Performance Analysis of Structure Factor Model-Based Scatterer Estimation Using the Cramér–Rao Bound

The ultrasound backscatter coefficient (BSC) provides insight into the properties of acoustic scatterers for the quantitative assessment of tissue microstructure. The structure factor model (SFM) is an advanced model, specifically adapted for concentrated media, that allows the extraction of key scatterer parameters from BSC measurements. These include the radius a, volume fraction ϕ, and relative impedance contrast γ<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Z</inf> which were found close to the values of cellular structures at high frequency (~40 MHz). In this study, we focused on deriving the Cramér–Rao bound and comparing it with the mean squared error of the BSC parameters estimated using the SFM to understand the fundamental performance limits of the estimation process. We evaluated the impact of different parameter values on estimation performance in the presence of a Gaussian noise. The results indicate that estimation becomes more challenging for low values of γ<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Z</inf>, a, and ϕ.