拖尾Rayleigh分布：基本性质及其应用

Heavy-tailed Rayleigh Distribution:Basic Properties and Their Applications

针对使用拖尾Rayleigh分布对合成孔径雷达(Synthetic aperture radar,SAR)幅值图像建模时遇到的问题,本文讨论了拖尾Rayleigh分布的相关性质及其应用.首先,基于负数阶矩理论,本文提出了拖尾Rayleigh分布的比值估计、对数矩估计和迭代对数矩估计三种参数估计方法,并通过Monte Carlo仿真实验比较了它们的估计性能.其次,本文使用渐近级数计算拖尾Rayleigh分布的概率密度函数,基于插值多项式拟合,提出了高效计算密度函数的三步方法.最后,本文给出了SAR幅值图像基于拖尾Rayleigh分布的建模实例。结果表明,和一般的Rayleigh分布相比,拖尾Rayleigh分布可以精确反映SAR幅值图像尖峰厚尾的统计特征,因此它是SAR幅值图像建模的有效工具。

In order to solve the problems appearing in the heavy-tailed Rayleigh modeling of synthetic aperture radar （SAR） amplitude images, some basic properties and their applications are introduced for the heavy-tailed Rayleigh distribution in this paper. Firstly, based on the negative-order moments, ratio method, logarithmic moment method and iterative logarithmic moment method are presented to estimate the parameters of the heavy-tailed Rayleigh distribution, and their performances are compared according to Monte Carlo simulations. Secondly, the asymptotic series are used to evaluate the density function of heavy-tailed Rayleigh distribution, and an efficient three-step method is proposed using the interpolating polynomial fit. Lastly, real SAR amplitude images are modeled with the heavy-tailed Rayleigh distribution. Compared to the conventional Rayleigh distribution, the heavy-tailed Rayleigh distribution can accurately reflect the high peak and heavy tail of SAR amplitude images, so it is a useful tool for the modeling of SAR amplitude images.