Stochastic resonance and improvement by noise in optimal detection strategies

A stochastic resonance effect, under the form of a noise-improved performance, is shown feasible for a whole range of optimal detection strategies, including Bayesian, minimum error-probability, Neyman-Pearson, and minimax detectors. In each case, situations are demonstrated where the performance of the optimal detector can be improved (locally) by raising the level of the noise. This is obtained with a nonlinear signal-noise mixture where a non-Gaussian noise acts on the phase of a periodic signal.