Delay Compression: Reducing Delay Calculation Requirements for 3D Plane-Wave Ultrasound

In 3D plane-wave ultrasound, computational requirements are directly proportional to the number of focal points in a volume. For a receive aperture of size of M
_x
M
_y
transducers, a beamforming aperture size of N
_x
N
_y
, and a depth of M
_z
focal points, M
_x
M
_y
M
_z
N
_x
N
_y
round-trip delays must be computed. To reduce this requirement, we decompose the planar transmit distance into two parts: (1) from the plane-wave's origin to the first point in each focal line, and (2) from the plane when it is touching the first point in each focal line to each subsequent focal point along that line. The latter distance, as well as the reflection distances, are symmetric across beamforming apertures, and thus their computation can be shared. This decomposition results in up to a M
_x
M
_y
reduction in the number of unique delays while retaining full image quality. Using our technique, precomputing delays and storing them in look-up tables (LUTs) is now possible for 3D plane-wave ultrasound for the first time, opening new doors for computational architectures in this field. Our method works with 2D, 3D, and 3D-separable variants of plane-wave ultrasound.