Study of compound generalized Nakagami–generalized inverse Gaussian distribution and related densities: application to ultrasound imaging

<Para ID="Par1">A new theoretical probability distribution generalized Nakagami–generalized inverse Gaussian distribution (GN–GIGD) is proposed to model the backscattered echo envelope in ultrasound imaging. This new probability distribution is a composite distribution derived by compounding generalized Nakagami (GN) and generalized inverse Gaussian (GIG) distributions. It is known in the literature that GN distribution better captures the randomness in backscattered echo envelope where as GIG distribution provides better modeling of randomness in average power. The proposed distribution is a generalized distribution and several special cases results in several composite distributions in which some are able to characterize RF envelope in ultrasound imaging. The expression of signal to noise ratio for these relevant cases are obtained. The efficacy of proposed GN–GIGD in relation to Nakagami Gamma and Nakagami–generalized inverse Gaussian distributions is established by fitting these distributions over Field II simulation generated uncompressed echo envelope data of kidney and fetus phantoms for different scattering concentrations. It is found that the proposed GN–GIGD performs better then the other distributions in terms of Jensen Shannon divergence goodness of fit. Copyright Springer-Verlag Berlin Heidelberg 2015