在椭圆域上使用D-bar方法对导电和绝缘目标进行重构。
Reconstructions of conductive and insulating targets using the D-bar method on an elliptical domain.
作者信息
Murphy E K, Mueller J L, Newell J C
机构信息
Department of Mathematics, Colorado State University, Fort Collins, CO 80523, USA.
出版信息
Physiol Meas. 2007 Jul;28(7):S101-14. doi: 10.1088/0967-3334/28/7/S08. Epub 2007 Jun 26.
Abstract
The D-bar algorithm based on A Nachman's 2D global uniqueness proof for the inverse conductivity problem (Nachman 1996 Ann. Math. 143 71-96) is implemented on an elliptical domain. The scattering transform is computed on an ellipse and the complete electrode model (CEM) for the forward problem is computed with the finite element method (FEM) in order to obtain static conductivity reconstructions of conductive and insulating targets in a saline-filled tank. It is demonstrated that the spatial artifacts in the image are significantly reduced when the domain is properly modeled in the reconstruction, as opposed to being modeled as a disk.
摘要
基于A·纳赫曼关于电导率逆问题的二维全局唯一性证明（纳赫曼，《数学年刊》，1996年，第143卷，第71 - 96页）的D-bar算法在一个椭圆形区域上实现。在椭圆上计算散射变换，并使用有限元方法（FEM）计算正向问题的完整电极模型（CEM），以便在充满盐水的水箱中获得导电和绝缘目标的静态电导率重建。结果表明，与将区域建模为圆盘相比，当在重建中对区域进行适当建模时，图像中的空间伪影会显著减少。
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