Autocorrelation techniques in color flow imaging: signal model and statistical properties of the autocorrelation estimates

A review of the scattering theory for moving blood, and a model for the signal in a multigated pulsed wave Doppler system is presented. The model describes the relation between a general time-variable velocity field and the signal correlation in space and time, including the effect of movement of the ultrasonic beam for color flow imaging systems with mechanical scanning. In the case of a constant and rectilinear velocity field, a parametric model for the autocorrelation function is deduced. General formulas for a full second order characterization of the set of autocorrelation estimates, with arbitrary lags in the spatial and temporal directions, are developed. The formulas are applied to the parametric model, and numerical results for the estimator variance are presented. A qualitative evaluation of the theoretical results has been performed by offline-processing of 2-D Doppler signals from a color flow imaging scanner. The benefit of spatial and temporal averaging is demonstrated by using different averaging filters to the same set of recorded data. >