Waveform and beamform design for Doppler ultrasound vector flow mapping
The authors consider the problem of producing an "optimal" range 2-D Doppler flow map in a finite amount of time. A range 2-D Doppler provides estimates of the magnitudes of the axial and two transverse flows in general as a function of range. By optimal image, the authors mean the closest image in a 2-norm sense to the actual the transverse and line-of-sight flows distribution as a function of range. They show that to obtain that optimal image one needs to adjust both the beamform and waveform of the transmitted ultrasound field to the flow distribution. The authors propose a beamform and waveform selection strategy that leads to a progressive refinement of resolution of the produced image along the range, and vector velocity axes. They discuss imaging scenarios in which the returns due to the optimal, beamforms and waveforms can be "synthesized" from those corresponding to a standard beamform and waveform and scenarios where one actually needs to generate different beamforms and waveforms to improve the quality of the final image.