while reducing by up to an order of magnitude the associated computational cost.Index Terms-Anomaly detection, Cramér-Rao bounds, GaussMarkov random field, hyperspectral imagery, least squares, maximum likelihood, multispectral imagery, ultraspectral imagery.

Anomaly subspace detection based on a multi-scale Markov random field model

“…Various methods for model estimation were developed over the years, e.g., [11,13,23,22,26]. A computationally efficient method for the GMRF model estimation is the least squares method, described in details in Hazel [11].…”

“…We investigate the receiver operating characteristics (ROC) of the algorithm with respect to different parameters. The ROC of the proposed algorithm is calculated using (22), (25), and (26). The SNR, given by (22), is a function of the target's shape and intensity, the variance of the background's innovations process and the interference subspace span.…”

“…The ROC of the proposed algorithm is calculated using (22), (25), and (26). The SNR, given by (22), is a function of the target's shape and intensity, the variance of the background's innovations process and the interference subspace span. The SNR increases with the norm of x; the number of independent layers (p), and the angle between x and hSi: Large background variance results in a smaller SNR and therefore, performance degradation.…”

“…Another factor which may influence the performance is the dimension of the interference subspace. According to (22), when the dimension of S 0 ' decreases, the SNR is lower and the performance is reduced. In this section we refer to the proposed method as ''Proposed Method III'' and compare it 3.…”

Innovative Statistical Inference for Anomaly Detection in Hyperspectral Imagery

“…An extended description of this dataset can be found, for example, in. 25 The results shown in this section for one data sub-cube are representative for other sub-cubes in the HYDICE (forest radiance) dataset. An illustrative sub-cube (shown as an average of 150 bands; 640 x 100 pixels) is shown in figure 1 (left 3 square meters at the given altitude.…”