Bernard R. Foy

Effect of signal contamination in matched-filter detection of the signal on a cluttered background

To derive a matched filter for detecting a weak target signal in a hyperspectral image, an estimate of the band-to-band covariance of the target-free background scene is required. We investigate the effects of including some of the target signal in the background scene. Although the covariance is contaminated by the presence of a target signal (there is increased variance in the direction of the target signature), we find that the matched filter is not necessarily affected. In fact, if the variation in plume strength is strictly uncorrelated with the variation in background spectra, the matched filter and its signal-to-clutter ratio (SCR) performance will not be impaired. While there is little a priori reason to expect significant correlation between the plume and the background, there usually is some residual correlation, and this correlation leads to a suppressing effect that limits the SCR obtainable even for strong plumes. These effects are described and quantified analytically, and the crucial role of this correlation is illustrated with some numerical examples using simulated plumes superimposed on real hyperspectral imagery. In one example, we observe an order-of-magnitude loss in SCR for a matched filter based on the contaminated covariance.

Elliptically Contoured Distributions for Anomalous Change Detection in Hyperspectral Imagery

We derive a class of algorithms for detecting anomalous changes in hyperspectral image pairs by modeling the data with elliptically contoured (EC) distributions. These algorithms are generalizations of well-known detectors that are obtained when the EC function is Gaussian. The performance of these EC-based anomalous change detectors is assessed on real data using both real and simulated changes. In these experiments, the EC-based detectors substantially outperform their Gaussian counterparts.

Characterizing non-Gaussian clutter and detecting weak gaseous plumes in hyperspectral imagery

To detect weak signals on cluttered backgrounds in high dimensional spaces (such as gaseous plumes in hyperspectral imagery) without excessive false alarms requires that the background clutter be effectively characterized. If the clutter is Gaussian, the well-known linear matched filter optimizes the sensitivity to a given plume signal while suppressing the effect of the background clutter. In practice, the background clutter is rarely Gaussian. Here we illustrate non-linear corrections to the matched filter that are optimal for two non-Gaussian clutter models and we report on parametric and nonparametric characterizations of background clutter.

Decision boundaries in two dimensions for target detection in hyperspectral imagery.

We present an approach to the problems of weak plume detection and sub-pixel target detection in hyperspectral imagery that operates in a two-dimensional space. In this space, one axis is a matched-filter projection of the data and the other axis is the magnitude of the residual after matched-filter subtraction. Although it is only two-dimensional, this space is rich enough to include several well-known signal detection algorithms, including the adaptive matched filter, the adaptive coherence estimator, and the finite-target matched filter. Because this space is only two-dimensional, adaptive machine learning methods can produce new plume detectors without being stymied by the curse of dimensionality. We investigate, in particular, the utility of the support vector machine for learning boundaries in this matched-filter-residual space, and compare the performance of the resulting nonlinearly adaptive detector to well-known alternatives.

Beyond the adaptive matched filter: nonlinear detectors for weak signals in high-dimensional clutter

For known signals that are linearly superimposed on gaussian backgrounds, the linear adaptive matched filter (AMF) is well-known to be the optimal detector. The AMF has furthermore proved to be remarkably effective in a broad range of circumstances where it is not optimal, and for which the optimal detector is not linear. In these cases, nonlinear detectors are theoretically superior, but direct estimation of nonlinear detectors in high-dimensional spaces often leads to flagrant overfitting and poor out-of-sample performance. Despite this difficulty in the general case, we will describe several situations in which nonlinearity can be effectively combined with the AMF to detect weak signals. This allows improvement over AMF performance while avoiding the full force of dimensionalitys curse.

EC-GLRT: Detecting Weak Plumes in Non-Gaussian Hyperspectral Clutter Using an Elliptically-Contoured Generalized Likelihood Ratio Test

We investigate the behavior of a detector for weak gaseous plumes in hyperspectral imagery that can be derived in terms of a generalized likelihood ratio test (GLRT) applied to an elliptically-contoured (EC) model for the distribution of background clutter. Two limiting cases of this EC-GLRT detector are the adaptive matched filter (AMF) and the adaptive coherence estimator (ACE). While the general EC-GLRT detector does not share the specific optimality or invariance properties exhibited by these limiting cases, it provides an in-between model that can be competitive with both of them over a broad range of scenarios.

Nonlinear signal contamination effects for gaseous plume detection in hyperspectral imagery

When a matched filter is used for detecting a weak target in a cluttered background (such as a gaseous plume in a hyperspectral image), it is important that the background clutter be well-characterized. A statistical characterization can be obtained from the off-plume pixels of a hyperspectral image, but if on-plume pixels are inadvertently included, then that background characterization will be contaminated. In broad area search scenarios, where detection is the central aim, it is by definition unknown which pixels in the scene are off-plume, so some contamination is inevitable. In general, the contaminated background degrades the ability of the matched-filter to detect that signal. This could be a practical problem in plume detection. A linear analysis suggests that the effect is limited, and actually vanishes in some cases. In this study, we take into account the Beers Law nonlinearity of plume absorption, and we investigate the effect of that nonlinearity on the signal contamination.

Scene analysis and detection in thermal infrared remote sensing using independent component analysis

Independent Component Analysis can be used to analyze cluttered scenes from remote sensing imagery and to detect objects. We show examples in the thermal infrared spectral region (8-12 μm) using both passive hyperspectral data and active multispectral data. The examples are from actual field data and computer simulations. ICA isolates spectrally distinct objects with nearly one-to-one correspondence with the independent component basis functions, making it useful for modeling the clutter in typical scenes. We show examples of chemical plume detection in real and simulated data.

Remote mapping of vegetation and geological features by lidar in the 9–11-µm region

We report examples of the use of a scanning tunable CO(2) laser lidar system in the 9-11-mum region to construct images of vegetation and rocks at ranges as far as 5 km from the instrument. Range information is combined with horizontal and vertical distances to yield an image with three spatial dimensions simultaneous with the classification of target type. Object classification is based on reflectance spectra, which are sufficiently distinct to allow discrimination between several tree species, between trees and scrub vegetation, and between natural and artificial targets. Limitations imposed by laser speckle noise are discussed.

Target characterization in 3D using infrared lidar

We report examples of the use of a scanning tunable CO2 laser lidar system in the 9-11 micrometers region to construct images of vegetation and rocks at ranges of up to 5 km from the instrument. Range information is combined with horizontal and vertical distances to yield an image with three spatial dimensions simultaneous with the classification of target type. Object classification is made possible by the distinct spectral signatures of both natural and man-made objects. Several multivariate statistical methods are used to illustrate the degree of discrimination possible among the natural variability of objects in both spectral shape and amplitude.