The effects of the correlation function estimators to the blood velocity estimation

In the estimation of blood velocity, the correlation method is widely used. In this method, the selection of different correlation function estimators could have significant effects on the estimation results, especially when the range of blood velocity is large. Due to calculation requirements, the biased and the unbiased correlation function estimators are widely used. In this work, the effects of the biased and the unbiased correlation function estimators to the blood velocity estimation are discussed. The results show that each estimator has better performance only for a certain range of velocities. The biased correlation estimator is suitable for signals with low velocities below the Nyquist velocity and the unbiased estimator is suitable for signals with velocities over the Nyquist velocity. Applying the biased estimator on a signal with high velocities, it likely causes global errors and the estimation value is usually lower than the true value. On the contrary, if applying the unbiased estimator on a signal with low velocities signal, it causes global errors frequently and the estimation value is usually higher than the true value. These effects are verified by computer simulation signals and RF-signals recorded from a patient with velocities up to 4 times the Nyquist velocity. Furthermore, a method which is suitable for estimation of large velocity ranges up to 4 times the Nyquist velocity is proposed in this work. The method uses bandwidth information as a criterion to determine which estimator is to be chosen or which velocity range is to be set. It is verified by both simulation and experiment data