4262 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 54, NO. 7, JULY 2016 Evaluation of ICA-Based ICTD for PolSAR Data Analysis Using a Sliding Window Approach: Convergence Rate, Gaussian Sources, and Spatial Correlation Leandro Pralon, Gabriel Vasile, Member, IEEE, Mauro Dalla Mura, Member, IEEE, Jocelyn Chanussot, Fellow, IEEE, and Nikola Besic Abstract—Polarimetric incoherent target decomposition aims at accessing physical parameters of illuminated scatters through the analysis of the target coherence or covariance matrix. In this framework, independent component analysis (ICA) was recently proposed as an alternative method to eigenvector decomposition to better interpret non-Gaussian heterogeneous clutter (inherent to high-resolution synthetic aperture radar systems). Until now, the two main drawbacks reported of the aforementioned method are the greater number of samples required for an unbiased estimation, when compared to the classical eigenvector decompo- sition, and the inability to be employed in scenarios under the Gaussian clutter assumption. In this paper, both drawbacks are analyzed. First, a Monte Carlo approach is performed in order to investigate the bias in estimating Touzi’s target-scattering-vector- model parameters when ICA is employed. Simulated data and a RAMSES X-band image acquired over Brétigny, France, are taken into consideration to investigate the bias estimation under different scenarios. Finally, the performance of the algorithm is also evaluated under the Gaussian clutter assumption and when spatial correlation is introduced in the model. Index Terms—Bias evaluation, independent component analysis (ICA), polarimetric incoherent target decomposition (ICTD). I. I NTRODUCTION P OLARIMETRIC target decomposition is one of the most powerful and widespread tools for polarimetric synthetic aperture radar (PolSAR) image interpretation. The analysis of the interaction between the illuminated area and the transmitted waveform, to each polarimetric state of the latter, allows for a better prediction of the basic scattering mechanisms present Manuscript received May 28, 2015; revised November 30, 2015; accepted January 18, 2016. Date of publication May 11, 2016; date of current version May 24, 2016. L. Pralon is with the Brazilian Army Technological Center, Rio de Janeiro- RJ 23020-470, Brazil, and also with the Grenoble Image Speech Signal Automatics Laboratory, Centre National de la Recherche Scientifique/l’Institut Polytechnique de Grenoble (Grenoble INP), Grenoble 38402, France (e-mail: pralon@ctex.eb.br). G. Vasile, M. D. Mura, and J. Chanussot are with the Grenoble Image Speech Signal Automatics Laboratory, Centre National de la Recherche Scientifique/ l’Institut Polytechnique de Grenoble (Grenoble INP), Grenoble 38402, France. N. Besic is with the Environmental Remote Sensing Laboratory (LTE), Ecole Polytechnique Federale de Lausanne, Lausanne 1015, Switzerland. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TGRS.2016.2538900 on the scene and to more efficiently propose classification, detection, and geophysical parameter inversion algorithms. Many methods have been proposed in the literature to both decompose an image pixel into basic target vectors as well as to correctly retrieve quantitative information from them (parame- terization). Concerning the latter, Cloude and Pottier’s param- eters (entropy, alpha, and anisotropy) [3] and Touzi’s target scattering vector model (TSVM) [2] are the most employed ones, whose usefullness have already been demonstrated by several authors. Regarding the decomposition, the algorithms are mainly classified in either coherent, if they are based on the scattering matrix analysis, or incoherent, if their interest lies in the Hermitian, semidefinite positive coherence or covari- ance matrix. Incoherent target decomposition (ICTD) theory assumes that the scattering process in most natural media is a combination of coherent speckle noise and random vector scattering effects. Therefore, not only a statistical analysis is often required, but also, it is a common practice to associate to the imaging cell the concept of average or dominant scat- tering mechanisms [1]. The eigenvector-based ICTD manages to decompose an image pixel into the three most dominant scatters from the averaged coherence matrix. Furthermore, it has an intrinsic property that the derived scatters are orthogonal and uncorrelated, which, for Gaussian clutters, also means independence. The drawback of this kind of method emerges when the clutter is not Gaussian or not composed by orthogonal mechanisms, situations where the performance of the algorithm could be compromised. Regarding the former, when low-resolution multivariate SAR is under investigation, the central limit theorem is taken into consideration, and the data can be locally modeled by a multi- variate zero-mean circular Gaussian stochastic process, which is completely determined by its covariance matrix. Neverthe- less, high-heterogeneous scenes (inherent to high-resolution systems) may eventually lead to non-Gaussian clutter modeling. Spherically invariant random vectors (SIRVs) have then been constantly employed for modeling high-resolution polarimetric synthetic aperture radar (POLSAR) data [11]. The SIRV is a multiplicative model expressed as a product between the square root of a scalar positive quantity (texture) and the description of an equivalent homogeneous surface (speckle). Despite of its widespread use among the community, many authors raised the 0196-2892 © 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.