We consider the problem of estimating the 2D vector displacement field in a heterogeneous elastic solid deforming under plane stress conditions. The problem is motivated by applications in quasistatic elastography. From precise and accurate measurements of one component of the 2D vector displacement field and very limited information of the second component, the method reconstructs the second component quite accurately. No a priori knowledge of the heterogeneous distribution of material properties is required. This method relies on using a special form of the momentum equations to filter ultrasound displacement measurements to produce more precise estimates. We verify the method with applications to simulated displacement data. We validate the method with applications to displacement data measured from a tissue mimicking phantom, and in-vivo data; significant improvements are noticed in the filtered displacements recovered from all the tests. In verification studies, error in lateral displacement estimates decreased from about 50% to about 2%, and strain error decreased from more than 250% to below 2%.

中文翻译：

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使用动量方程的稀疏松弛恢复准静态弹性成像中的矢量位移估计

我们考虑在平面应力条件下在异质弹性固体变形中估计二维矢量位移场的问题。这个问题是由准静态弹性成像中的应用引起的。根据对 2D 矢量位移场的一个分量的精确测量和第二个分量的非常有限的信息，该方法非常准确地重建了第二个分量。不需要材料特性的异质分布的先验知识。该方法依赖于使用特殊形式的动量方程来过滤超声位移测量值以产生更精确的估计。我们通过对模拟位移数据的应用来验证该方法。我们通过对从组织模拟体模和体内数据测量的位移数据的应用来验证该方法；从所有测试中恢复的过滤位移都有显着的改进。在验证研究中，横向位移估计的误差从大约 50% 下降到大约 2%，应变误差从超过 250% 下降到低于 2%。