Automated threshold determination for a family of matched subspace filters for target detection in hyperspectral images

Abstract

The detection of subpixel targets in hyperspectral images is complicated by interference arising from other background materials. This paper describes three target detection algorithms implemented in Data Fusion Corporation's HYPERTOOLS, a suite of hyperspectral image analysis tools. The matched subspace filter (MSF) is a generalized likelihood ratio test designed to detect target signatures while suppressing known interference signatures in a hyperspectral image. The fill-factor matched subspace filter (FFMSF) and the mixture-modeled matched subspace filter (MMMSF) extend the MSF by fusing geometrical (i.e., material abundance) and statistical (i.e., an assessment of the applicability of a linear replacement mixture model) information with the MSF output. The MSF, FFMSF, and MMMSF require one, two, and three thresholds, respectively. Automated means of determining these thresholds are proposed and justified. The MSF is further designed to allow the processing of multirank target and interference spectral matrices. As more information about a target or targets is included in the MSF, the detection performance of the MSF is expected to improve. If the target and/or interference matrices are singular or nearly singular, however, the performance of the MSF may instead be degraded. Singular value decomposition (SVD) may be employed to prepare spectral data matrices for optimal performance of the MSF. Although the use of singular value decomposition for preprocessing data matrices is well-known in signal processing, the determination of thresholds for the selection of left-singular vectors spanning the data space remains more of “an art.” An automated method for determining the number of useful left-singular vectors is proposed based on an interpretation of the singular values and on the analysis of the dimensions of the measurement space.