合成孔径雷达（SAR）作为一种高精度，全天候的遥感技术自问世以来便备受重视，针对合成孔径雷达图像信号的统计学模型更是层出不穷。合成孔径雷达由于成像原理复杂，利用直方图展示数据分布时通常会有相当一部分数值很高的像素点聚集在远离中位数的区域，形成所谓的“重尾”分布，而该领域的一大难点即是针对SAR图像数据的重尾分布特性进行建模并分析。 在针对SAR图像数据提的众多统计学模型中，基于alpha稳定分布的复各向同性模型因为满足格涅坚科的具有帕累托重尾的广义中心极限定理而在该领域备受欢迎。然而鉴于alpha稳定分布本身解析表达式的缺失，学界始终难以进一步推进该模型分支的研究进展。本论文针对现有的alpha稳定模型提出了一类高效的闭式解，并在此基础上提出了更为全面的三参数复各向同性alpha稳定模型。 本论文主要涉及两大贡献点：首先，论文通过对传统矩估计方法的推广，创新性地采用代数式及贝塞尔函数作为实验函数，解决了现有alpha稳定家族普遍面临的解析解缺失问题，同时为其它模型的参数估计问题提供了新思路；其次，论文对现有的复各向同性alpha稳定模型进行推广，提出了名为CIαSR的进阶模型。该模型首次将非对称alpha稳定分布应用到二维场景并提出了有效的类解析解。论文通过对大量模拟数据和真实SAR图像进行测试，证明了该模型在对城市、港口等高度异构的SAR图像分析中取得了更为先进的实验结果，并且通过一系列实验将CIαSR模型参数与实际SAR成像规律联系起来，提高模型的可阐释性。 最后，论文在总结已完成的阶段性工作的同时，提出了对现有模型的进一步推广——即含有beta参量的四参数复各向同性alpha稳定模型的初步表达形式与可能的解析解法，分析了本论文所提出的参数估计方法在该模型下的不足与改进空间，为针对二维alpha稳定模型的未来工作奠定了基础。
Synthetic aperture radar is a powerful remote-sensing technology widely adopted for airborne or spaceborne geo-sensing and surveillance applications due to its significant advantages of high azimuthal resolution and weather-independent operation. However, the complicated imaging mechanism of SAR has risen difficulties in the analysis of image data, since SAR image data generally exhibit a long, thick tail in the histogram, commonly described as the heavy-tail distribution. Numerous statistical models have been theorized and implemented on SAR image processing, but the accurate characterization of heterogeneous SAR image data such as urban scenes remains an obstinate problem that awaits paramount attention. Amongst the versatile statistical models established for SAR images, generalizing alpha-stable distribution to the complex isotropic scenario has been proved as one of the most influential models for heterogeneous SAR data. The success of this particular family of statistical models largely benefits from the superiority of the alpha-stable distribution for satisfying Gnedenko and Kolmogorov‘s generalization of the central limit theorem under heavy-tail assumptions. Yet the lack of analytical representation for the model restricted its further development. This thesis aims to develop closed-form parameter estimators to effectively resolve existing alpha-stable-based SAR image models. On top of that, the thesis also proposes a novel, generalized model based on complex isotropic alpha-stable with improved versatility. Contribution of the thesis is delivered in two sections. In the first section, a novel parameter estimation method is proposed to address the existing alpha-stable models that is otherwise resolved through computation-demanding, data-driven methods. The proposed method generalizes the method of moments with various test functions such as algebraic function or Bessel function to achieve analytical solution with tremendous improvement in calculation efficiency. The proposed estimation method may also provide new insights into the estimation of generic models. The thesis also proposes a novel statistical model named CIαSR that combines the merit of prior works in this field to attain state-of-the-art performance in modelling heterogeneous SAR data, which is for the first time that the asymmetric version of alpha-stable distribution is generalized to a bi-variate scenario. Physical meaning of the CIαSR is extensively studied to reveal the link between the model and SAR image features. The thesis concludes its work with discussions regarding a further advanced complex isotropic alpha-stable model that incorporates as well the beta parameter to control the skewness of distribution. This section analyses the limitation of the generalized method of moments proposed in this work and explores potential solutions to the ultimate model in bi-variate alpha-stable family.
