基于平面上卡尔德隆方法的各向异性逆电导率问题的直接重建算法
A DIRECT RECONSTRUCTION ALGORITHM FOR THE ANISOTROPIC INVERSE CONDUCTIVITY PROBLEM BASED ON CALDERÓN'S METHOD IN THE PLANE.
作者信息
Murthy Rashmi, Lin Yi-Hsuan, Shin Kwancheol, Mueller Jennifer L
机构信息
Department of Mathematics, University of Helsinki, Finland.
Department of Applied Mathematics, National Chiao Tung University, Hsinchu, Taiwan.
出版信息
Inverse Probl. 2020 Dec;36(12). doi: 10.1088/1361-6420/abbe5f. Epub 2020 Dec 3.
A direct reconstruction algorithm based on Calderón's linearization method for the reconstruction of isotropic conductivities is proposed for anisotropic conductivities in two-dimensions. To overcome the non-uniqueness of the anisotropic inverse conductivity problem, the entries of the unperturbed anisotropic tensors are assumed known , and it remains to reconstruct the multiplicative scalar field. The quasi-conformal map in the plane facilitates the Calderón-based approach for anisotropic conductivities. The method is demonstrated on discontinuous radially symmetric conductivities of high and low contrast.
提出了一种基于卡尔德隆线性化方法的直接重建算法，用于二维各向异性电导率的各向同性电导率重建。为了克服各向异性逆电导率问题的非唯一性，假设未扰动各向异性张量的元素已知，剩下的就是重建乘法标量场。平面中的拟共形映射促进了基于卡尔德隆方法的各向异性电导率研究。该方法在高对比度和低对比度的不连续径向对称电导率上得到了验证。
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