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.

翻译：合成孔径雷达（SAR）是一种高效且广泛应用的遥感工具。然而，从SAR图像中提取的数据受到散斑污染，这阻碍了基于加性正态分布噪声假设的技术应用。描述此类数据最成功的方法之一是乘性模型，其中强度可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。尽管已有多种$\mathcal{G}^0_I$参数估计方法被提出，但目前尚无研究探索该模型的回归结构。这种结构可使我们根据可用数据推断未观测值。在本工作中，我们提出了一种$\mathcal{G}^0_I$回归模型，并用其描述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：费舍尔信息矩阵、残差度量及影响分析工具。提出了最大似然点估计与区间估计方法，并通过蒙特卡洛实验进行评估。模拟数据与实际数据的分析结果表明，新模型对SAR图像分析具有重要价值。