Effective Density Estimators Based on the K Distribution: Interest of Low and Fractional Order Moments

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Abstract
The K distribution is an efficient model to the nonRayleigh statistics of the envelope of backscattered signals in random media. This modeling leads to estimate a parameter of effective density by means of the calculation of statistical moments of the envelope signal. In this study, we propose a mathematical analysis of an effective density estimator previously used and based on superior order moments. In order to improve the effective density estimate, we propose several estimators based on low and fractional order moments. The performances of these estimators are evaluated both with simulated signals and in an experimental context with synthetic foams. Estimators based on low and fractional moments appear to be more robust than superior moment-based estimator and an improvement of the spatial resolution of the estimate can be obtained. Results also confirm the capability of the effective density parameter to characterize the spatial distribution of scattering structures.