中国物理B ›› 2026, Vol. 35 ›› Issue (7): 74301-074301.doi: 10.1088/1674-1056/ae42b9

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

Huchang Guan(关虎昌)1, Chen Jiang(江晨)2,†, Kailiang Xu(许凯亮)1,3,‡, and Dean Ta(他得安)1,3   

  1. 1 College of Biomedical Engineering, Fudan University, Shanghai 200438, China;
    2 Yiwu Research Institute of Fudan University, Yiwu 322000, China;
    3 State Key Laboratory of Integrated Chips and Systems, Fudan University, Shanghai 201203, China
  • 收稿日期:2025-12-13 修回日期:2026-02-05 接受日期:2026-02-06 发布日期:2026-07-21
  • 通讯作者: Chen Jiang, Kailiang Xu E-mail:Cjiang17@fudan.edu.cn;xukl@fudan.edu.cn
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No. 12574495), the National Key Research and Development Program of China (Grant No. 2023YFC2410900), and the Natural Science Foundation of Gansu Province (Grant No. 25JRRG038).

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

Huchang Guan(关虎昌)1, Chen Jiang(江晨)2,†, Kailiang Xu(许凯亮)1,3,‡, and Dean Ta(他得安)1,3   

  1. 1 College of Biomedical Engineering, Fudan University, Shanghai 200438, China;
    2 Yiwu Research Institute of Fudan University, Yiwu 322000, China;
    3 State Key Laboratory of Integrated Chips and Systems, Fudan University, Shanghai 201203, China
  • Received:2025-12-13 Revised:2026-02-05 Accepted:2026-02-06 Published:2026-07-21
  • Contact: Chen Jiang, Kailiang Xu E-mail:Cjiang17@fudan.edu.cn;xukl@fudan.edu.cn
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No. 12574495), the National Key Research and Development Program of China (Grant No. 2023YFC2410900), and the Natural Science Foundation of Gansu Province (Grant No. 25JRRG038).

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摘要： 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.

关键词: total focusing method, full matrix capture, frequency-wavenumber, two-dimensional matrix array

Abstract: 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.

Key words: total focusing method, full matrix capture, frequency-wavenumber, two-dimensional matrix array

中图分类号:  (Acoustical medical instrumentation and measurement techniques)

  • 43.80.Vj
43.60.Tj (Wave front reconstruction, acoustic time-reversal, and phase conjugation) 87.57.nf (Reconstruction)