Rhombic Grids Reduce the Number of Voxels in Fast Pulse-Echo Ultrasound Imaging

Ultrafast imaging modes, such as coherent plane-wave compounding (CPWC), capture a large field of view in a single pulse-echo measurement using parallel receive focusing. The number of foci or, equivalently, the number of volume elements (voxels) in the image determines the computational costs and the memory consumption of the image formation. Herein, 120{\deg} rhombic grids are proposed to specify the voxel positions and reduce the number of voxels in comparison to orthogonal grids. The proposed grids derive from the bivariate sampling theorem and the spectral properties of the images formed by the delay-and-sum algorithm in CPWC. A phantom experiment validated the proposed grids and showed reductions in the number of voxels by 81.4 % and 14.7 % in comparison to the usual and optimal orthogonal grids, respectively. Mean structural similarity indices above 96.6 % and relative root mean-squared errors below 6.8 % confirmed the visual equivalence of all images after interpolations to the usual orthogonal grid.

Frequency-Dependent $F$-Number Increases the Contrast and the Spatial Resolution in Fast Pulse-Echo Ultrasound Imaging

Fixed $F$-numbers reduce grating lobe artifacts in fast pulse-echo ultrasound imaging. Such $F$-numbers result in dynamic receive subapertures whose widths vary with the focal position. These subapertures, however, ignore useful low-frequency components in the excluded radio frequency (RF) signals and, thus, reduce the lateral resolution. Here, we propose a frequency-dependent $F$-number to simultaneously suppress grating lobe artifacts and maintain the lateral resolution. This $F$-number, at high frequencies, reduces the receive subaperture to remove spatially undersampled components of the RF signals and suppress grating lobes. The $F$-number, at low frequencies, enlarges the receive subaperture to use the components of all RF signals and maintain the lateral resolution. Experiments validated the proposed $F$-number and demonstrated improvements in the contrast and the widths of wire targets of up to 3.2 % and 12.8 %, respectively.