The statistics of speckle depends on the density of scatterers and the resolution cell volume. The resolution cell volume depends on the impulse response of the imaging system. A fully developed speckle results from interference of scattered waves from a high density of random scatterers within a resolution cell volume. In such cases, the envelope detected signal is known to possess a Rayleigh distribution and a signal to noise ratio (SNR) of 1.91 whereas the intensity signal has a limiting SNR value of 1. Previous publications have shown that SNR can drop below this value when scatterer density departs from high density limit. It has been suggested that SNR be used as a tissue characterization parameter. In this paper, we show that a similar behavior can be observed when resolution cell volume is varied for a fixed scatterer density, and demonstrate it's usefulness in tissue characterization. A three dimensional (3D) simulation phantom that takes into account 3D distribution of scatterers and the 3D nature of resolution cell volume, has been used. The medium is modeled as a uniform matrix material with discrete scatterers distributed randomly. Envelope detection from the simulated RF signal is carried out using Hibert transform. Several simulations were performed to study the effect of scatterer number density (n) and the resolution cell volume on the SNR. We report results with several major implications: (i) It is the number of scatterers within a resolution cell volume that determine the high density limiting behavior. We find this number to be around 10 for a full width at half maximum analysis of the resolution cell volume. (ii) A plot of SNR vs. resolution cell volume of the imaging system for various scatterer number densities reveals the sensitivity of different systems for tissue characterization. (iii) If we have the information about the system's resolution cell volume, then the scatterer number density can be estimated from the SNR measurements. (iv) Higher order moments can be more useful in number density estimation. But our analysis shows that higher moments are even more sensitive to variations in resolution cell volume.
Date of creation, presentation, or exhibit
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Chester F. Carlson Center for Imaging Science (COS)
Rao, Navalgund; Mehra, Sumat; and Zhu, Hui, "Ultrasound speckle statistics variations with imaging system impulse response" (1990). Accessed from
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