This dissertation shows how noise can benefit nonlinear signal processing. These "stochastic resonance" results include deriving necessary and sufficient conditions for noise benefits, optimal noise distributions, and algorithms that find the optimal or near-optimal noise. The results apply to broad classes of signal and noise distributions. Applications include Neyman-Pearson and maximum-likelihood signal detection in single detectors and in parallel arrays, digital watermark decoding, retinal signal detection, and signal detection in feedback neurons. |