Regression model for speckled data with extreme variability

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 $G_I^0$ model is among the most successful ones. Although several estimation methods for the $G_I^0$ 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 $G_I^0$ 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.