A nonlinear multigrid for imaging electrical conductivity and permittivity at low frequency

We propose a nonlinear multigrid approach for imaging the electrical conductivity and permittivity of a body Ω, given partial, usually noisy knowledge of the Neumann-to-Dirichlet map at the boundary. The algorithm is a nested iteration, where the image is constructed on a sequence of grids in Ω, starting from the coarsest grid and advancing towards the finest one. We show various numerical examples that demonstrate the effectiveness and robustness of the algorithm and prove local convergence.

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