Estimation of the Scatterer Size Distributions in Quantitative Ultrasound Using Constrained Optimization

Quantitative ultrasound (QUS) parameters such as the effective scatterer diameter (ESD) reveal tissue properties by analyzing ultrasound backscattered echo signal. ESD can be attained through parametrizing backscatter coefficient using form factor models. However, reporting a single scatterer size cannot accurately characterize a tissue, particularly when the media contains scattering sources with a broad range of sizes. Here we estimate the probability of contribution of each scatterer size by modeling the measured form factor as a linear combination of form factors from individual sacatterer sizes. We perform the estimation using two novel techniques. In the first technique, we cast scatterer size distribution as an optimization problem, and efficiently solve it using a linear system of equations. In the second technique, we use the solution of this system of equations to constrain the optimization function, and solve the constrained problem. The methods are evaluated in simulated backscattered coefficients using Faran theory. We evaluate the robustness of the proposed techniques by adding Gaussian noise. The results show that both methods can accurately estimate the scatterer size distribution, and that the second method outperforms the first one.