ON THE JOINT PROBABILITY DENSITY-FUNCTION FOR THE AUTOCORRELATION ESTIMATES IN ULTRASOUND COLOR-FLOW IMAGING

Autocorrelation estimates of the Doppler signal with zero and unity la g are commonly used for color coding algorithm in 2-D color flow imagi ng. Signal power, center frequency, and bandwidth are derived from the se two autocorrelation estimates, and combined in a color coding schem e. In this paper computer simulations show that the joint probability density function (PDF) for the autocorrelation estimates has a form wh ich differs significantly from a Gaussian distribution. However, the P DF for the normalized autocorrelation estimates is shown to have a for m closer to a Gaussian distribution, which means that the first- and s econd-order moments gives an adequate statistical description of the s et of estimators. Analytical approximations for the first- and second- order moments in the joint PDF for the normalized autocorrelation esti mates of all lags are derived, and the expressions are verified by com puter simulations. Using this results, an expression for the probabili ty density function of the correlation angle estimate is derived, show ing a close fit to simulation results. Numerical results show that the performance of the correlation angle estimate can be improved signifi cantly by applying spatial averaging to the autocorrelation estimates.