Burr Distribution Describes Ultrasound Speckle Statistics of Soft Biological Tissues

Estimates of speckle statistics of soft tissues provide quantitative measures for characterizing the underlying tissues. The statistical behavior of speckle has been studied for over 100 years, evolving into a number of well-established statistical models such as the Rayleigh. In this study, we propose a new framework for describing the speckle statistics of soft biological tissues, focusing on the presence of multiscale (rather than identical) scatterers with different shapes (cylindrical, spherical, or irregular inhomogeneities) within tissues. In this framework, we assume that the size distributions of any set of multiscale subresolved scatterers follows a power law distribution, leading to a two-parameter model for describing the underlying speckle statistics (probability density function or PDF), characterized by a key power law exponent and a scale parameter. The derivation under this framework results in the Burr distribution, which has not previously been employed in the field of medical imaging. We tested this hypothesis using 3D simulations of ultrasound scans from multiscale cylindrical or spherical scattering structures, and ultrasound scans from in vivo and ex vivo soft tissues. The Burr distributions provided promising results for describing speckle statistics in simulations and tissue scans, with its two parameters showing sensitivity to the changes in scattering media.