Spatial-angular baseband delay multiply and sum beamforming with coherence factor for 3D power Doppler imaging

Three-dimensional power Doppler imaging (3D PDI) provides volumetric visualization of microvascular networks, but 3D PDI using matrix arrays remains limited by the small effective aperture and low element sensitivity of matrix arrays. This study proposes spatial-angular baseband delay multiply and sum (SA-DMAS) beamforming and a coherence-weighted version, SA-DMAS-CF, to improve 3D PDI quality. SA-DMAS jointly incorporates all delayed channel data from multiple plane wave transmissions within a unified baseband DMAS framework, whereas SA-DMAS-CF further applies voxel-wise coherence weighting to suppress incoherent components. The proposed beamformers are evaluated against delay and sum (DAS), spatial and angular coherence factor (SACF), and baseband DMAS using point-target simulations, intersecting-microtube simulations, phantom experiments, and in vivo 3D PDI experiments, including contrast-free rat brain, contrast-free rat kidney, contrast-free mouse brain, and transcranial contrast-enhanced rat brain imaging. In the simulations, SA-DMAS-CF achieves the smallest full width at half maximum (FWHM, 0.181 mm) and the lowest sidelobe level (SLL, -84.97 dB). It also achieves the highest contrast-to-noise ratios (CNRs) in the intersecting-microtube simulations and the smallest minimum separable distances based on peak-to-valley level analysis. In phantom experiments, SA-DMAS-CF provides the smallest FWHM and the strongest sidelobe suppression. In vivo, SA-DMAS-CF consistently yields the highest CNRs in contrast-free rat brain, contrast-free rat kidney, contrast-free mouse brain, and transcranial contrast-enhanced rat brain imaging: 37.81, 89.09, 24.85, and 41.11 dB, respectively, compared with 7.29, 27.20, 1.48, and 24.66 dB for DAS. These results indicate that SA-DMAS-CF improves spatial resolution, vessel-to-background separability, and weak blood flow visualization for 3D PDI using matrix arrays.