With the improvements in modern radar resolution,the Gaussian-fluctuation model based on the central limit theorem does not accurately describe the scattering echo from targets.In contrast,the heavytailed Rayleigh distribution,based on the generalized central limit theorem,performs well in modeling the synthetic aperture radar(SAR) images,whereas its application to multi-look image processing is difficult.We describe successful modeling of multilook polarimetric SAR images with the heavy-tailed Rayleigh distribution and present novel parameter estimators based on matrix log-cumulants for the heavy-tailed Rayleigh distribution including the equivalent number of looks(ENL).First,a compound variable of heavy-tailed Rayleigh distribution is divided into a product of a positive alpha-stable variable and a complex Gaussian variable.The parameter estimations of the characteristic exponent and scale parameter based on log-cumulants in a single polarization channel are then derived.Second,the matrix log-cumulants(MLCs) for full polarization in multilook images are obtained,which can be applied to estimate model parameters.Therefore,a novel ENL estimator based on MLC is presented that describes the model more precisely.Extended to all other multivariable product models,this estimator performs better than existing methods.Finally,calculations on both simulated and real data are performed that give good fits with theoretical results.Multilook processing in one image with a fixed pixel number can improve parameter estimations over single-look processing.Our heavy-tailed Rayleigh model with its parameter estimation provides a new method to analyze the multilook polarimetric SAR images for target detection and classification. With the improvements in modern radar resolution, the Gaussian-fluctuation model based on the central limit theorem does not accurately describe the scattering echo from targets. In contrast, the heavytailed Rayleigh distribution, based on the generalized central limit theorem, performs well in modeling the synthetic aperture radar (SAR) images, and its application to multi-look image processing is difficult. We describe successful modeling of multilook polarimetric SAR images with the heavy-tailed Rayleigh distribution and present novel parameter estimators based on matrix log-cumulants for the heavy -tailed Rayleigh distribution including the equivalent number of looks (ENL). First, a compound variable of heavy-tailed Rayleigh distribution is divided into a product of a positive alpha-stable variable and a complex Gaussian variable. The parameter estimations of the characteristic exponent and scale parameter based on log-cumulants in a single polarization channel are then derived. Second, the m atrix log-cumulants (MLCs) for full polarization in multilook images are obtained, which can be applied to estimate model parameters. Before, a novel ENL estimator based on MLC is presented that describes the model more precisely. Extended to all other multivariable product models , this estimator performs better than existing methods. Finally, calculations on both simulated and real data are performed that give good fits with theoretical results. Multilook processing in one image with a fixed pixel number can improve parameter estimations over single-look processing. -tailed Rayleigh model with its parameter estimation provides a new method to analyze the multilook polarimetric SAR images for target detection and classification.