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基于貝葉斯準則的隨機共振算法研究

劉書君,  楊婷,  唐明春,  王品,  李勇明

劉書君, 楊婷, 唐明春, 王品, 李勇明. 基于貝葉斯準則的隨機共振算法研究[J]. 電子與信息學報, 2017, 39(2): 293-300. doi: 10.11999/JEIT160361
引用本文: 劉書君, 楊婷, 唐明春, 王品, 李勇明. 基于貝葉斯準則的隨機共振算法研究[J]. 電子與信息學報, 2017, 39(2): 293-300. doi: 10.11999/JEIT160361
LIU Shujun, YANG Ting, TANG Mingchun, WANG Pin, LI Yongming. Study on Stochastic Resonance Algorithm Based on Bayes Criterion[J]. Journal of Electronics & Information Technology, 2017, 39(2): 293-300. doi: 10.11999/JEIT160361
Citation: LIU Shujun, YANG Ting, TANG Mingchun, WANG Pin, LI Yongming. Study on Stochastic Resonance Algorithm Based on Bayes Criterion[J]. Journal of Electronics & Information Technology, 2017, 39(2): 293-300. doi: 10.11999/JEIT160361

基于貝葉斯準則的隨機共振算法研究

doi: 10.11999/JEIT160361
基金項目: 

重慶市基礎與前沿研究(cstc2016jcyjA0134, cstc2016 jcyjA0043)，國家自然科學基金(61501072, 61301224, 41404027, 61108086, 61471072)，重慶市社會事業(yè)與民生保障專項(cstc2016 shmszx40002)，中央高校重點基金(CDJZR155507)

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: 該文針對二元假設檢驗問題，首先在貝葉斯準則的基礎上，分析了最小化貝葉斯代價所對應的最優(yōu)噪聲，將貝葉斯代價的最小化問題等價為虛警概率和/或檢測概率的最優(yōu)化。其次，在保證一定虛警概率和檢測概率的前提下，建立起能同時改善檢測概率和虛警概率的模型。然后分別給出當檢測概率一定時虛警概率最小和虛警概率一定時檢測概率最大這兩種極限情況下對應的最優(yōu)加性噪聲，并對其進行線性凸組合以獲得模型所需的最優(yōu)加性噪聲，進一步分析并證明了該模型能夠成立的充分條件。再次，獲得先驗概率已知和未知兩種情況下最小化貝葉斯代價時所對應的加性噪聲，且當先驗知識發(fā)生改變時，該算法只需調(diào)整加性噪聲中一個可變參數(shù)即可獲得相應的最優(yōu)貝葉斯代價。最后，結合具體的檢測問題，通過仿真驗證了所提算法的有效性。
    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.
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出版歷程
  • 收稿日期:  2016-04-14
  • 修回日期:  2016-10-18
  • 刊出日期:  2017-02-19

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