Modeling ultrasound echoes in skin tissues using symmetric α-stable processes

Starting from the widely accepted point-scattering model, this paper establishes, through analytical developments, that ultrasound signals backscattered from skin tissues converge to a complex Levy flight random process with non- Gaussian α-stable statistics. The envelope signal follows a generalized (heavy-tailed) Rayleigh distribution. It is shown that these signal statistics imply that scatterers have heavy-tailed power-law cross sections. This model generalizes the Gaussian framework and provides a formal representation for a new case of non-Gaussian statistics, in which both the number of scatterers and the variance of their cross sections tend to infinity. In addition, analytical expressions are derived to relate the α-stable parameters to scatterer properties. Simulations show that these expressions can be used as rigorous interpretation tools for tissue characterization. Several experimental results supported by excellent goodness-of-fit tests confirm the proposed analytical model. Finally, these fundamental results set the basis for new echography processing methods and quantitative ultrasound characterization tools.