Ultrasound echoes, backscattered from an inhomogeneous medium, have the character of a random signal, which is mainly responsible for the speckle pattern observed in the images. These random signals, nevertheless. bear information related to the random scattering structure of the medium. If the medium is represented as a uniform matrix material with scattering bodies distributed randomly, then the scatterer number density can be estimated from the second and higher statistical moments of the signal. However, the estimate is biased because the statistical nature of the signal also depends on the resolution cell volume of the imaging system, which in turn depends on the center frequency lo, and the bandwidth Af of the interrogating short pulse and the beam profile of the transducer. If a frequency modulated pulse is used for imaging, an additional cross correlation step is needed to compress the pulse, but f, and AI can be varied independently. Using such a pulse, we have performed A-line simulation of the backscattered signal from a specially designed mathematical phantom. Such a phantom allows us to study the signal variations as a function of changing resolution cell volume. The model predicts that Kurtosis, calculated from 2nd and 4th moments, should change linearly with another parameter Fs, that depends on the resolution cell volume. The slope depends on the scatterer number density, and serves as an unbiased estimator (Refer to PDF file for exact formulas).
Date of creation, presentation, or exhibit
Department, Program, or Center
Chester F. Carlson Center for Imaging Science (COS)
Rao, Navalgund and Zhu, Hui, "Scatterer number density estimation using frequency modulated pulse" (1989). Accessed from
RIT – Main Campus