The Linearized Inverse Problem in Multifrequency Electrical Impedance Tomography
The Linearized Inverse Problem in Multifrequency Electrical Impedance Tomography
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DOI：
10.1137/16m1061564
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发表时间：
2016-01-01
影响因子：
2.1
通讯作者：
Zhang, Wenlong
中科院分区：
文献类型：
--
作者：
Alberti, Giovanni S.;Ammari, Habib;Zhang, Wenlong
本文分析了多频电阻抗成像中的线性化反问题。我们考虑一个各向同性的电导率分布与有限数量的未知夹杂物与不同的频率依赖性，是经常看到的生物组织。我们讨论重建方法完全已知和部分已知的光谱轮廓，并证明在后者的情况下，成功就业的差异成像。我们还研究了重建与不完全已知的边界，并表明，多频方法可以消除建模误差，恢复几乎所有的夹杂物。此外，我们开发了一个有效的组稀疏恢复算法的鲁棒解决相关的线性逆问题。几个数值模拟来说明和验证的方法。
This paper provides an analysis of the linearized inverse problem in multifrequency electrical impedance tomography. We consider an isotropic conductivity distribution with a finite number of unknown inclusions with different frequency dependence, as is often seen in biological tissues. We discuss reconstruction methods for both fully known and partially known spectral profiles and demonstrate in the latter case the successful employment of difference imaging. We also study the reconstruction with an imperfectly known boundary and show that the multifrequency approach can eliminate modeling errors and recover almost all inclusions. In addition, we develop an efficient group sparse recovery algorithm for the robust solution of related linear inverse problems. Several numerical simulations are presented to illustrate and validate the approach.