A two dimensional sub-sample estimator based on zero phase crossing in ultrasound

Displacement estimation in ultrasound is a common yet important task for various applications, including tissue/blood motion estimation, elastography imaging, temperature estimation, etc. Accuracy of displacement estimation in the lateral direction is primarily limited by the coarse image resolution in this direction. Therefore, large lateral interpolation factors are needed to achieve fine sub-sample displacement estimation. In this paper, a zero phase crossing method is presented based on two dimensional complex normalized cross correlations (NCCs). Due to the fact that there is no analytic signal in the lateral direction, the phase of complex cross correlation is not necessarily linear. However, the subsample of maximum magnitude of complex correlation still lies on the zero phase line. Therefore, 2D 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. We present 2D displacement estimation results, both simulations and experimental, to demonstrate the advantages of the proposed method over existing estimators.