Reconstruction in the Calder贸n problem on a fixed partition from finite and partial boundary data
Henrik Garde
Published: 2025/7/25
Abstract
This short note modifies a reconstruction method by the author (Comm.~PDE, 45(9):1118--1133, 2020), for reconstructing piecewise constant conductivities in the Calder\'on problem (electrical impedance tomography). In the former paper, a layering assumption and the local Neumann-to-Dirichlet map were needed since the piecewise constant partition also was assumed unknown. Here I show how to modify the method in case the partition is known, for general piecewise constant conductivities and only a finite number of partial boundary measurements. Moreover, no lower/upper bounds on the unknown conductivity are needed.