Change Detection for Hyperspectral Sensing in a Transformed Low-dimensional Space

Change detection in hyperspectral imagery is the process of comparing two spectral images of the same scene acquired at different times, and finding a small set of pixels that has the largest apparent spectral change. We present an approach that operates in a two-dimensional space rather than in the original high-dimensional space of the images, which can be greater than 100 spectral channels. The coordinates in the 2-D space are related to Mahalanobis distances for the combined (“stacked”) data and the individual hyperspectral scenes. Several previously developed change detection algorithms can be represented as straight lines in this space, including the hyperbolic anomalous change detector, based on Gaussian scene clutter, and the EC-uncorrelated detector based on heavy-tailed (elliptically contoured) clutter. We show that adaptive machine learning methods can produce new change detectors with good performance that can avoid problems associated with the curse of dimensionality. We investigate, in particular, the utility of the support vector machine for learning boundaries in this 2-D space, using two classes of data to represent pervasive and simulated changes. 1.0 Introduction Hyperspectral Imaging (HSI) has wide utility for both military and civilian purposes. Change detection is an application of hyperspectral sensors that is important for finding possible new features of interest in a cluttered scene, either a target of interest or activity such as disturbed earth or new structures. Acquiring datasets at two different times, and possibly even with two different sensors, a comparison can reveal the appearance or disappearance of objects with distinct spectra. Unlike target detection, however, the goal in change detection is to detect an entity using no prior information on its spectrum. A common feature of existing change detection algorithms for spectral data is to reduce the multi-dimensional spectral vector (corresponding to one scene pixel) to a scalar quantity, whose magnitude indicates the likelihood of that pixel representing a substantial change. 2 In this paper, we introduce a scheme in which two of these scalar quantities are produced, and a change detection decision boundary is “learned” from the data in this 2D space. Two classes of data can be generated to facilitate this process: one class consists of pixels with only minor changes (e.g. environmental changes, illumination changes, instrumental noise, etc.), and a second class consisting of major changes whose detection is desired (e.g. grassy vegetation changing to vehicle or structure). Classification algorithms can then be used to discriminate between the minor and major changes. The Support Vector Machine (SVM) can be useful in this regard, and it can be implemented not in the original highdimensional space of the HSI data but rather in a lower dimensional space derived from the original data. We apply this concept to two examples of HSI data in different spectral regions, the long-wavelength infrared (LWIR) and the visible/near-infrared (VNIR). 2.0 Framework for Anomalous Change Detection We would like to compare two hyperspectral images, the x-image and the y-image, and find a small set of pixels for which the x-to-y change is unusual compared to the changes exhibited by the rest of the pixels. We recognize at the outset that all of the pixels exhibit some degree of change, as a result of environmental or instrumental factors or both. Let denote the observed radiance spectrum observed at one pixel in the x-image, and x d  x R y d R  y be the corresponding pixel in the y-image. We assume that the images are registered, i.e. that corresponding pixels x and y correspond to the same location in the scene, but we acknowledge that this registration is not always precise. The number of spectral channels in the