G分布族参数估计新方法

摘要

提出了G分布族参数估计的新方法,首先详细分析了当前普遍采用的基于矩估计的G分布族参数估计方法存在的理论缺陷,在此基础上,提出了一种基于Mellin变换的G分布族统一的参数估计方法.该方法以Mellin变换为出发点,详细推导了G分布族中各分布对应的第一个、第二个第二类型的特征函数和它们各自对应的对数矩和对数累积量,最终获得了各分布参数估计简洁的迭代表达式.文中所提方法不但克服了各分布的矩估计器面临的诸多不足,更重要的是把视数同其他参数一样视为待估计的参数,且能够快速、准确地迭代出它们的估计值,保证了G分布族中各分布的拟合精度.以KL(Kullback-Leibler)度量、MSE( Mean Square Error)度量和K-S (Kolmogorov-Smirnov)检验为定量评估准则,对不同分辨率、不同视数的实测SAR图像分别采用文中所提各分布估计器与对应的矩估计器进行拟合实验,实验结果的全面对比分析证明了所提方法的有效性.%A novel parameter estimation method for the family of G distribution is proposed. This paper first analyzes the limitations of the common method of moments (MoM) for estimating the parameters of the family of G distribution. Then, based on the analysis, a fast and robust method of parameter estimation for the family of G distribution based on the Mellin transform is presented. The novel estimation method has the following advantages: firstly, it solves the problems of MoM used to estimate the parameters of the family of G distribution;secondly, it regards the number of looks as a parameter to be estimated, like the other parameters; thirdly, the parameter estimation values can be quickly and accurately acquired, all of which guarantee the family of G distribution' s fitting precision. According to the experiments performed on different clutter areas, with the Kullback-Leibler (KL) distance, mean square error (MSE) and Kolmogorov-Smirnov (KS) test as similarity measurements, the proposed estimators show better fitting performance than the MoM estimators.