基于Mellin变换的K分布参数估计新方法

A Novel Parameter Estimation Method for the K Distribution Based on the Mellin Transform

K分布是目前SAR图像建模领域应用最广泛、最著名的统计模型之一.当前普遍采用的是基于矩估计的参数估计方法,但其存在等效视数值需要经验获取、容易出现错误估计以及造成K分布失效等问题.为此,本文提出了一种基于Mellin变换的K分布参数估计新方法.该方法以Mellin变换为基础,详细推导了K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K分布参数估计简洁的迭代表达式.所提方法不但有效克服了K分布失效的问题,更为重要的是,其把视数同形状参数、尺度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K分布的拟合精度.实验结果证明了所提方法的有效性.

The K distribution,one of the most important distributions for modeling synthetic aperture radar（SAR） data,shows great capability of fitting different clutter regions,such as the ocean area,the forest and the cropland with growing crops etc.However,the classical method of moments（MoM） for estimating the parameters of the K distribution,which is widely adopted,has the limitations of acquiring the number of looks by prior knowledge of the SAR image,poor estimation veracity and leading the invalidation of the K distribution and so on.Therefore,this paper proposes a fast and robust method of parameter estimation for the K distribution based on the Mellin transform.The novel method has the following advantages：firstly,it gets rid of the problem of invalidating the K distribution;secondly,it regards the number of looks as a parameter to be estimated,like the shape and scale parameters;thirdly,estimation values of the three parameters can be quickly and accurately acquired,all of which guarantee the K distribution＇s fitting precision.According to the results of the experiments,the proposed estimator shows better fitting performance than the MoM estimators.