The product model is assumed to be an appropriate statistical model for multilook polarimetric synthetic radar data (PolSAR). According to this model, the observed signal is considered as the product of independent random variates of a complex Gaussian speckle and a non-Gaussian texture. With different texture distributions, the product model leads to different expressions for the compound distribution considered as an infinite mixture model. In this paper, the maximum-likelihood (ML) estimator is derived to jointly estimate the speckle and texture parameters in the compound distribution model using the multilook polarimetric radar data. In particular, we estimate: 1) the equivalent number of looks; 2) the covariance matrix of the speckle component; and 3) the texture distribution parameters. The expectation-maximization algorithm is developed to compute the ML estimates of the unknown parameters. The hybrid Cramer-Rao bounds (HCRBs) are also derived for these parameters. First, a general HCRB expression is derived under an arbitrary texture distribution. Then, this expression is simplified for a specific texture distribution. The performance of the ML is compared with the performance of other known estimators using the simulated and real multilook PolSAR data. For real data, a goodness of fit of multilook PolSAR data histograms is used to assess the fitting accuracy of the compound distributions using different estimators. Index Terms-Expectation-maximization (EM) algorithm, maximum likelihood (ML), multilook polarimetric synthetic aperture radar (PolSAR) data, parameter estimation, product model. N. Bouhlel was with the Laboratoire des Sciences du Numériques (LS2N), École Centrale de Nantes (ECN), 44300 Nantes, France. He is now with the SAR & Hyperspectral multi-modal Imaging and sigNal processing, Electromagnetic modeling team (SHINE),
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