An axial velocity estimator for ultrasound blood flow imaging, based on a full evaluation of the Doppler equation by means of a two-dimensional autocorrelation approach

This paper introduces a new velocity estimator, referred to as the 2D autocorrelator, which differs from conventional Doppler techniques in two respects: the derivation of axial velocity values by evaluating the Doppler equation using explicit estimates of both the mean Doppler and the mean RF frequency at each range gate location; and, the 2D nature (depth samples versus pulse transmissions) of processing within the range gate. The estimator's output can be calculated by evaluating the 2D autocorrelation function of the demodulated (baseband) backscattered echoes at two lags. A full derivation and mathematical description of the estimator is presented, based on the framework of the 2D Fourier transform. The same framework is adopted to analyze two other established velocity estimators (the conventional 1D autocorrelator and the crosscorrelator) in a unifying manner, and theoretical arguments as well as experimental results are used to highlight the common aspects of all three estimators. In addition, a thorough performance evaluation is carried out by means of extensive simulations, which document the effect of a number of factors (velocity spread, range gate length, ensemble length, noise level, transmitted bandwidth) and provide an insight into the optimum parameters and trade-offs associated with individual algorithms. Overall, the 2D autocorrelator is shown to offer the best performance in the context of the specific simulation conditions considered here. Its superiority over the crosscorrelator is restricted to cases of low signal-to-noise ratios. However, the 2D autocorrelator always outperforms the conventional 1D autocorrelator by a significant margin. These comparisons, when linked to the computational requirements of the proposed estimator, suggest that it combines the generally higher performance of 2D broadband time-domain techniques with the relatively modest complexity of 1D narrowband phase-domain velocity estimators.<
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