Optimal doppler frequency estimators for ultrasound and optical coherence tomography

The Kasai autocorrelation estimator is widely used in Doppler optical coherence tomography and ultrasound to determine blood velocities. However, as a non-parametric estimator, it may not be optimal. Assuming an additive white Gaussian noise (AWGN) model, we show that the Kasai estimator variance is far from the Cramer-Rao lower bound. Moreover, paradoxically, the Kasai estimator performance degrades as the acquisition rate is increased. By contrast, the additive white Gaussian noise maximum likelihood estimator (AWGN MLE) variance asymptotically approaches the Cramer-Rao lower bound, making it a better estimator at high acquisition rates. Nevertheless, the Kasai estimator outperforms the AWGN MLE under moderate levels of multiplicative decorrelation noise, and could therefore be considered more robust. These findings motivate further work in maximum likelihood estimators under conditions of both additive and multiplicative noise.