Statistical limitations of the effective density based on the K-distribution [echography]

In echography, the radiofrequency signal envelope which comes from non-periodic media with low density or clustered scatterers shows deviations from Rayleigh statistics, It has been shown recently that the K-distribution is then a good model. This model contains a parameter, α, from which an estimation of the effective density of scatterers in media can be made. In this work, some statistical properties of this estimator, i.e. its bias and variance versus the sample size, are studied. The bias and variance have been analytically calculated and compared with numerical simulation for media with scatterers densities ranging in a 1 to 20 ratio. The effects induced by attenuation and noise are also discussed. These results give the limits of the experimental conditions for which the bias and variance of α estimation are acceptable. The effective density of 3 types of foams has been estimated and compared with other acoustical parameters