Generalized likelihood ratio test detector for a modified replacement model target in a multivariate t-distributed background

TL;DR

This paper develops a GLRT detector for a subpixel target in multispectral images with a multivariate t-distributed background, extending previous Gaussian-based models to better handle heavy-tailed data.

Contribution

It derives a closed-form GLRT detector for a modified replacement model in a multivariate t-distributed background, improving detection performance over Gaussian-based methods.

Findings

EC-based detector outperforms Gaussian-based detectors in simulations.

Performance depends on target strength and background occlusion.

The new detector is more robust to heavy-tailed background distributions.

Abstract

A closed-form expression is derived for the generalized likelihood ratio test (GLRT) detector of a subpixel target in a multispectral image whose area and brightness are both unknown. This expression extends a previous result (which assumed a Gaussian background distribution) to a fatter tailed elliptically-contoured (EC) multivariate t-distributed background. Numerical experiments with simulated data indicate that the EC-based detector outperforms the simpler Gaussian-based detectors, and that the relative performance of the new detector, compared to other EC-based detectors, depends on the regime of target strength and background occlusion.