title: Modeling ultrasound echoes in skin tissues using symmetric α-stable processes.
abstract: 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.
authors.affiliation: University of Toulouse, Ecole Nationale Supérieure d’Électrotechnique, d’Électronique, d’Informatique, d’Hydraulique et des Télécommunications (IRIT/INP-ENSEEIHT), Toulouse, France. Marcelo.Pereyra@enseeiht.fr
authors.forename: Marcelo
authors.initials: M
authors.lastname: Pereyra
authors.forename: Hadj
authors.initials: H
authors.lastname: Batatia
mesh_terms: D003198:Computer Simulation; D020405:Dermis / Q000000981:diagnostic imaging; D006801:Humans; D008962:Models, Theoretical; D012542:Scattering, Radiation; D012815:Signal Processing, Computer-Assisted; D012867:Skin / Q000000981:diagnostic imaging*; D018709:Statistics, Nonparametric; D014463:Ultrasonography / Q000379:methods*