基于Bayes决策的奇异点检测

Bayes decision-based singularity detection

针对奇异信号中奇异点的检测和定位问题,提出了一个新的信号奇异点检测方法。根据脉冲奇异点的特点,首先将脉冲奇异点的检测建模为一个分类问题:信号中的脉冲奇异点为一类,非脉冲奇异点为另一类。然后,基于Bayes决策和Neyman-Pearson准则,在限定脉冲奇异点漏检概率的情况下,导出了两类点之间的分界面。据此设计了一个新的脉冲奇异点检测方法——基于Bayes决策的脉冲奇异点检测(BDPSD)方法。模拟及真实信号上的实验结果表明,与基于小波变换的模极大法相比,BDPSD方法在检测质量和定位精度方面都有很大的改善,证明BDPSD是一个有效、可行的信号奇异点检测方法。

This paper proposed a new method for detecting and locating the singularities in the signal. By analyzing the characteristics of singular signal, the detection of the pulse singularities was first modeled as a classification task of two classes： one class consisted of the pulse singularities and the other contained the other points in the signal. Then, based on the Bayes decision rule and Neyman-Pearson criterion, a decision surface was derived by constraining the probability of missed detection for the class containing the pulse singularities to be fixed. As a result, a Bayes Decision Based Pulse Singularity Detection （BDPSD） method was directly developed. The experimental results on a number of artificial and real signals show that the BDPSD method can greatly improve the detection quality and locating accuracy of the pulse singularity, compared with the singularity detection method based on the wavelet transform local modulus maximum theory. This also shows that BDPSD is indeed an effective and practical singularity detection method.