The performance of deterministic matched subspace detectors when using subspaces estimated from noisy, missing data

We consider a matched subspace detection problem where a signal vector residing in an unknown low-rank k subspace is to be detected using a subspace estimate obtained from noisy signal-bearing training data with missing entries. The resulting subspace estimate is inaccurate due to limited training data, missing entries, and additive noise. Recent results from random matrix theory (RMT) precisely quantify these subspace estimation errors for the setting where the signal has low coherence. We analytically quantify the ROC performance of the resulting plug-in detector and derive a new detector which explicitly accounts for these subspace estimation errors. The realized increase in performance can be attributed to the new detector only using the k
_eff
≤ “informative” signal subspace components. The fraction of observed entries determines k
_eff
via a simple relationship that we describe. Detection performance better than random guessing is only achievable when the percent of observed data is above a critical threshold which we explicitly characterize.