双水平集算法及其在函数轮廓估计中的应用  

Dual-Level Set Algorithm and its Application in Function Contour Estimation

作　　者：李晓杉 夏界宁[1,2] LI Xiao-shan;XIA Jie-ning(Hubei Key Laboratory of Earthquake Early Warning,Institute of Seismology,China Earthquake Administration,Wuhan Hubei 430071,China;Engineering Technology Research Center for Earthquake Monitoring and Early Warning Disposal of Major Projects in Hubei Province,Wuhan Hubei 430071,China)

机构地区：[1]中国地震局地震研究所地震预警湖北省重点实验室,湖北武汉430071 [2]湖北省重大工程地震安全监测与预警处置工程技术研究中心,湖北武汉430071

出　　处：《计算机仿真》2022年第5期309-313,共5页Computer Simulation

基　　金：地震星火计划项目(XH17024)。

摘　　要：针对小样本、带噪声随机信号的双水平集估计问题,提出了D_LSE算法。采用构造隐函数的方法,将二维曲线问题转换为三维曲面的水平集估计问题,以高斯过程描述随机信号的统计特性,考虑两个不同阈值,将样本点划分为超水平集、中水平集、次水平集。给出了D_LSE算法的理论框架分析,进行了充分的数值实验,修改了相关参数(精度参数、采样点数)进行对比分析,采用F1分数评价方法给出了算法质量评估结果,将D_LSE算法应用于函数最优化问题。改进了LSE算法,使其更适用于双阈值问题。经过验证,D_LSE算法具有较高分类质量与较低复杂度,能够有效处理小样本空间下随机信号的双阈值问题,可广泛应用于有限随机信号的研究。A D_LSE algorithm is proposed for the problem of Dual-Level Set Estimation of small samples and random signals with noise.The method of constructing implicit function is adopted to transform the two-dimensional curve problem into the level set estimation problem of the three-dimensional surface.The Gaussian process is used to describe the statistical properties of random signals.Two different thresholds are considered,and the sample points are divided into super-level sets,medium-level sets,and sub-level sets.The theoretical framework analysis of the D_LSE algorithm is given.Sufficient numerical experiments were carried out,and relevant parameters(precision parameters,number of sampling points) were modified for comparative analysis.The algorithm quality evaluation result is given by the F1 score evaluation method.D_LSE algorithm is applied to the function optimization problem.LSE algorithm has been improved to make it more suitable for dual-threshold problems.D_LSE algorithm has been verified,has high classification quality and low complexity,and can effectively deal with the double threshold problem of random signals in a small sample space.It can be widely used in the research of limited random signals.

关 键 词：双水平集估计 隐函数 算法质量 优化 

分 类 号：TP301.6[自动化与计算机技术—计算机系统结构]