Time delay estimation using wavelet transform for pulsed-wave ultrasound

The windowed cross-correlation (WCC) technique has recently attracted attention in pulsed-wave (PW) ultrasound for measurement of tissue motion and blood flow velocity because of its performance advantages over the conventional Doppler method. The WCC measures tissue motion and blood flow velocity via estimation of time delays of backscattered signals in two consecutive echoes. In this paper, we propose a wavelet transform-based cross-correlation (WTCC) technique for the time delay estimation in PW ultrasound. The WTCC consists of three steps: (i) computing wavelet transforms (WTs) of received echoes, (ii) computing cross-correlations in the wavelet domain, and (iii) estimating the time delays by maximizing the estimated cross-correlations. Dyadic or continuous wavelets may be used in the proposed approach. The WTCC has a unique feature of using varying time-frequency windows in processing compared with the WCC which only uses a single fixed window. Our computer simulations show that, compared with the WCC, the WTCC provides a better estimation of time delays (lower failure rate and lower estimate error) and its performance is more consistent under various conditions, and more robust with window size. In the simulations, we also tested a specific continuous wavelet for the WTCC that was the emitted pulse itself and found the corresponding WTCC outperforms the WTCC with a regular dyadic wavelet.