Abstract: In traditional pulse-echo ultrasound imaging, transmitted waves are steered to one focus at a time, resulting in poor transmit resolution elsewhere. Synthetic transmit aperture (STA) methods achieve a dynamic transmit focus via retrospective transmit beamforming of the data from multiple transmits. We present an end-to-end matrix formulation of STA pulse-echo ultrasound that includes state-of-the-art methods for retrospective transmit beamforming. This universal framework provides a common context to describe and compare traditional transmit beamforming and multistatic, virtual source, and coded aperture STA, and can reconstruct images from arbitrary transmits, vastly expanding the set of feasible transmit sequences. We further identify optimization objectives that can be leveraged for optimal transmit sequence design, overhauling the traditional principles of transmit sequence design.
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