Random Projection-Based Sub-Pixel Target Detection for Hyperspectral Image With t-Distribution Background

Abstract

Sub-pixel target detection is a challenging task in hyperspectral image processing. Most statistical detectors rely on the estimation of the background covariance matrix. In contrast to the traditional approaches by adopting global covariance matrix estimation from all image pixels, the local estimation within image segments can significantly improve detection performance for complex backgrounds in many scenarios. However, the local covariance matrix estimate may be unstable due to the high spectral dimension of the hyperspectral image, especially when the size of the local sample representing background pixels, is relatively small. In this work, a random projection (RP) is employed to reduce the spectral dimension, and a spectral similarity-based dual-window (SSDW) strategy is suggested to appropriately extract the local background statistical properties. So, a kind of sub-pixel target detector is developed in a statistical hypothesis testing framework for different observation models under t-distribution background. Especially, the projection dimension is determined without any extra experiment or training and ensures asymptotic optimality of detection power under some conditions. The superior performance of the proposed detectors is demonstrated by some synthetic data and real hyperspectral images.