Optimal noise benefits in Neyman-Pearson signal detection

We present an algorithm to find near-optimal "stochastic resonance" (SR) noise benefits for Neyman-Pearson (N-P) hypothesis testing or signal-detection problems. The optimal N-P SR noise is no more than two randomized noise realizations when the optimal noise exists. We give necessary and sufficient conditions for the existence of such optimal noise in fixed detectors. There exists a sequence of noise variables whose detection performance limit is optimal when such noise does not exist. An upper bound limits the number of iterations that the algorithm requires to find such near-optimal noise.