The optimal noise that minimizes Bayes risk for a binary hypothesis testing problem is analyzed firstly. As a result, the minimization of Bayes risk can be equivalent as the optimization of the detection probability and/or false alarm probability . Secondly, a noise enhanced model, which can increase and decrease simultaneously, is established under the premise of maintaining predefined and . Then the optimal additional noise of this model is obtained by a convex combination of two optimal noises of two limit cases, which are the minimization of with maintaining the predefined and the maximization of with maintaining the predefined , respectively. Furthermore, the sufficient conditions for this model are given. What’s more, the additive noise that minimizes the Bayes risk is determined when the prior probabilities are known or not, and the corresponding additive noise can be obtained by recalculating a parameter only if the prior information changes. Finally, the availability of algorithm is proved through the simulation combined with a specific detection example.
刘书君,杨婷,唐明春,王品,李勇明. 基于贝叶斯准则的随机共振算法研究[J]. 电子与信息学报, 2017, 39(2): 293-300.
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