Statistics of Speckle in Ultrasound B-Scans
In the ultrasound imaging process, the complex summation at the transducer face is assumed to be linear. The envelope detection process in B-scanning is a nonlinear step which yields essentially the magnitude of the complex field or voltage. (A square law detector, as in the analogous laser case, yields the square of the magnitude, i.e., the intensity, of the field.) It is shown that Rayleigh statistics govern the first-order behavior of the magnitude; and the autocorrelation of the resulting image speckle is obtained by the method of Middleton. The corresponding power spectrum follows immediately by Fourier transformation. Theoretical and experimentally determined autocorrelation functions and power spectra derived from B-scans of a scattering phantom containing many scatterers per resolution cell are presented. These functions lead naturally to the definition of the average speckle spot or cell size, and this in turn is comparable to the resolution cell. Each independent speckle serves as a degree of freedom that determines the number of samples of tissue available over a target. As the speckle cell size decreases this number increases in a manner predictable from the physical parameters of the cell size. However, it is found that the speckle cell is broadened, the degrees of freedom diminished, when the object structure is correlated. This yields the possibility of deducing information about the object structure from the second-order statistics of the speckle texture, in addition to that obtainable from the first-order statistics. Copyright © 1983 by The Institute of Electrical and Electronics Engineers, Inc.
