A New Energy Inversion for Parameter Identification in Saddle Point Problems with an Application to the Elasticity Imaging Inverse Problem of Predicting Tumor Location
A New Energy Inversion for Parameter Identification in Saddle Point Problems with an Application to the Elasticity Imaging Inverse Problem of Predicting Tumor Location
复制标题
鞍点问题参数识别的新能量反演及其在预测肿瘤位置的弹性成像反问题中的应用
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
B. Winkler
中科院分区：
文献类型：
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作者：
M. Doyley;B. Jadamba;A. A. Khan;M. Sama;B. Winkler
这项工作的主要目标是对人体内肿瘤识别的弹性成像反问题进行详细的理论和计算研究。除了这个反问题的重要和有趣的应用之外，它还提出了值得注意的数学挑战，因为基础数学模型是涉及不可压缩性的弹性系统。这就产生了“锁定”效应，对于正问题和逆问题都需要特殊处理。为了研究优化框架中的逆问题，我们引入了处理鞍点问题中的参数识别的通用计算方案，并引入和分析了新的能量输出最小二乘目标函数。我们还提出了一种使用全变分正则化方法来识别不连续弹性系数的方法。给出了连续问题及其离散模拟的系数解图计算和完整收敛分析的通用公式。详细讨论了离散公式和实现问题，并给出了平滑和不连续系数的数值示例。
The primary objective of this work is a detailed theoretical and computational study of the elasticity imaging inverse problem for tumor identification within the human body. Apart from this inverse problem's important and interesting application, it also poses noteworthy mathematical challenges since the underlying mathematical model is a system of elasticity involving incompressibility. This gives rise to the “locking” effect and special treatment is necessary for both the direct and inverse problems. To study the inverse problem in an optimization framework, we introduce a general computational scheme for handling parameter identification in saddle point problems along with the introduction and analysis of a new energy output least-squares objective functionals. We also present a treatment of the identification of discontinuous elasticity coefficients using the total variation regularization method. General formulas for the computation of the coefficient-to-solution map and a complete convergence analysis are given for the continuous problem as well as for its discrete analogue. Discrete formulas and implementation issues are discussed in detail and numerical examples for smooth and discontinuous coefficients are given.
影响因子：
2.9
作者：
PARKER, KJ;HUANG, SR;LERNER, RM
通讯作者：
LERNER, RM