Bayesian speckle tracking. Part II: biased ultrasound displacement estimation

Ultrasonic displacement estimates have numerous clinical uses, including blood flow estimation, elastography, therapeutic guidance, and acoustic radiation force imaging (ARFI). These clinical tasks could be improved with better ultrasonic displacement estimates. Traditional ultrasonic displacement estimates are limited by the Cramer-Rao lower bound (CRLB). The CRLB can be surpassed using biased estimates. In this paper, a framework for biased estimation using Bayes' theorem is described. The Bayesian displacement estimation method is tested against simulations of several common types of motion: bulk, step, compression, and acoustic-radiation-force-induced motion. Bayesian estimation is also applied to in vivo ARFI of cardiac ablation lesions. The Bayesian estimators are compared with the unbiased estimator, normalized cross-correlation. As an example, the peak displacement of the simulated acoustic radiation force response is reported because this position results in the noisiest estimates. Estimates were made with a 1.5-λ kernel and 20 dB SNR on 100 data realizations. Estimates using normalized cross-correlation and the Bayes' estimator had mean-square errors of 17 and 7.6 μm², respectively, and contextualized by the true displacement magnitude, 10.9 μm. Biases for normalized cross-correlation and the Bayes' estimator are -0.12 and -0.28 μm, respectively. In vivo results show qualitative improvements. The results show that with small amounts of additional information, significantly improved performance can be realized.