Detection Theory for Union of Subspaces

TL;DR

This paper develops detection methods based on generalized likelihood ratio tests for signals modeled as unions of subspaces, providing performance bounds and validating results through experiments on synthetic and real data.

Contribution

It introduces bounds on GLRT performance for union of subspaces detection and offers a geometric interpretation validated by extensive experiments.

Findings

Performance bounds depend on subspace geometry

GLRTs effectively detect active subspaces

Experimental validation confirms theoretical insights

Abstract

The focus of this paper is on detection theory for union of subspaces (UoS). To this end, generalized likelihood ratio tests (GLRTs) are presented for detection of signals conforming to the UoS model and detection of the corresponding "active" subspace. One of the main contributions of this paper is bounds on the performances of these GLRTs in terms of geometry of subspaces under various assumptions on the observation noise. The insights obtained through geometrical interpretation of the GLRTs are also validated through extensive numerical experiments on both synthetic and real-world data.