[Paper Review] Far-field compressive ultrasound beamforming

Nikunj Khetan, Jerome Mertz|arXiv (Cornell University)|Mar 23, 2026

Ultrasound Imaging and Elastography0 citations

TL;DR

The paper proposes KK beamforming, a far-field, plane-wave-based compressive method for CPWC ultrasound imaging that recasts data into k-space, enabling substantial RF data compression (≈ an order of magnitude) with image quality comparable to conventional CPWC DAS.

ABSTRACT

We present a compressive beamforming method for coherent plane-wave compounding (CPWC) ultrasound imaging based on a far-field decomposition of the received radiofrequency (RF) data into virtual plane waves. This decomposition recasts the imaging operation entirely in the spatial frequency domain ($k$-space), allowing direct and flexible control over $k$-space sampling distributions based on the principle of coarrays. We present vernier-type sampling strategies designed to optimize the tradeoff between image contrast and resolution with minimum redundancy, including strategies that favor dense low-frequency sampling for high contrast, shifted schemes that extend the frequency support for improved resolution, and confocal or hybrid compounding schemes that approximate the spatial-frequency transfer function of conventional DAS beamforming. Our method, called KK beamforming, is validated with a calibration phantom and in-vivo human tissue data, demonstrating compression factors of an order of magnitude while maintaining image qualities comparable to conventional DAS. We further demonstrate that KK beamforming yields improvements in computational speed owing to its reduced memory footprint and more efficient cache utilization of the compressed data and associated look-up tables.

Motivation & Objective

• Motivate data-efficient ultrasound imaging by reducing CPWC data demands without sacrificing image quality.
• Develop a far-field, k-space-based decomposition of RF data for CPWC that enables controllable sampling via coarrays.
• Propose vernier-type and confocal sampling strategies to balance contrast and resolution under compression.
• Introduce KK beamforming and demonstrate compression factors up to an order of magnitude with phantom and in-vivo data.

Proposed method

• Recade RF data into the spatial-frequency domain by a temporal shear and sum operation to obtain RF_theta from RF_u (Eq. 3).
• Form KK beamforming with a fully far-field, plane-wave transmit/receive model; compute B_KK using delays based on s_i and s_o (Eq. 5).
• Control k-space sampling via selectable receive angles theta_o and transmit angles theta_i to achieve vernier-type, shifted, or confocal sampling (Eqs. 6, 9).
• Compounded KK images can be formed coherently or incoherently to trade contrast and resolution (Eqs. 7–8).
• Reduce memory and compute load with triangular/layered look-up tables and FFT-based processing; compare performance against conventional CPWC DAS.

Experimental results

Research questions

• RQ1 Can KK beamforming achieve substantial RF data compression for CPWC without severe degradation in image quality?
• RQ2 How does controlling transmit/receive angular sampling in k-space affect image contrast and resolution?
• RQ3 What are the tradeoffs between coherent, incoherent, and hybrid KK compounding in terms of image quality and data compression?

Key findings

• KK beamforming achieves data compression factors up to an order of magnitude while preserving image quality comparable to conventional CPWC DAS.
• Different k-space sampling schemes (vernier-type, shifted, confocal) provide tunable tradeoffs between image contrast and resolution.
• Hybrid coherent/incoherent compounding can yield improved contrast under compression, potentially outperforming DAS in some metrics (gCNR).
• In vivo and phantom experiments with a GE9LD linear array show KK can maintain image quality under substantial RF data reduction.
• KK beamforming offers faster processing and reduced memory footprint due to compressed data and efficient LUT usage.