Delay-and-Sum Consistent Wavenumber Algorithm

Fourier-domain beamforming methods offer a computationally efficient alternative to time domain methods in ultrasound imaging. Among these, the wavenumber algorithm (WA) achieves fast image reconstruction from full-matrix capture (FMC) data but introduces amplitude distortions due to its inherent weighting. In this study, we present a modified Fourier-domain beamforming method that operates on FMC data and reproduces the amplitude response of the conventional delay-and-sum (DAS) method while maintaining the computational efficiency of WA. This is achieved through a derivation of a correction factor that restores DAS-like amplitude characteristics in WA. The correction is implemented in two stages, consisting of a matrix multiplication to the data in the Fourier domain and a subsequent scaling with the z coordinate in the reconstructed image. Validation on simulated point targets, phantom experiment, and in-vivo imaging demonstrates that the proposed method produces images nearly indistinguishable from DAS but with significantly reduced computational burden. We also investigate the role of zero-padding, showing how interpolation accuracy affects reconstruction fidelity and computational efficiency. The proposed approach can, for example, facilitate the development of ultrasound systems with reduced power consumption.