基于贝叶斯准则的随机共振算法研究

刘书君; 杨婷; 唐明春; 王品; 李勇明

doi:10.11999/JEIT160361

基于贝叶斯准则的随机共振算法研究

doi: 10.11999/JEIT160361

基金项目:

重庆市基础与前沿研究(cstc2016jcyjA0134, cstc2016 jcyjA0043)，国家自然科学基金(61501072, 61301224, 41404027, 61108086, 61471072)，重庆市社会事业与民生保障专项(cstc2016 shmszx40002)，中央高校重点基金(CDJZR155507)

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出版历程
- 收稿日期: 2016-04-14
- 修回日期: 2016-10-18
- 刊出日期: 2017-02-19

Study on Stochastic Resonance Algorithm Based on Bayes Criterion

Funds:

The Basic and Advanced Research Project in Chongqing (cstc2016jcyjA0134, cstc2016jcyjA0043), The National Natural Science Foundation of China (61501072, 61301224, 41404027, 61108086, 61471072), The Chongqing Social Undertaking and People,s Livelihood Guarantee Science and Technology Innovation Special Foundation (cstc2016shmszx40002), The Fundamental Research Funds for the Central Universities (CDJZR155507)

摘要

摘要: 该文针对二元假设检验问题，首先在贝叶斯准则的基础上，分析了最小化贝叶斯代价所对应的最优噪声，将贝叶斯代价的最小化问题等价为虚警概率和/或检测概率的最优化。其次，在保证一定虚警概率和检测概率的前提下，建立起能同时改善检测概率和虚警概率的模型。然后分别给出当检测概率一定时虚警概率最小和虚警概率一定时检测概率最大这两种极限情况下对应的最优加性噪声，并对其进行线性凸组合以获得模型所需的最优加性噪声，进一步分析并证明了该模型能够成立的充分条件。再次，获得先验概率已知和未知两种情况下最小化贝叶斯代价时所对应的加性噪声，且当先验知识发生改变时，该算法只需调整加性噪声中一个可变参数即可获得相应的最优贝叶斯代价。最后，结合具体的检测问题，通过仿真验证了所提算法的有效性。
- 信号处理 /
- 贝叶斯准则 /
- 噪声增强模型 /
- 加性噪声 /
- 假设检验
Abstract: 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. Whats 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.
- Signal processing /
- Bayes criterion /
- Noise enhanced model /
- Additive noise /
- Hypothesis testing

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