Distributed Aberration Correction in Liver Imaging via Iterative Model-Based Sound Speed Estimation

Benjamin N. Frey1, Robin van Velzen2, Jihye Baek3, Hoda S. Hashemi3,
Martin Schneider3, Sergio J. Sanabria3, Jeremy J. Dahl3
Departments of 1Applied Physics and 3Radiology, Stanford University
2Department of Biomedical Engineering, Eindhoven University of Technology
Video Poster

Overview

Overweight and obesity affect 73% of adults in the United States1 (42% worldwide2), and these conditions are associated with excess adipose tissue. Ultrasound imaging is a non-invasive, portable, and inexpensive imaging modality. However, image quality can be degraded by adipose tissue layers which have varying speed of sound distributions, causing aberration artifacts. We present a novel method for distributed aberration correction in liver imaging using differentiable beamforming and iterative model-based sound speed estimation.

Differentiable Beamforming for Sound Speed Estimation

We adapted a differentiable beamforming model for aberration correction via sound speed estimation3 to work with experimental curvilinear transducer data. Please see the presentation video for more information on model changes and physical lens calibration.

Technical approach diagram

Figure description: (A) First, a full-synthetic aperture (FSA) ultrasound dataset is collected. However, any ultrasound transmit sequence can be used with the proposed method in combination with REFoCUS4. (B-C) Next, a time of flight is calculated by interpolating ray paths onto a discrete grid and integrating slowness along the ray path. (D) A synthetic-aperture delay-and-sum (DAS) image is beamformed using these time of flight values. (E-F) The common-midpoint phase error term is computed, which is a term in the loss function ℒ. (G) The differential of the loss with respect to the sound speed map is backpropagated through the differentiable beamforming model to update the sound speed assumption c(r). This iterative process is repeated for a pre-defined number of iterations.

Data Acquisition

We validated our aberration correction model on k-Wave simulation and in vivo human liver data.

Technical approach diagram

Simulation Results

Here are the aberration correction results on the simulated data. We can see delay-and-sum B-modes using a traditional 1540 m/s sound speed. Across all four targets, non of the keyboard letters are legible. Next, we swept over a range of sound speed values and found the value with the lowest common-midpoint phase error to initialize each model with. While this first step provides good global aberration correction, we achieve fantastic local aberration correction after the iterative optimization process has been applied.

Experimental Results

Model performance on in vivo human liver data is visualized below for four subjects. MimickNet6 was used to post-process our in vivo B-modes, a neural network used to make research ultrasound data look more like clinical data. In all cases, B-mode focusing is improved compared with the 1540 m/s beamforming assumption.

Regarding quantitative metrics evaluated on the in-vivo data, we see that contrast, contrast-to-noise ratio, and global image quality metrics all improve. However, due to the significant aberration and sound speed variations between subjects, we believe that better evaluation metrics would be useful for the assessment of sound speed-based aberration correction methods.

Metric results

Related Projects

Check out some related projects on adaptive ultrasound imaging with automatic differentiation!

UltraFlex abstract image
UltraFlex: Iterative Model-Based Ultrasonic Flexible-Array Shape Calibration

Benjamin N. Frey, Dongwoon Hyun, Walter Simson, Louise Zhuang, Hoda S. Hashemi, Martin Schneider, Jeremy J. Dahl

IEEE T-UFFC (Under Revision), 2025 (project page)

UltraFlex is a framework for iterative model-based ultrasonic flexible-array shape calibration and image autofocusing.

Differentiable Beamforming for Distributed Attenuation Estimation and Spatial Gain Compensation (SGC)

Benjamin N. Frey, Dongwoon Hyun, Walter Simson, Thurston Brevett, Louise Zhuang, Jihye Baek, Sergio J. Senabria, Jeremy J. Dahl

IEEE Ultrasonics, Ferroelectrics, and Frequency Control Joint Symposium, 2024 (project page)

Distributed attenuation estimation can enable local application of gain compensation in space, compensating for energy loss due to attenuation through Spatial Gain Compensation (SGC).

Differentiable Beamforming for Ultrasound Autofocusing

Walter Simson, Louise Zhuang, Sergio J. Senabria, Neha Antil, Jeremy J. Dahl, Dongwoon Hyun

MICCAI, 2023 (project page)

Applying differentiable beamforming to auto-focus ultrasound and high-resolution estimate sound speed in tissue.

References

[1] Fryar, C. D., Carroll, M. D., & Ogden, C. L. (2018). Prevalence of overweight, obesity, and severe obesity among adults aged 20 and over: U.S., 1960–1962 through 2015–2016.

[2] World Health Organization. (2022). Obesity and overweight. https://who.int/news-room/fact-sheets/detail/obesity-and-overweight

[3] Simson, W., Zhuang, L., Frey, B. N., Sanabria, S. J., Dahl, J. J., & Hyun, D. (2025, Sep.). Ultrasound Autofocusing: Common Midpoint Phase Error Optimization via Differentiable Beamforming. IEEE T-MI (Manuscript Published in Early-Access).

[4] Ali, R., Herickhoff, C. D., Hyun, D., Dahl, J. J., & Bottenus, N. (2019). Extending retrospective encoding for robust recovery of the multistatic data set. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 67(5), 943-956.

[5] Brevett, T. (2024). QUPS: A MATLAB Toolbox for Rapid Prototyping of Ultrasound Beamforming and Imaging Techniques. Journal of Open Source Software, 9(101), 6772.

[6] Huang, O., Long, W., Bottenus, N., … & Palmeri, M. L. (2020). Mimicknet, mimicking clinical image post-processing under black-box constraints. IEEE T-MI, 39(6), 2277-2286.

BibTeX


      @inproceedings{frey2025distributed,
        title={Distributed Aberration Correction in Liver Imaging via Iterative Model-Based Sound Speed Estimation},
        author={Frey, Benjamin N. and van Velzen, Robin and Baek, Jihye and Hashemi, Hoda S. and Schneider, Martin and Sanabria, Sergio J. and Dahl, Jeremy J.},
        booktitle={Proceedings of the IEEE International Ultrasonics Symposium (IUS)},
        year={2025},
        note={Lecture Presentation}
      }