Rectified wavenumber algorithms for efficient ultrasound imaging

Wavenumber-domain beamforming offers substantial computational advantage over conventional time-domain algorithms in ultrasound image formation. However, these methods are found to introduce distortions at large angles and greater depths, making it nontrivial to replace conventional processing pipelines with wavenumber-domain approaches. This paper presents a wavenumber-domain framework that produces images consistent with conventional delay-and-sum (DAS) beamforming, while retaining the computational efficiency of Fourier-domain processing. Building on recent work on DAS-consistent imaging for multistatic acquisition data, the key utility of this novel algorithm is its applicability in plane-wave, focused-transmit, and diverging-wave imaging. The approach compensates for the implicit spatial-frequency filtering of earlier wavenumber-domain formulations through a modified Fourier-domain weighting and an axial scaling to the reconstructed image. Using data from simulations, phantom experiments, and in-vivo liver imaging, we demonstrate that the proposed method preserves DAS-equivalent amplitude, speckle statistics, resolution, and contrast. Quantitative image comparison confirms a close agreement between DAS and the proposed method with Structural Similarity (SSIM) values exceeding 0.99, whereas SSIM between earlier wavenumber-domain beamformers and DAS is lower, ranging from 0.67 to 0.92 depending on the transmit scheme. The proposed method yields approximately one order-of-magnitude reduction in computational cost compared to conventional DAS, making it well-suited for real-time and resource-constrained ultrasound systems.