So you think you can DAS? A viewpoint on delay-and-sum beamforming (2007.11960v3)

Abstract: Delay-and-sum (DAS) is the most widespread digital beamformer in high-frame-rate ultrasound imaging. Its implementation is simple and compatible with real-time applications. In this viewpoint article, we describe the fundamentals of DAS beamforming. The underlying theory and numerical approach are detailed so that users can be aware of its functioning and limitations. In particular, we discuss the importance of the f-number and speed of sound on image quality, and propose one solution to set their values from a physical viewpoint. We suggest determining the f-number from the directivity of the transducer elements and the speed of sound from the phase dispersion of the delayed signals. Simplified Matlab codes are provided for the sake of clarity and openness. The effect of the f-number and speed of sound on the lateral resolution and contrast-to-noise ratio was investigated in vitro and in vivo. If not properly preset, these two factors had a substantial negative impact on standard metrics of image quality (namely CNR and FWHM). When beamforming with DAS in vitro or in vivo, it is recommended to optimize these parameters in order to use it wisely and prevent image degradation.

• The paper demonstrates that precise calibration of f-number and speed of sound significantly enhances image quality in ultrasound imaging.
• It validates theoretical formulations with in vitro and in vivo experiments, showing improvements in metrics like CNR and FWHM.
• The study underscores DAS beamforming’s ongoing relevance despite emerging adaptive methods and deep learning integration.

An Expert Perspective on Delay-and-Sum Beamforming in Ultrasound Imaging

The paper by Perrot et al. presents an in-depth analysis of the Delay-and-Sum (DAS) beamforming, a prevalent technique in high-frame-rate ultrasound imaging. DAS is favored for its simplicity, numerical robustness, and compatibility with real-time applications. The paper elucidates the underlying principles of DAS beamforming, emphasizing critical factors such as the speed of sound and f-number, which significantly influence image quality.

DAS has its origins not only in ultrasound imaging but also in radar technology, showcasing its multidisciplinary applications. The paper highlights the fundamental concept of DAS, which involves steering and summing array signals to reinforce signals from a desired direction while minimizing interference from others. This technique, crucial in radar and sonar, also applies to geophysical explorations and telecommunications, where it is denoted as "diffraction summation" or "Kirchhoff migration." In ultrasound imaging, DAS beamforming achieves image formation by focusing on the signals backscattered from within tissues, which behave as primary point sources, emitting spherical waves.

The paper thoroughly examines two parameters, the f-number and the speed of sound, which significantly affect DAS beamforming. The f-number is associated with the directivity of array elements, providing control over the aperture of the beamformed signal. This parameter is vital in balancing bias and variance in signal processing, thus impacting image resolution and contrast. The authors propose determining the f-number from transducer directivity using specific mathematical formulations, ensuring optimal use of the receive aperture.

The speed of sound is another critical factor, influencing the shape of the hyperbolic paths upon which the signals are summed. An optimal speed of sound leads to minimal phase dispersion along these paths, enhancing image quality. Importantly, the paper introduces a phase-based metric for optimizing this parameter, which involves analyzing phase uniformity to calculate an expected average speed of sound that maximizes this metric.

In vitro and in vivo experiments underscore the significance of correctly setting these parameters. The research employs datasets from PICMUS, demonstrating that both f-number and speed of sound considerably affect Contrast-to-Noise Ratio (CNR) and Full Width at Half Maximum (FWHM). The findings advocate for the precise calibration of DAS parameters to avoid biases in evaluations against adaptive beamformers or when integrated into deep learning-based systems.

The authors acknowledge the advantages of DAS but also recognize its limitations and the exploration of alternatives. Adaptive beamformers, which adjust weights based on data, offer improvements over DAS in specific scenarios, though potentially at the cost of computational complexity and unsteady phase information. Additionally, recent advancements explore the integration of deep learning to expedite high-quality image generation. Therefore, ensuring the optimal configuration of DAS remains crucial for generating reliable training datasets in deep learning frameworks.

Overall, the paper presents DAS as an essential yet underappreciated technique in ultrasound imaging. Perrot et al. propose systematic methods for appropriately setting DAS parameters, emphasizing that a well-implemented DAS can substantially improve image quality. Future explorations into advanced beamforming techniques can thereby benefit from a proper understanding and application of DAS methodologies, fostering enhancements in both theoretical and practical dimensions of ultrasound imaging and beyond.