论文标题

使用传输几何形状对波束形成速度的分析估计

Analytical Estimation of Beamforming Speed-of-Sound Using Transmission Geometry

论文作者

Bezek, Can Deniz, Goksel, Orcun

论文摘要

储层计算是预测湍流的有力工具,其简单的架构具有处理大型系统的计算效率。然而,其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间,然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用,该系统模拟了湍流的若干特征。我们表明,使用径向基函数作为非线性投影器,即使只有部分观测并且不知道控制方程,也能稳健地捕捉复杂的系统非线性。最后,我们表明,当测量稀疏、不完整且带有噪声,甚至控制方程变得不准确时,我们的网络仍然可以产生相当准确的预测,从而为实际湍流系统的无模型预测铺平了道路。

Most ultrasound imaging techniques necessitate the fundamental step of converting temporal signals received from transducer elements into a spatial echogenecity map. This beamforming (BF) step requires the knowledge of speed-of-sound (SoS) value in the imaged medium. An incorrect assumption of BF SoS leads to aberration artifacts, not only deteriorating the quality and resolution of conventional brightness mode (B-mode) images, hence limiting their clinical usability, but also impairing other ultrasound modalities such as elastography and spatial SoS reconstructions, which rely on faithfully beamformed images as their input. In this work, we propose an analytical method for estimating BF SoS. We show that pixel-wise relative shifts between frames beamformed with an assumed SoS is a function of geometric disparities of the transmission paths and the error in such SoS assumption. Using this relation, we devise an analytical model, the closed form solution of which yields the difference between the assumed and the true SoS in the medium. Based on this, we correct the BF SoS, which can also be applied iteratively. Both in simulations and experiments, lateral B-mode resolution is shown to be improved by $\approx$25% compared to that with an initial SoS assumption error of 3.3% (50 m/s), while localization artifacts from beamforming are also corrected. After 5 iterations, our method achieves BF SoS errors of under 0.6 m/s in simulations and under 1 m/s in experimental phantom data. Residual time-delay errors in beamforming 32 numerical phantoms are shown to reduce down to 0.07 $μ$s, with average improvements of up to 21 folds compared to initial inaccurate assumptions. We additionally show the utility of the proposed method in imaging local SoS maps, where using our correction method reduces reconstruction root-mean-square errors substantially, down to their lower-bound with actual BF SoS.

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