POLSAR图像杂波L分布建模及其参数估计

基于乘积模型的杂波统计建模是进行高分辨极化合成孔径雷达(POLSAR)图像非均匀区域杂波统计特性分析的有效方法,其核心在于纹理分量随机分布的类型选择.广义伽马分布(GΓD)是一种普适性很强的分布类型,Weibull分布、伽马分布、逆伽马分布等都是GΓD分布的特例,因此基于GΓD分布的图像乘性杂波建模既满足杂波建模的高精度要求,同时成为各种雷达杂波辨识的有效工具.本文首先推导了服从GΓD分布的随机变量的高阶矩特征及其对数累积量(MLC),利用纹理分量服从GΓD分布情形构建了乘积相干斑模型,得到了适用于POLSAR图像处理的L分布杂波多视处理的协方差矩阵的概率分布函数,同时推导了其高阶矩特征及其对数累积量,提出了基于对数累积量的L分布参数估计新方法.针对样本数较少的情况下对数累积量参数估计失效问题提出了基于混合矩(MME)的参数估计方法来解决.然后给出了不同分布的高阶矩和对数累积量,通过二三阶对数累积量关系图辨析了常用分布与L分布的内在关系,得到了L分布是目前乘积模型中适用范围较为广泛的统计分布的结论.最后用仿真数据验证了理论推导的正确性,并将基于对数累积量的参数估计方法与已有方法进行了比较,结果证明新参数估计方法具有更高的估计精度和运算效率;另外,还用实测数据进行了统计模型检验,其结果验证了理论推导的正确性.极化SAR中多视图像L分布杂波的统计建模及其参数估计方法为极化SAR目标检测和识别等领域的新技术研究提供了新手段.

Modeling polarimetric SAR images with L-distribution and novel parameter estimation method

The statistical modeling based on the product model is an effective method to analysis high-resolution POLSAR images, whlie the core is the selection of texture model. The generalized gamma distribution （GFD） is a generic model which includes Weibull distribution, Gamma distribution and Inverse Gamma distribution. So we can expect that if we modeling the texture component with GFD, the product model will not only accurate, but also generally to the POLSAR images modeling. In this paper, we firstly derive the high moments and matrix log-cumulants （MLCs） of the GFD random variables. Then we find that we can model the POLSAR images with L-distribution when the GFD is applied to the texture component of the product model. Also we get a novel estimation based on the MLCs of L-distributed random variables. In this paper, a parameter estimation method based on the mixed moments is proposed, in order to solve the problem that the estimation based on matrix logocumulants is invalid when the number of samples is small. What is more, the manifolds of theoretical MLCs for several distributions show the intrinsic relationship of the widespread distribution and L-distribution which can prove the universal of the latter. Finally, the correctness of modeling with L-distribution and the validity of the derivation of the estimator are verified though simulated data and real data.