Optimal Design of Noise-Enhanced Binary Threshold Detector Under AUC Measure

This letter considers the binary threshold system (TS) based detector for a general binary testing problem. First, the optimal binary TS that maximizes the area under the ROC curve (AUC), where ROC stands for the receiver operating characteristic, is derived. Then the noise-enhanced effect is investigated. The optimal noise that can achieve the maximum AUC is derived and shown to be deterministic. An example is shown to help justify the derived results.