First-Order and Second-Order Detectors for Matched Subspace Detection on Graphs

Abstract

Matched subspace detection (MSD) is a powerful tool recently generalized from Euclidean data to graph signal processing. However, existing graph-based MSD methods are often limited by assumptions of known noise variance and by overlooking the statistical properties of the graph Fourier transform (GFT) coefficients thereby limiting practical applicability. To address these gaps, this paper introduces two novel generalized likelihood ratio (GLR) tests for graph-based MSD. The first-order GLR test operates without knowledge of the noise variance and the GFT coefficients by estimating them via maximum likelihood. The second-order GLR test further incorporates a Gaussian prior on the GFT coefficients, yielding a more powerful and comprehensive statistical model. Experimental results demonstrate that our proposed detectors are robust and effective, particularly in challenging noisy scenarios, highlighting their importance for detection tasks in graph signal processing.