[论文解读] The SVD Beamformer: Physical Principles and Application to Ultrafast Adaptive Ultrasound

Hanna Bendjador, Thomas Deffieux+1 more|arXiv (Cornell University)|Oct 13, 2019

Ultrasound Imaging and Elastography参考文献 38被引用 61

一句话总结

本论文提出一种基于 SVD 的方法，用于超快速超声的像差校正和自适应波束形成，利用来自多次平面波透射的散射数据，实现异质介质中的实时自适应成像。

ABSTRACT

A shift of paradigm is currently underway in biomedical ultrasound thanks to plane and diverging waves for ultrafast imaging. One remaining challenge consists in the correction of phase and amplitude aberrations induced during propagation through complex layers. Unlike conventional line-per-line imaging, ultrafast ultrasound provides for each transmission, backscattering information from the whole imaged area. Here, we take benefit from this feature and propose an efficient approach to perform fast aberration correction based on the Singular Value Decomposition of an ultrafast compound matrix built from backscattered data for several plane wave transmissions. First, we explain the physical signification of SVD and associated singular vectors within the ultrafast matrix formalism. We theoretically demonstrate that the spatial and angular variables separation, rendered by SVD on ultrafast data, provides an elegant and straightforward way to optimize angular coherence of backscattered data. In heterogeneous media with an aberrating phase screen approximation, we demonstrate that the first spatial and angular singular vectors retrieve on one side the non-aberrated image, and on the other, the phase and amplitude of the aberration law. In vitro results prove the efficiency of the image correction, but also the accuracy of the aberrator determination. Based on spatial and angular coherence, we introduce a complete methodology for adaptive beamforming of ultrafast data, performed on successive isoplanatism patches undergoing SVD beamforming. The simplicity of this method paves the way to real-time adaptive ultrafast ultrasound imaging and provides a theoretical framework for future quantitative ultrasound applications.

研究动机与目标

• 推动采用超快速平面/发散波超声以实现快速成像，并识别残留的相位/幅度像差。
• 开发一种数据驱动的方法，使用在聚合的超快速数据矩阵上的 SVD 来纠正像差。
• 在超快速矩阵形式中解释奇异向量的物理意义及其在相干优化中的作用。
• 提出基于 SVD、在等像平面块上实现的实用自适应波束形成工作流，以实现实时成像。

提出的方法

• 从若干平面波透射的散射信息构建一个超快速的复合数据矩阵。
• 应用奇异值分解（SVD）以分离空间信息和角度信息。
• 从理论上将第一组空间奇异向量和角度奇异向量与非像差图像以及像差规律联系起来。
• 体外结果表明基于 SVD 的校正提升了图像质量，并能准确检索 aberrator。
• 在连续的等像平面块上基于 SVD 开发完整的自适应波束形成管线。

实验结果

研究问题

• RQ1 如何通过对超快速散射数据的 SVD 将空间分量和角度分量分离以纠正像差？
• RQ2 第一组空间奇异向量和角度奇异向量是否能在异质介质中重建非像差图像及像差规律？
• RQ3 基于 SVD 的自适应波束形成框架是否在存在相位和幅度像差时改善超快速超声成像？
• RQ4 该方法是否对跨越等像平面的实时自适应超快速超声成像可行？

主要发现

• SVD 分离提供了一种直接的方法来优化散射数据的角度相干。
• 第一组空间和角向奇异向量分别能够恢复非像差图像和像差规律。
• 体外结果证实了有效的影像校正和准确的 aberrator 估计。
• 提出了一种基于 SVD 相干性原理的在等像平面块上的完整自适应波束形成方法。
• 该方法支持实时自适应超快速超声成像的潜力。