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Proceedings Paper

Statistical Physics Of Medical Ultrasonic Images
Author(s): R. F. Wagner; M. F. Insana; D. G. Brown; S. W. Smith
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Paper Abstract

The physical and statistical properties of backscattered signals in medical ultrasonic imaging are reviewed in terms of: 1) the radiofrequency signal; 2) the envelope (video or magnitude) signal; and 3) the density of samples in simple and in compounded images. I INTRODUCTION There is a wealth of physical information in backscattered signals in medical ultrasound. This information is contained in the radiofrequency spectrum--which is not typically displayed to the viewer--as well as in the higher statistical moments of the envelope or video signal--which are not readily accessed by the human viewer of typical B-scans. This information may be extracted from the detected backscattered signals by straightforward signal processing techniques at low resolution. II THE RADIOFREQUENCY SIGNAL In the weak scattering regime of medical ultrasonic imaging (1), (2) the Born approximation is valid and yields the frequency dependence of back-scattered radiofrequency signals from a diffuse cloud of similar scatterers. The result in the acoustic application (3) is similar to that found in electro-magnetic wave scattering and the frequency dependence of the backscattered intensity is given by I cc f4 F 2 (1) where the frequency to the fourth power is the dependence associated with Rayleigh scattering, and I F I 2 is the square of the scattering form factor: the Fourier transform of the distribution of the scattering potential, here the change in compressibility or acoustic impedance of the medium. F I 2 has the form of a low pass filter. Some examples of Eq.(1) are given in Figure la for Gaussian form factors with diameters (four standard deviations) as shown, and in reference (4) this simplified treatment is shown to agree well with an exact calculation after the method of Faran when the product of the wave number k and particle radius a is less than unity. In Figure lb the same curves are presented after spatial attenuation by a factor exp(-, f), a reasonable approximation to the round trip attenuation at a depth x and at fre-quency f. The attenuation has appreciable effect only at the higher frequencies, as in many other applications.

Paper Details

Date Published: 10 September 1987
PDF: 6 pages
Proc. SPIE 0768, Pattern Recognition and Acoustical Imaging, (10 September 1987); doi: 10.1117/12.940244
Show Author Affiliations
R. F. Wagner, FDA (United States)
M. F. Insana, FDA (United States)
D. G. Brown, FDA (United States)
S. W. Smith, Duke University Medical Center (United States)

Published in SPIE Proceedings Vol. 0768:
Pattern Recognition and Acoustical Imaging
Leonard A. Ferrari, Editor(s)

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