Gabor representation and signal detection

Abstract

A common assumption in studies on Gabor based signal detection is that the Gabor representation of the signal is sparse, in the sense that the vector of Gabor coefficients contains only a few nonzero entries at known locations. Under this assumption the problem of detecting a Gabor transient becomes the problem of detecting a subspace signal in background noise. Extending the theory of matched subspace detection to complex signals, we derive matched subspace detectors for this problem and discuss their optimality. We investigate the sensitivity of matched subspace detectors to mismatch in the model parameters. Motivated by the sensitivity analysis, we develop robust matched subspace detectors and analyze their performance.