Generalized Fourier Beamformer Based on the Cross-Correlation of Transmitted and Received Wavefields
Fourier beamforming is generally used to form medical ultrasound images using specific transmission sequences. Fourier beamforming is distinct from delay-and-sum beamforming in that the diffraction process is used to focus ultrasound signals rather than selecting signal values based on times-of-flight. The Fourier beamformer shown here is applicable to any transmit sequence as long as the element-wise transmit apodizations and delays are known along with their corresponding receive channel data.
We provide sample data and algorithms presented in
R. Ali, “Fourier-based Synthetic-aperture Imaging for Arbitrary Transmissions by Cross-correlation of Transmitted and Received Wave-fields,” Ultrasonic Imaging, p. 016173462110263, Jul. 2021, doi: 10.1177/01617346211026350. [Online]. Available: http://dx.doi.org/10.1177/01617346211026350 *
for the reconstruction ultrasound images based on conventional dynamic-receive beamforming, virtual source synthetic aperture, REFoCUS (https://github.com/nbottenus/REFoCUS), and the proposed Fourier beamforming technique (called "full-waveform reconstruction" here, but "shot-profile migration" in the paper).
If you use the code/algorithm for research, please cite the above paper.
You can reference a static version of this code by its DOI number:
Each image reconstruction algorithm is implemented in both MATLAB and Python:
- Conventional dynamic-receive beamforming (FocTxRecon.m and FocTxRecon.py)
- Virtual source synthetic aperture (VirtualSourceRecon.m and VirtualSourceRecon.py)
- REFoCUS (AdjointBasedREFoCUS.m and AdjointBasedREFoCUS.py)
- Full-Waveform Reconstruction in Time Domain (TimeDomFullWaveRecon.m and TimeDomFullWaveRecon.py) and Frequency Domain (FreqDomFullWaveRecon.m and FreqDomFullWaveRecon.py)
Please see any supporting functions in beamforming_functions.
Please download the sample data (FocTxDataset.mat) under the releases tab for this repository, and place that data in the main directory (FourierDomainBeamformer).
The Fourier beamforming technique provided is equivalent to the time-domain cross-correlation process shown here:
Here are results for conventional dynamic-receive beamforming, virtual source synthetic aperture, REFoCUS, and the proposed Fourier beamforming technique ("full-waveform reconstruction" here but "shot-profile migration" in the paper):
