Interpolation methods for time-delay estimation using cross-correlation method for blood velocity measurement

The cross-correlation method (CCM) for blood flow velocity measurement usin g Doppler ultrasound is based on time delay estimation of echoes from pulse -to-pulse. The sampling frequency of the received signal is usually kept as low as possible in order to reduce computational complexity, and the peak in the correlation function is found by interpolating the correlation funct ion. The parabolic-fit interpolation method introduces a bias at low sampli ng rate to the ultrasound center frequency ratio. In this study, four diffe rent methods are suggested to improve the estimation accuracy: (1) Paraboli c interpolation with bias-compensation, derived from a theoretical signal m odel. (2) Parabolic interpolation combined with linear filter interpolation of the correlation function. (3) Parabolic interpolation to the complex co rrelation function envelope. (4) Matched filter interpolation applied to th e correlation function. The new interpolation methods are analysed both by computer simulated signals and RF-signals recorded from a patient with time delay larger than 1/f(0), where f(0) is the center frequency. The simulati on results show that these methods are more accurate than the parabolic-fit method. From the simulation, the worst estimation accuracy is about 1.25% of 1/f(0) for the parabolic-fit interpolation, and it is improved by the ab ove methods to less than 0.5% of 1/f(0) when the sampling rate is 10 MHz, t he center frequency is 2.5 MHz and the bandwidth is 1 MHz. This improvement also can be observed in the experimental data. Furthermore, the matched fi lter interpolation gives the best performance when signal-to-noise ratio (S NR) is low. This is verified both by simulation and experimentation.