A New Convex Inversion Framework for Parameter Identification in Saddle Point Problems with an Application to the Elasticity Imaging Inverse Problem of Predicting Tumor Location
A New Convex Inversion Framework 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凸反演框架及其在预测肿瘤位置的弹性成像反演问题中的应用
DOI：
--
复制
发表时间：
2014
影响因子：
1.9
通讯作者：
B. Winkler
中科院分区：
文献类型：
--
作者：
B. Jadamba;A. A. Khan;Guillermo Rus;M. Sama;B. Winkler
本文对人体软组织肿瘤识别的弹性成像反问题进行了深入的理论和数值分析。除了其应用的明显优点之外，这个问题还带来了重大的数学挑战。线性弹性模型中固有的近不可压缩性引起了“锁定效应”，并需要对正问题和逆问题进行独特的处理。沿着一个新的修改输出最小二乘（MOLS）目标泛函的鞍点问题的参数识别的一般优化框架。的MOLS功能被证明是凸的，从而克服了经典的输出最小二乘（OLS）功能的非凸性，和新的框架被证明是能够容纳光滑和不连续的参数。广义导数公式的系数解决方案的映射也给出了沿着与一个完整的收敛性分析.
This work presents a thorough theoretical and numerical analysis of the elasticity imaging inverse problem of tumor identification in the soft tissue of the human body. Beyond the obvious merits of its applications, this problem also presents significant mathematical challenges. The near incompressibility inherent in the model of linear elasticity in the body gives rise to the “locking effect” and necessitates a unique treatment of both the direct and inverse problems. A general optimization framework for the identification of parameters in saddle point problems is presented along with a new modified output least-squares (MOLS) objective functional. The MOLS functional is shown to be convex, thus overcoming the nonconvexity of the classical output least-squares (OLS) functional, and the new framework is shown to be capable of accommodating both smooth and discontinuous parameters. Generalized derivative formulas for the coefficient-to-solution map are also given along with a complete convergence analysis....
影响因子：
2.9
作者：
PARKER, KJ;HUANG, SR;LERNER, RM
通讯作者：
LERNER, RM