一种带有修正项和先验信息的二阶卡尔德隆方法。
A second order Calderón's method with a correction term and a priori information.
作者信息
Shin Kwancheol, Mueller Jennifer L, Mueller Jennifer L
机构信息
Department of Mathematics, Colorado State University, USA.
Department of Mathematics and School of Biomedical Engineering, Colorado State University, USA.
出版信息
Inverse Probl. 2020 Dec;36(12). doi: 10.1088/1361-6420/abb014. Epub 2020 Dec 3.
Abstract
Calderón's method is a direct linearized reconstruction method for the inverse conductivity problem with the attribute that it can provide absolute images of both conductivity and permittivity with no need for forward modeling. In this work, an explicit relationship between Calderón's method and the D-bar method is provided, facilitating a "higher-order" Calderón's method in which a correction term is included, derived from the relationship to the D-bar method. Furthermore, a method of including a spatial prior is provided. These advances are demonstrated on simulated data and on tank data collected with the ACE1 EIT system.
摘要
卡尔德隆方法是一种用于解决电导率逆问题的直接线性化重建方法，其特点是无需正向建模就能提供电导率和介电常数的绝对图像。在这项工作中，给出了卡尔德隆方法与D-bar方法之间的明确关系，从而促成了一种“高阶”卡尔德隆方法，其中包含一个从与D-bar方法的关系中推导出来的校正项。此外，还提供了一种纳入空间先验的方法。这些进展在模拟数据以及使用ACE1电阻抗断层成像（EIT）系统收集的水槽数据上得到了验证。
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