A Two Dimensional Speckle Tracking Method Based on Zero Phase Crossing in Ultrasound

Abstract

Displacement estimation in ultrasound is a common yet important task for various applications, including tissue/blood motion estimation, elastography imaging, temperature estimation, and shear wave elasticity imaging. A variety of speckle tracking methods have been proposed for displacement estimation using pulse-echo ultrasound. The performance of these estimators, in terms of bias and variance, could greatly impact the reliability of the imaging markers derived from the initial displacement estimate. Therefore, a comparison between these methods in a variety of imaging scenarios is highly significant. In addition to considering several published displacement estimation methods, this theses introduces a new estimator based on the complex two-dimensional (2D) cross correlation. The approach builds on the 1D complex cross correlation which results from the analytic nature of pulse-echo ultrasound data in medical imaging applications. It is well established that the use of complex cross correlation in 1D displacement tracking allows for sub-sample displacement estimation without the need for interpolation. The complex cross correlation is obtained from the Hilbert transform of the echo data and the sub-sample displacement estimate is obtained by using the zero crossing of the phase in the vicinity of the peak in the correlation amplitude. Recently, this property was extended to 2D by exploiting the coupling between the axial and lateral displacements in the phase of the 2D cross correlation of the analytic ultrasound echo data from multiple A-lines. It was theoretically shown that the maximum magnitude of complex correlation still lies on the zero phase line. The so-called ``Phase-coupled 2D speckle tracking (PCST) algorithm" was the first to extend the analytic nature of ultrasound data to two dimensions. However, this algorithm applies geometric methods to finding the sub-sample displacements, which may hinder its efficient real-time implementation. The main contribution of this thesis is the introduction of a new displacement estimator with sub-sample accuracy in both axial and lateral dimensions. A two-dimensional (2D) zero phase crossing method is derived based on two 2D complex normalized cross correlations (NCCs), i.e., displacement can be estimated by the intersection point of two zero phase lines, one from Hilbert transformation in the axial direction and the other one from Hilbert transformation in the lateral direction. Unlike the 2D PCST, the proposed algorithm lends itself to efficient implementation. Furthermore, comparison of simulation results from flow experiments suggests that the new algorithm produces more accurate estimation in terms of variance. The proposed algorithm was compared with the 2D PCST and other displacement estimators proposed by other groups. In particular, we have compared the performance with algorithms based on parabolic and cosine fitting of the 2D correlation of raw 2D radiofrequency (RF) data. In addition to the validation studies based on simulation, experimental validation of the new algorithm was carried both \textit{in vitro} and \textit{in vivo}. These results suggest that the new algorithm is applicable in realistic medical imaging scenarios where tissue motion and/or flow may be of interest, e.g. imaging atherosclerosis burden in peripheral vessels.