Comparison between 2-D cross correlation with 2-D sub-sampling and 2-D tracking using beam steering

Abstract

We have previously presented multi-dimensional sub-sample motion estimation techniques that use multi-dimensional polynomial fitting to the discrete cross-correlation function to jointly estimate the sub-sample motion in all three spatial directions. Previous simulation and experimental results showed that these estimators significantly improve the performance of the motion estimation in 2-D and 3-D. In this short communication, we present additional simulation results and compare these techniques to 2-D tracking using beam steering. The results show that beam steering technique performs better in estimating the motion vector especially the lateral component.

Normal and shear strain imaging using 2D deformation tracking on beam steered linear array datasets

“…Several investigators have also reported on the use of only three beam-steered datasets to estimate both axial and lateral displacement vectors and strain tensors. 21,30 The premise employed by these investigators is that the 0 • dataset would provide axial strain information, while the beam-steered data acquired at the largest possible steered angle could be utilized for lateral strain computation by estimation of the lateral components along the beam-steered data. Larger beamsteered angles provide more lateral deformation information at the cost of introducing additional noise artifacts into both the strain tensor images.…”

“…However, this approach utilizes lateral displacement information from only two beam-steered angles and utilize a geometrical rotational transformation to register these displacements onto the 0 • Cartesian spatial grid. 15,27 Azar et al 30 have also demonstrated the improved performance of 2D tracking using beam steering for estimating the lateral component of the displacement vector.…”

Band-pass filtering for optimal displacement estimation in the presence of grating lobes at large beam steering angles

“…Nevertheless, it can be expected that the found optimal filter settings are also optimal for strain and displacement estimation in arbitrary other directions. This, because the derivation of both other displacement components as well as strains is achieved by post-processing steps, like angular compounding and first order derivation/least squares strain estimation [3][4][5][6].…”

“…And consequently, also the direction in which accurate displacement estimation is possible changes. From two independent projections of the displacement vector, displacements in any direction can be derived [3][4][5][6]. It has been shown that the projection of angular axial displacement estimates obtained at beam steering angles up to 10 degrees enables a more accurate estimation of the vertical displacement (perpendicular to the transducer footprint) than can be obtained from a single nonsteered acquisition [7;8].…”