具有极端变异性的斑点数据回归模型
Regression Model for Speckled Data with Extremely Variability
AI总结：
针对SAR斑点数据，本文提出了$\mathcal{G}^0_I$回归模型，推导了其理论性质并提出了最大似然估计方法，模拟与实际数据验证表明该模型能有效用于SAR图像分析。
摘要：
合成孔径雷达（SAR）是一种高效且广泛使用的遥感工具。然而，从SAR图像中提取的数据会受到斑点噪声的污染，这使得基于加性和正态分布噪声假设的技术无法应用。描述此类数据最成功的方法之一是乘性模型，其强度可以遵循多种具有正支撑的分布。$\mathcal{G}^0_I$ 模型是其中最成功的模型之一。尽管已经提出了几种针对 $\mathcal{G}^0_I$ 参数的估计方法，但目前尚无工作探讨该模型的回归结构。这种结构能够允许我们从可观测值推断未观测值。在本研究中，我们提出了一种 $\mathcal{G}^0_I$ 回归模型，并用它来描述来自其他极化通道强度的影响。我们推导了新模型的一些理论性质：Fisher信息矩阵、残差度量以及影响工具。我们提出了最大似然点估计和区间估计方法，并通过Monte Carlo实验进行了评估。模拟和实际数据的结果表明，新模型对SAR图像分析很有帮助。
英文摘要：
Synthetic aperture radar (SAR) is an efficient and widely used remote sensing tool. However, data extracted from SAR images are contaminated with speckle, which precludes the application of techniques based on the assumption of additive and normally distributed noise. One of the most successful approaches to describing such data is the multiplicative model, where intensities can follow a variety of distributions with positive support. The $\mathcal{G}^0_I$ model is among the most successful ones. Although several estimation methods for the $\mathcal{G}^0_I$ parameters have been proposed, there is no work exploring a regression structure for this model. Such a structure could allow us to infer unobserved values from available ones. In this work, we propose a $\mathcal{G}^0_I$ regression model and use it to describe the influence of intensities from other polarimetric channels. We derive some theoretical properties for the new model: Fisher information matrix, residual measures, and influential tools. Maximum likelihood point and interval estimation methods are proposed and evaluated by Monte Carlo experiments. Results from simulated and actual data show that the new model can be helpful for SAR image analysis.
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