Optimum velocity estimation in ultrasound color flow imaging in presence of clutter noise

Ultrasound color flow imaging (CFI) is an important clinical tool in the diagnosis of the human circulatory system. Current methods provide a 2D map of estimated flow velocities in real-time, at frame rates sufficient for following the dynamics of the flow in the heart and arteries. Signal from tissue is a major source of estimation error in CFI velocity estimators. The clutter signal power can be as high as 50-80 dB compared to the blood flow signal, and must be accounted for in order to achieve unbiased flow velocity estimates. This is usually done by high-pass filtering the Doppler signal prior to velocity estimation, a challenging task due to the small ensemble length available for processing (8-16 samples). The clutter filter may introduce bias and variance, giving suboptimal performance. To investigate the potential of more advanced estimation schemes, we compared the performance of a conventional method to the optimal estimator assuming full knowledge of the clutter statistics, and the Cramér-Rao lower bound (CRLB). Based on a simplified model of the received ultrasound Doppler signal from both clutter and locally rectilinear flow, a maximum likelihood (ML) estimator for blood flow velocity has been developed, and an analytical expression for the CRLB has been found. The optimal asymptotic properties of the ML-estimator has been evaluated and compared to the performance of the autocorrelation method (ACM) for the estimation of flow velocity using FIR and polynomial regression clutter filters. It is shown that for practical CFI ensemble lengths, the ML estimator outperformed the ACM estimator, even though the ML estimator variance was substantially higher than the CRLB. When the ML-estimator was expanded to include data from neighbouring spatial positions, the variance rapidly decreased, approaching the CRLB for 9 spatial positions. By spatial averaging of the correlation estimates, the ACM performance improved substantially in the filter pass band. For a realistic case with a clutter-to-blood signal ratio of 30 dB, the standard deviation of the ML and ACM estimators relative to the CRLB decreased from 70% and 150%, to 4% and 90% respectively. The clutter filter had a large impact on ACM performance in the transition region of the filter. FIR filters were shown in general to have a lower bias then polynomial regression filters, but exhibited a higher variance. In conclusion, with spatial averaging over a limited region, close to minimum variance estimators exists. The autocorrelation method gives suboptimal performance, with a standard deviation exceeding the CRLB by 90%.