Volumetric ultrasound via 3D Null Subtraction Imaging with matrix array

This study introduces three-dimensional Null Subtraction Imaging (3D NSI), a nonlinear beamforming framework designed to extend the computationally efficient null-subtraction process to volumetric imaging with matrix arrays. This is accomplished by designing specialized NSI apodizations (a zero-mean window and two DC-offset variants) for 2D receive apertures, enabling simultaneous synthetic beam narrowing and sidelobe suppression in both azimuthal and elevational dimensions. The versatility of the framework was demonstrated on a 1024-element matrix array using three aperture configurations: a fully-addressed circular aperture and two sparse Fermat's spiral apertures, chosen for comparable aperture sizes. By further implementing a spiral no-reuse apodization that enforces non-overlapping element sets across transmit-receive events, we achieved up to a 16-fold increase in acquisition volume rate using only 240 active elements. In computer simulations and tissue-mimicking phantom experiments, 3D NSI achieved an average improvement of 36% in azimuthal and elevational resolutions, along with an approximately 20% higher contrast ratio, compared to the conventional Delay-and-Sum (DAS) beamformer under matched transmit/receive configurations. When implemented with the spiral no-reuse aperture, the 3D NSI framework achieved an acquisition rate exceeding 1000 volumes per second with a computational load less than three times that of DAS, making it a practical solution for real-time 4D imaging. Preliminary in vivo carotid imaging corroborated the efficacy of the framework in biological tissues, indicating that 3D NSI represents a general and efficient beamforming method for matrix arrays with a potential to impact real-time 4D ultrasound imaging in cardiovascular and other dynamic applications.