A PSF-shape-based beamforming strategy for robust 2D motion estimation in ultrafast data

This paper presents a framework for motion estimation in ultrafast ultrasound data. It describes a novel approach for determining the sampling grid for ultrafast data based on the system's point-spread-function (PSF). As a consequence, the cross-correlation functions (CCF) used in the speckle tracking (ST) algorithm will have circular-shaped peaks, which can be interpolated using a 2D interpolation method to estimate subsample displacements. Carotid artery wall motion and parabolic blood flow simulations together with rotating disk experiments using a Verasonics Vantage 256 are used for performance evaluation. Zero-degree plane wave data were acquired using an ATL L5-12 (f_c = 9 MHz) transducer for a range of pulse repetition frequencies (PRFs), resulting in 0-600 μm inter-frame displacements. The proposed methodology was compared to data beamformed on a conventionally spaced grid, combined with the commonly used 1D parabolic interpolation. The PSF-shape-based beamforming grid combined with 2D cubic interpolation showed the most accurate and stable performance with respect to the full range of inter-frame displacements, both for the assessment of blood flow and vessel wall dynamics. The proposed methodology can be used as a protocolled way to beamform ultrafast data and obtain accurate estimates of tissue motion.