  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.
