Adaptive non-Zero Mean Gaussian Detection and Application to Hyperspectral Imaging

TL;DR

This paper develops adaptive detection methods for hyperspectral imaging when the background mean vector is unknown, deriving closed-form false-alarm regulation formulas and validating them through simulations and real data.

Contribution

It introduces novel adaptive detectors that handle unknown background means in hyperspectral imaging, ensuring constant false alarm rates with theoretical and empirical validation.

Findings

Closed-form expressions for false-alarm regulation derived.

Detectors achieve Constant False Alarm Rate property.

Validated effectiveness on real hyperspectral data.

Abstract

Classical target detection schemes are usually obtained deriving the likelihood ratio under Gaussian hypothesis and replacing the unknown background parameters by their estimates. In most applications, interference signals are assumed to be Gaussian with zero mean or with a known mean vector that can be removed and with unknown covariance matrix. When mean vector is unknown, it has to be jointly estimated with the covariance matrix, as it is the case for instance in hyperspectral imaging. In this paper, the adaptive versions of the classical Matched Filter and the Normalized Matched Filter, as well as two versions of the Kelly detector are first derived and then are analyzed for the case when the mean vector of the background is unknown. More precisely, theoretical closed-form expressions for false-alarm regulation are derived and the Constant False Alarm Rate property is pursued to allow the detector to be independent of nuisance parameters. Finally, the theoretical contribution is validated through simulations and on real hyperspectral scenes.