Continuous delay estimation with polynomial splines

Abstract

Delay estimation is used in ultrasonic imaging to estimate blood flow, determine phase aberration corrections, and to calculate elastographic images. Several algorithms have been developed to determine these delays. The accuracy of these methods depends in differing ways on noise, bandwidth, and delay range. In most cases relevant to delay estimation in ultrasonics, a subsample estimate of the delay is required. We introduce two new delay algorithms that use cubic polynomial splines to continuously represent the delay. These algorithms are compared to conventional delay estimators, such as normalized cross correlation and autocorrelation, and to another spline-based method. We present simulations that compare the algorithms' performance for varying amounts of noise, delay, and bandwidth. The proposed algorithms have better performance, in terms of bias and jitter, in a realistic ultrasonic imaging environment. The computational requirements of the new algorithms also are considered.