Stochastic resonance noise modified decision solution for binary hypothesis-testing under minimax criterion

In this paper, on the premise that the prior probability is unknown, a noise enhanced binary hypothesis-testing is investigated under the Minimax criterion for a general nonlinear system. Firstly, for lowering the decision risk, an additive noise is intentionally injected to the input and a decision is made under Minimax criterion based on the noise modified output. Then an optimization problem for minimizing the maximum of Bayesian conditional risk under an equality constraint is formulated via analyzing the relationship between the additive noise and the optimal noise modified Minimax decision rule. Furthermore, lemma and theorem are proposed to prove that the optimal noise is a constant vector, which simplifies the optimization problem greatly. An algorithm is also developed to search the optimal constant and the key parameter of detector, and further to determine the decision rule and the Bayes risk. Finally, simulation results about the original (in the absence of additive noise) and the noise-modified optimal decision solutions under Minimax criterion for a sine transform system are provided to illustrate the theoretical results.