IEEE Trans Ultrason Ferroelectr Freq Control. 2022 Mar;69(3):1008-1019. doi: 10.1109/TUFFC.2022.3141686. Epub 2022 Mar 2.
Time delay estimation (TDE) between two radio-frequency (RF) frames is one of the major steps of quasi-static ultrasound elastography, which detects tissue pathology by estimating its mechanical properties. Regularized optimization-based techniques, a prominent class of TDE algorithms, optimize a nonlinear energy functional consisting of data constancy and spatial continuity constraints to obtain the displacement and strain maps between the time-series frames under consideration. The existing optimization-based TDE methods often consider the L2 -norm of displacement derivatives to construct the regularizer. However, such a formulation over-penalizes the displacement irregularity and poses two major issues to the estimated strain field. First, the boundaries between different tissues are blurred. Second, the visual contrast between the target and the background is suboptimal. To resolve these issues, herein, we propose a novel TDE algorithm where instead of L2 -, L1 -norms of both first- and second-order displacement derivatives are taken into account to devise the continuity functional. We handle the non-differentiability of L1 -norm by smoothing the absolute value function's sharp corner and optimize the resulting cost function in an iterative manner. We call our technique Second-Order Ultrasound eLastography (SOUL) with the L1 -norm spatial regularization ( L1 -SOUL). In terms of both sharpness and visual contrast, L1 -SOUL substantially outperforms GLobal Ultrasound Elastography (GLUE), tOtal Variation rEgulaRization and WINDow-based time delay estimation (OVERWIND), and SOUL, three recently published TDE algorithms in all validation experiments performed in this study. In cases of simulated, phantom, and in vivo datasets, respectively, L1 -SOUL achieves 67.8%, 46.81%, and 117.35% improvements of contrast-to-noise ratio (CNR) over SOUL. The L1 -SOUL code can be downloaded from http://code.sonography.ai.
时移估计 (TDE) 是超声弹性成像的主要步骤之一，它通过估计组织的机械特性来检测组织病理学。基于正则化优化的技术是 TDE 算法的一个主要类别，它优化由数据一致性和空间连续性约束组成的非线性能量泛函，以获得所考虑的时间序列帧之间的位移和应变图。现有的基于优化的 TDE 方法通常考虑位移导数的 L2 范数来构建正则化项。然而，这种公式过度惩罚了位移不规则性，并对估计的应变场提出了两个主要问题。首先，不同组织之间的边界变得模糊。其次，目标和背景之间的视觉对比度不是最佳的。为了解决这些问题，本文提出了一种新的 TDE 算法，该算法不仅考虑了位移一阶和二阶导数的 L1 范数，还考虑了连续性泛函。我们通过平滑绝对值函数的尖锐角来处理 L1 范数的不可微性，并以迭代的方式优化得到的代价函数。我们将该技术称为基于 L1 范数空间正则化的二阶超声弹性成像 (SOUL) (L1-SOUL)。在清晰度和视觉对比度方面，L1-SOUL 在本研究中进行的所有验证实验中均显著优于最近发布的三种 TDE 算法，即 GLobal Ultrasound Elastography (GLUE)、tOtal Variation rEgulaRization 和 WINDow-based time delay estimation (OVERWIND)。在模拟、 phantom 和体内数据集的情况下，L1-SOUL 分别实现了对比度噪声比 (CNR) 相对于 SOUL 的 67.8%、46.81%和 117.35%的提高。L1-SOUL 代码可从 http://code.sonography.ai 下载。
