ARMA process for speckled data

Abstract

Synthetic aperture radar (SAR) systems are efficient to deal with remote sensing issues. In contrast, SAR images are affected by speckle noise, due to the use of coherent illumination in their capturing. This noise imposes both a granular interference on such images (precluding their interpretability) and a multiplicative and non-Gaussian nature on their data. The multiplicative modelling is often used to surpass previous difficulties, mainly its particular case the GI0 distribution. In this paper, we introduce a new time series modelling for SAR imagery, called GI0 autoregressive-moving-average (ARMA) process. We derive some of its mathematical properties: score vector, Fisher information matrix, residual analysis and prediction equations. The maximum likelihood estimation procedure for GI0-ARMA parameters is discussed and some asymptotic behaviours for its estimates are quantified by Monte Carlo experiments. Applications to Munich and Foulum SAR actual images are made. Results show the proposed model can outperform the Γ-ARMA model.