Statistical modelling of polarimetric SAR data

Abstract

A statistical modelling technique is developed to analyse polarimetric synthetic aperture radar (PolSAR) images. Polarimetric SAR data consists of four complex scattering coefficients at each image location, requiring multivariate modelling techniques, and this work focuses on a simple class of multivariate distributions, the scale mixture of Gaussians.

Three parametric model families of that class, the multivariate Laplacian, K and normal inverse Gaussian distributions, are chosen because closed form expressions have been derived for these models and because their general characteristics, i.e., sparse symmetric non-Gaussian distributions, have been observed in experimental SAR data. The primary aim is to investigate whether any particular model has advantages over the others, or the Gaussian, with a secondary aim of using the produced parametric features for image classification.

The models are characterised and parameter estimation methods are discussed and tested. Each of the models, plus the multivariate Gaussian, are inter-compared and assessed in terms of their goodness-of-fit to both simulated distributions and real PolSAR data. Goodness-of-fit methods are reviewed, and the Log-likelihood method is the preferred choice for this work. The modelling assessment concludes that a single flexible (two parameter) model is sufficient to characterise the majority of the PolSAR data’s statistical distributions.

Analysis of the PolSAR data with a single model produces a new parametric image description, of which the theoretically most relevant terms are extracted. Feature space investigations indicated functional relations between the features and transforms were determined to simplify the data set, effectively converting the two scalar model parameters into the model independent statistical measures of width and non-Gaussianity. The interpretation of the new feature space indicates that it is essentially a multivariate Gaussian analysis with one additional feature of non-Gaussianity.

Initial results produced realistically segmented images, and the main class features are visually consistent with a coarse land cover map of the same area. However, the methods effectiveness cannot be rigourously determined due to inadequate ground truth data.