Comparison of basis-vector selection methods for target and background subspaces as applied to subpixel target detection

Abstract

This paper focuses on comparing three basis-vector selection techniques as applied to target detection in hyperspectral imagery. The basis-vector selection methods tested were the singular value decomposition (SVD), pixel purity index (PPI), and a newly developed approach called the maximum distance (MaxD) method. Target spaces were created using an illumination invariant technique, while the background space was generated from AVIRIS hyperspectral imagery. All three selection techniques were applied (in various combinations) to target as well as background spaces so as to generate dimensionally-reduced subspaces. Both target and background subspaces were described by linear subspace models (i.e., structured models). Generated basis vectors were then implemented in a generalized likelihood ratio (GLR) detector. False alarm rates (FAR) were tabulated along with a new summary metric called the average false alarm rate (AFAR). Some additional summary metrics are also introduced. Impact of the number of basis vectors in the target and background subspaces on detector performance was also investigated. For the given AVIRIS data set, the MaxD method as applied to the background subspace outperformed the other two methods tested (SVD and PPI).

Matched Filter Stochastic Background Characterization for Hyperspectral Target Detection

“…This will allow for a comparison of detection results without calculating probabilities and making a general statement of algorithm performance. For more direct comparison, we can reduce the ROC curve to a single numerical value by taking an average false alarm rate (AFAR) [10]. This representation of the area above the ROC curve is a good indication of detection performance in finding all target pixels.…”

Evaluation of the graphics processing unit architecture for the implementation of target detection algorithms for hyperspectral imagery

“…The performance of the SVD and MaxD methods as basis-vector selection techniques for target detection was previously studied by Bajorski et al 23 Other works comparing different techniques for background subspace generation, including SVD and MaxD, were recently presented by Peña-Ortega and Velez-Reyes.…”

“…In this case, the number of basis vectors is selected to enclose a given percentage of variability. 23 MaxD is an endmember selection method proposed by Schott et al 24 The basis vectors selected by this method, which are pixels from the original image, are the set of vectors that best approximate a simplex defining the background subspace. The steps involved in the MaxD method can be summarized as follows:…”

“…In the implementation of this detector, two methods for estimating the matrix B of background basis vectors were evaluated: singular value decomposition (SVD) 23 and Maximum Distance (MaxD). 24 In the SVD approach, the basis vectors are selected as first M left singular vectors of the matrix X representing the image in bands × pixels format.…”

Forward Modeling and Atmospheric Compensation in hyperspectral data: Experimental analysis from a target detection perspective

“…As is evident, in this paper we are interested in physics-based techniques rather than scene-based empirical approaches [4]. In this framework, though much work has been performed in this area [3,5,6], there is still not enough work that critically discuss differences and advantages of both AC and FM approaches to target detection (i.e., with emphasis on the final detection step in the processing chain).…”