Fourier Beamformation for Convex-Array Diverging Wave Imaging Using Virtual Sources

Convex probes have been widely used in clinical abdominal imaging for providing deep penetration and wide field of view. Ultrafast imaging modalities have been studied extensively in the ultrasound community. Specifically, broader wavefronts, such as plane wave and spherical wave, are used for transmission. For convex array, spherical wavefront can be simply synthesized by turning all elements simultaneously. Due to the lack to transmit focus, the image quality is suboptimal. One solution is to adopt virtual sources behind the transducer and compound corresponding images. In this work, we propose two novel Fourier-domain beamformers (vs1 and vs2) for nonsteered diverging wave imaging and an explicit interpolation scheme for virtual-source-based steered diverging wave imaging using a convex probe. The received echoes are first beamformed using the proposed beamformers and then interpolated along the range axis. A total of 31 virtual sources located on a circular line are used. The lateral resolution, the contrast ( $C$ ), and the contrast-to-noise ratio (CNR) are evaluated in simulations, phantom experiments, ex vivo imaging of the bovine heart, and in vivo imaging of the liver. The results show that the two proposed Fourier-domain beamformers give higher contrast than dynamic receive focusing (DRF) with better resolution. In vitro results demonstrate the enhancement on CNR: 6.7-dB improvement by vs1 and 5.9-dB improvement by vs2. Ex vivo imaging experiments on the bovine heart validate the CNR enhancements by 8.4 dB (vs1) and 8.3 dB (vs2). In vivo imaging on the human liver also reveals 6.7- and 5.5-dB improvements of CNR by vs1 and vs2, respectively. The computation time of vs1 and vs2, depending on the image pixel number, is shortened by 2–73 and 4–216 times than the DRF.