Ultrasonic echoes, backscattered from an inhomogeneous medium have the character of a random signal, which is mainly responsible for the observed speckle in medical images. Such a medium can be modeled as a uniform matrix with scattering bodies distributed randomly. When the number of density of scatterers is high, the individual scatterers are not resolved by the imaging process, and a speckle pattern is produced as a result of interference of waves from many scatterers within the resolution cell volume. This cell volume depends on the beam profile and the pulse width of the interrogating pulse. We have used a 3 dimensional (3D) simulation phantom that takes into account the 3D distribution of scatterers and the 3D nature of the resolution cell volume. Several simulations were performed to study the effect of scatterer number density (SND) and resolution cell volume on the backscattered signal. Assuming the process is linear and the stochastic signal is ergodic and stationary, Kurtosis (K), which involves 2nd and 4th moments, was estimated in each case. We find that Kurtosis varies linearly with another parameter F that depends on the resolution cell volume. The results are analyzed in the light of theoretical predictions. Reasonable estimates of SND can be derived from the slope of Kurtosis vs. parameter F graph.
Department, Program, or Center
Chester F. Carlson Center for Imaging Science (COS)
Navalgund A. H. K. Rao, Hui Zhu, "Modeling ultrasound speckle formation and its dependence on imaging system's response", Proc. SPIE 1443, Medical Imaging V: Image Physics, (1 July 1991); doi: 10.1117/12.43432; https://doi.org/10.1117/12.43432
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