Baseband delay multiply and sum beamformer for three-dimensional ultrasound localization microscopy

Three-dimensional (3D) ultrasound localization microscopy (ULM) provides super-resolution volumetric microvascular imaging, but implementations with matrix arrays are often limited by reduced effective aperture and sensitivity, which degrade the point spread function (PSF) and compromise microbubble (MB) localization and tracking. In this study, we present a baseband delay-multiply-and-sum (DMAS) beamformer for 3D ULM and derive a computationally efficient implementation for 1024-element matrix arrays. Compared with delay-and-sum (DAS), coherence factor (CF), and spatial and angular coherence factor (SACF), DMAS yields improved volumetric ULM reconstructions in simulations, phantom experiments, and in vivo rat brain imaging. Although CF and SACF achieve superior PSF metrics, DMAS provides the highest effective spatial resolution as measured by Fourier shell correlation (FSC) and substantially increases the number of tracked trajectories, particularly under high MB infusion. DMAS yields approximately 2.34 million tracks at the low infusion rate and 3.07 million tracks at the high infusion rate, compared with approximately 0.91 to 1.49 million tracks for the other beamformers, and achieves consistently higher vascular saturation (about twofold at the end of acquisition), indicating faster convergence and more complete microvascular depiction. The computationally efficient implementation of baseband DMAS achieves a computational speedup of approximability 370 times. These results highlight baseband DMAS as a robust and computationally efficient beamforming strategy for 3D ULM, and suggest that PSF metrics alone do not necessarily predict final ULM reconstruction quality.