A Posteriori Error Estimates and Adaptive Error Control for Permittivity Reconstruction in Conductive Media

Paper in proceeding, 2023

An inverse problem of reconstruction of the spatially distributed dielectric permittivity function in the Maxwell’s system is considered. The reconstruction method is based on the optimization approach to find stationary point of the Tikhonov functional. A posteriori estimates for the corresponding Tikhonov functional and for the reconstructed dielectric permittivity function are derived. Based on these estimates two adaptive conjugate gradient algorithms are formulated. Our numerical tests show feasibility of application of an adaptive optimization algorithm for reconstruction of dielectric permittivity function using anatomically realistic breast phantom of MRI database produced in University of Wisconsin [53].