Unmixing $K$ -Gaussians With Application to Hyperspectral Imaging

Abstract

In this paper, we consider the parameter estimation of K-Gaussians, given convex combinations of their realizations. In the remote sensing literature, this setting is known as the normal compositional model (NCM) and has shown promising gains in modeling hyperspectral images. Current NCM parameter estimation techniques are based on Bayesian methodology and are computationally slow and sensitive to their prior assumptions. Here, we introduce a deterministic variant of the NCM, named DNCM, which assumes that the unknown mixing coefficients are nonrandom. This leads to a standard Gaussian model with a simple estimation procedure, which we denote by K-Gaussians. Its iterations are provided in closed form and do not require any sampling schemes or simplifying structural assumptions. We illustrate the performance advantages of K-Gaussians using synthetic and real images, in terms of accuracy and computational costs in comparison to state of the art. We also demonstrate the use of our algorithm in hyperspectral target detection on a real image with known targets.