Adaptive sub-pixel target detection in hyperspectral images based on the stochastic mixing model

Abstract

This paper addresses the problem of sub-pixel target detection in hyperspectral images assuming that the target spectral signature is deterministic and known. Hyperspectral image pixels are frequently a combination or mixture of disparate materials or components. The need of a quantitative pixel decomposition arises in many civilian and military applications such as material classification, anomaly and target detection. The Linear Mixing Model (LMM) is a widely used method in hyperspectral data analysis. It represents a mixed pixel as the sum of the spectra of known pure materials, called endmembers, weighted by their relative concentrations called abundance coefficients. However, the LMM does not take into account the natural spectral variability of the endmembers. This variability is well represented by the Stochastic Mixing Model (SMM), which provides a model for describing both mixed pixels in the scene and endmember spectral variations through a statistical model. Modeling the background spectrum as a Gaussian random vector with known mean spectrum and unknown covariance matrix, a novel SMM based Detector (ASMMD) is derived in this paper. The ASMMD theoretical performances are evaluated in a case study referring to actual conditions. The analysis is conducted by estimating the ASMMD parameters on an experimental data set acquired by the AVIRIS hyperspectral sensor and the results are compared with the ones achieved by the Adaptive Matched Subspace Detector (AMSD), based on the LMM.