Estimation of High Velocities in Synthetic Aperture Imaging: I: Theory

The paper describes a new pulse sequence design and estimation approach, which can increase the maximum detectable velocity in synthetic aperture (SA) velocity imaging. In SA N spherical or plane waves are emitted, and the sequence is repeated continuously. The N emissions are combined to form a High Resolution Image (HRI). Correlation of HRIs is employed to estimate velocity, and the combination of N emissions lowers the effective pulse repetition frequency by N. Inter-leaving emission sequences can increase the effective pulse repetition frequency to the actual pulse repetition frequency, thereby increasing the maximum detectable velocity by a factor of N. This makes it possible to use longer sequences with better focusing properties. It can also increase the possible interrogation depth for vessels with large velocities. A new cross-correlation vector flow estimator is also presented, which can further increase the maximum detectable velocity by a factor of three. It is based on Transverse Oscillation (TO), a pre-processing stage, and cross-correlation of signals beamformed orthogonal to the ultrasound propagation direction. The estimator is selfcalibrating without estimating the lateral TO wavelength. This paper develops the theory behind the two methods. The performance is demonstrated in the accompanying paper for convex and phased array probes connected to the SARUS scanner for parabolic flow for both conventional and SA imaging.