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 matrixmultiplication 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.