3D normalized cross-correlation for estimation of the displacement field in ultrasound elastography

This paper introduces a novel technique to estimate tissue displacement in quasi-static elastography. A major challenge in elastography is estimation of displacement (also referred to time-delay estimation) between pre-compressed and post-compressed ultrasound data. Maximizing normalized cross correlation (NCC) of ultrasound radio-frequency (RF) data of the pre- and post-compressed images is a popular technique for strain estimation due to its simplicity and computational efficiency. Several papers have been published to increase the accuracy and quality of displacement estimation based on NCC. All of these methods use 2D spatial windows in RF data to estimate NCC, wherein displacement is assumed to be constant within each window. In this work, we extend this assumption along the third dimension. Two approaches are proposed to get third dimension. In the first approach, we use temporal domain to exploit neighboring samples in both spatial and temporal directions. Considering temporal information is important since traditional and ultrafast ultrasound machines are, respectively, capable of imaging at more than 30 frame per second (fps) and 1000 fps. Another approach is to use time-delayed pre-beam formed data (channel data) instead of RF data. In this method information of all channels that are recorded as pre-beam formed data of each RF line will be considered as 3^rd dimension. We call these methods as spatial temporal normalized cross correlation (STNCC) and channel data normalized cross correlation (CNCC) and show that they substantially outperforms NCC using simulation, phantom and in-vivo experiments. Given substantial improvements of results in addition to the relative simplicity of implementing STNCC and CNCC, the proposed approaches can potentially have a large impact in both academic and commercial work on ultrasound elastography.