Two-dimensional speckle tracking using zero phase crossing with Riesz transform

Ultrasound speckle tracking (ST) provides robust estimates of fine tissue displacements along the beam direction due to the analytic nature of echo data. A multi-dimensional ST method (MDST) with subsample accuracy in all dimensions is introduced. The algorithm is based on the gradient of the magnitude and the zero-phase crossing of 2D complex correlation of the generalized analytic signal. The generalization method utilizes the Riesz transform, which is the vector extension of the Hilbert transform. Robustness of the tracking algorithm is investigated using realistic synthetic data sequences created with (Field II) for which the bench mark displacement was known. In addition, the new MDST method is used in the estimation of the flow and surrounding tissue motion on human carotid artery in vivo. The data were collected using a linear array probe of a Sonix RP ultrasound scanner at 325 frames per second (fps). The vessel diameter was calculated from the upper and lower vessel wall displacements, and clearly showed a blood pressure wave-like pattern. The results obtained show that using the Riesz transform produces a more robust estimation of the true displacement of the simulated model compared to previously published results. This could have significant impact on strain calculations near vessel walls.