A least-squares vector flow estimator for synthetic aperture imaging

This paper presents a least-squares (LS) vector flow estimator that is intended to calculate axial and lateral velocities using aperture-domain Doppler data from multiple transmit point sources and multiple receive apertures realized via the synthetic aperture (SA) technique. Our new estimator comprises two main stages. First, for each transmit point and receive aperture, we obtain aperture-domain Doppler ensembles and use them to compute a frequency estimate (via the lag-one autocorrelator) for every spatial point in imaging view. Subsequently, by noting that each transmit point and receive aperture deviates in flow angle, we estimate flow vectors through creating a set of Doppler equations with two unknowns (i.e. axial and lateral velocities) from the frequency estimates and solving this equation set as an over-determined LS problem. To evaluate the performance of new estimator, Field II simulations were performed for a scenario with a 5 mm-diameter steady flow tube (tube angle: 0°-90°, center velocity: 0-25 cm/s). For these simulations, a 5.5 MHz linear array with 128 elements was used; pre-beamform data was acquired for 97 virtual point sources (0.3 mm spacing, 32 elements), and 12 two-cycle pulses were fired through each point source (PRF: 5 kHz). Our LS estimator was then applied to a few different transmit-receive SA imaging configurations (e.g. 97 transmit points and 3 receive apertures). Results show that, if a multi-transmit configuration is used, the LS estimator is more capable of providing vector flow maps that roughly resemble the theoretical profile.