Reduced Boundary Sensitivity and Improved Contrast of the Regularized Inverse Problem Solution in Elasticity
Reduced Boundary Sensitivity and Improved Contrast of the Regularized Inverse Problem Solution in Elasticity
复制标题
弹性正则逆问题解的降低边界敏感性和改进对比度
DOI：
10.1115/1.4031937
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
S. Goenezen
中科院分区：
文献类型：
--
作者：
Yue Mei;S. Kuznetsov;S. Goenezen
我们观察到，构成的逆问题作为一个约束下的正则化最小化问题，导致边界依赖的解决方案。在本文中，我们提出了一个修改的目标函数，并显示与二维的例子，我们的方法很好地减少边界敏感的解决方案。例子包括两个刚性夹杂物嵌入在一个较软的单位正方形。这些内含物可以代表肿瘤，其通常比其背景组织更硬，因此可以基于其硬度对比潜在地检测到。我们修改的位移相关项的目标函数的加权依赖于应变场的函数。在一个简化的一维耦合模型中，我们推导出一个解析表达式，并观察到相同的趋势，在重建的二维模型。本文的分析仅限于尺寸相似的夹杂物，在水平轴上投影时可能不重叠。然而，它们的位置可以沿垂直轴沿着变化。此外，我们的分析适用于任意数量的夹杂物具有不同的刚度值。最后，为了增加肿瘤的整体对比度，同时提高平滑度，我们在后一步中利用空间变化的正则化因子来解决正则化逆问题。
We observe that posing the inverse problem as a constrained minimization problem under regularization leads to boundary dependent solutions. In this paper, we propose a modified objective function and show with 2D examples that our method works well to reduce boundary sensitive solutions. The examples consist of two stiff inclusions embedded in a softer unit square. These inclusions could be representative of tumors, which are in general stiffer than their background tissues, thus could potentially be detected based on their stiffness contrast. We modify the objective function for the displacement correlation term by weighting it with a function that depends on the strain field. In a simplified 1D coupled model, we derive an analytical expression and observe the same trends in the reconstructions as for the 2D model. The analysis in this paper is confined to inclusions of similar size and may not overlap when projected on the horizontal axis. They may, however, vary in position along the vertical axis. Furthermore, our analysis holds for an arbitrary number of inclusions having distinct stiffness values. Finally, to increase the overall contrast of the tumors and simultaneously improve the smoothness, we solve the regularized inverse problem in a posterior step, utilizing a spatially varying regularization factor.
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