Multigrid solution of a linearized, regularized least-squares problem in electrical impedance tomography

A multigrid-type method for solving the parameter identification problem in electrical impedance tomography is developed. The task is to minimize an output least squares functional over a set of admissible conductivity parameters. The functional measures the deviation from observed data of the boundary values of the solution of an elliptic system based on a given parameter. To make the functional well posed, it is regularized by the addition of a term involving the Laplacian. A multigrid method is then developed to minimize a quadradicization of the regularized functional. Numerical experiments exploring the effects of the regularization on the solution and on the performance of the multigrid solver are presented.