Reconstruction in the Calderón problem on a fixed partition from finite and partial boundary data
Henrik Garde
这个简短的说明修改了作者的重建方法(Comm. PDE,45(9):1118-1133,2020),用于重建卡尔德龙问题(电阻抗断层扫描)的分段恒定导电性。 在前一篇论文中,需要分层假设和本地的Neumann-to-Dirichlet地图,因为零碎的恒定分区也被认为是未知的。 在这里,我展示了如何修改方法,以防分区是已知的,对于一般的分段常数导电性和有限数量的部分边界测量。 此外,不需要对未知的导电性进行较低/上限。
This short note modifies a reconstruction method by the author (Comm. PDE, 45(9):1118–1133, 2020), for reconstructing piecewise constant conductivities in the Calderón problem (electrical impedance tomography). In the former paper, a layering assumption and the local Neumann-to-Dirichlet map was needed since the piecewise constant partitioning also was assumed unknown. Here I show how to modify the method in case the partitioning is known, for general piecewise constant conductivities and only a...