Doppler frequency estimators under additive and multiplicative noise

Abstract

In optical coherence tomography (OCT), unbiased and low variance Doppler frequency estimators are desirable for blood velocity estimation. Hardware improvements in OCT mean that ever higher acquisition rates are possible. However, it is known that the Kasai autocorrelation estimator, unexpectedly, performs worse as acquisition rates increase. Here we suggest that maximum likelihood estimators (MLEs) that utilize prior knowledge of noise statistics can perform better. We show that the additive white Gaussian noise maximum likelihood estimator (AWGN MLE) has a superior performance to the Kasai autocorrelation estimate under additive shot noise conditions. It can achieve the Cramer-Rao Lower Bound (CRLB) for moderate data lengths and signal-to-noise ratios (SNRs). However, being a parametric estimator, it has the disadvantages of sensitivity to outliers, signal contamination and deviations from noise model assumptions. We show that under multiplicative decorrelation noise conditions, the AWGN MLE performance deteriorates, while the Kasai estimator still gives reasonable estimates. Hence, we further develop a multiplicative noise MLE for use under multiplicative noise dominant conditions. According to simulations, this estimator is superior to both the AWGN MLE and the Kasai estimator under these conditions, but requires knowledge of the decorrelation statistics. It also requires more computation. For actual data, the decorrelation MLE appears to perform adequately without parameter optimization. Hence we conclude that it is preferable to use a maximum likelihood approach in OCT Doppler frequency estimation when noise statistics are known or can be accurately estimated.