ENVIRONMETRICS Environmetrics 2005; 16: 13–31 Published online 19 August 2004 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/env.658 The polarimetric G distribution for SAR data analysis Corina C. Freitas 1 , Alejandro C. Frery 2 * ,y and Antonio H. Correia 3 1 Instituto Nacional de Pesquisas Espaciais, Divisa ˜o de Processamento de Imagens, Av. dos Astronautas, 1758, 12227-010 Sa ˜o Jose ´ dos Campos, SP, Brazil 2 Departamento de Tecnologia da Informac ¸a ˜o, Universidade Federal de Alagoas, Campus A. C. Simo ˜es, BR 104 Norte km 14, Bloco 12, 57072-970 Maceio ´, AL, Brazil 3 Centro de Cartografa Automatizada do Exe ´rcito, EPCT km 4,5, 70084-970 Sobradinho, DF, Brazil SUMMARY Remote sensing data, and radar data in particular, have become an essential tool for environmental studies. Many airborne polarimetric sensors are currently operational, and many more will be available in the near future including spaceborne platforms. The signal-to-noise ratio of this kind of imagery is lower than that of optical information, thus requiring a careful statistical modelling. This modelling may lead to useful or useless techniques for image processing and analysis, according to the agreement between the data and their assumed properties. Several distributions have been used to describe synthetic aperture radar (SAR) data. Many of these univariate laws arise by assuming the multiplicative model, such as Rayleigh, square root of gamma, exponential, gamma, and the class of K I distributions. The adequacy of these distributions depends on the detection (amplitude, intensity, complex, etc.), the number of looks, and the homogeneity of the data. In Frery et al. (1997), another class of univariate distributions, called G, was proposed to model extremely heterogeneous clutter, such as urban areas, as well as other types of clutter. This article extends the univariate G family to the multivariate multi-look polarimetric situation: the G p law. The new family has the classical polarimetric multi-look K p distribution as a particular case, but another special case is shown to be more flexible and tractable, while having the same number of parameters and fully retaining their interpretability: the G 0 p law. The main properties of this new multivariate distribution are shown. Some results of modelling polarimetric data using the G 0 p distribution are presented for two airborne polarimetric systems and a variety of targets, showing its expressiveness beyond classical models. Copyright # 2004 John Wiley & Sons, Ltd. key words: speckle; radar polarimetry; synthetic aperture radar; data models; statistics; covariance matrices; radar clutter 1. INTRODUCTION The last decade was marked by the affirmation of SAR images as a tool for Earth monitoring. Several studies were made confirming the relevance of these images, and specific image processing techniques were developed. Some of the applications of SAR imagery to environmental monitoring are deforestation and secondary forest regrowth for carbon cycle assessment, biomass quantification, oil slick detection, crop growth monitoring, flood prediction, and stand-off day-and-night surveillance of military activity in crisis situations. Received 6 February 2003 Copyright # 2004 John Wiley & Sons, Ltd. Accepted 16 November 2003 *Correspondence to: A. C. Frery, Departamento de Tecnologia da Informac ¸a ˜o, Universidade Federal de Alagoas, Campus A. C. Simo ˜es, BR 104 Norte km 14, Bloco 12, 57072-970 Maceio ´, AL, Brazil. y E-mail: frery@tci.ufal.br