Three-dimensional frequency-wavenumber method for efficient and high-quality volumetric ultrasound imaging

Total focusing method (TFM) using full matrix capture (FMC) data provides high-quality ultrasound imaging by enabling pixel-level dynamic focusing during both transmission and reception. However, when applied to three-dimensional (3D) ultrasound imaging with a two-dimensional (2D) matrix array (MA), TFM suffers from computational inefficiency due to the conventional delay-and-sum (DAS) algorithm, which limits its applicability in high-volume imaging scenarios. To address this challenge, we introduce an efficient beamforming framework, designated MA-FMC-fk, leveraging the frequency-wavenumber (f-k) domain to accelerate 3D FMC imaging. The proposed method achieves a computational complexity of $O(N_u^2{N}_v^2{N}_z{\log }_2(N_u^2{N}_v^2{N}_z))$, compared to $O(N_u^2{N}_v^2{N}_z{N}_x{N}_y)$ for the conventional DAS algorithm. The imaging performance of the proposed method was evaluated using simulations, phantom experiments, and in-vivo studies. Quantitative results demonstrate that MA-FMC-fk improves the average lateral resolution by 25.00% for the simulated point targets and by 19.18% for the phantom wire experiments compared to the DAS algorithm. In addition, MA-FMC-fk enhances the average contrast-to-noise ratio (CNR) by 11.73% and the speckle signal-to-noise ratio (sSNR) by 11.16% for the phantom cyst. The MA-FMC-fk algorithm achieves a several-fold reduction in computation time on a CPU-based MATLAB platform relative to DAS. The human experimental results further demonstrate the effectiveness of the proposed method, in which the sSNR and CNR are improved by 19.74% and 18.18%, respectively. The results demonstrate that the MA-FMC-fk method improves image quality while reducing computational cost for 3D TFM imaging using a 2D matrix array.