Compensation of the bias caused by the wall filter on the mean Doppler frequency

In the presence of noise, any wall filter induces a bias on the mean Doppler frequency estimated by the algorithm based on the calculation of the phase of the autocorrelation function at lag 1. In this paper, it is shown that the bias results from the nonzero value of the autocorrelation function of the filtered noise at lag 1. A general method for compensating the bias was then deduced. It consists of a preliminary estimation of the filtered noise contribution and its subtraction from the autocorrelation function of the Doppler signal. The method is independent of the nature of the noise and wall filter. An evaluation of this method on simulated Doppler signals and on measurements from a moving-string phantom showed that effective compensation of the bias was obtained, but at the expense of a higher variance. Taking into account both the bias and the variance, however, it was shown that this method offers an improvement over the noncompensated method. Finally, the performance of this method was demonstrated using in vivo measurements taken from a human aorta.