Noise enhanced detection in restricted Neyman-Pearson framework

Noise enhanced detection is studied for binary composite hypothesis-testing problems in the presence of prior information uncertainty. The restricted Neyman-Pearson (NP) framework is considered, and a formulation is obtained for the optimal additive noise that maximizes the average detection probability under constraints on worst-case detection and false-alarm probabilities. In addition, sufficient conditions are provided to specify when the use of additive noise can or cannot improve performance of a given detector according to the restricted NP criterion. A numerical example is presented to illustrate the improvements obtained via additive noise.