A wave-splitting based optimization approach to multi-dimensional time-domain electromagnetic inverse problems

An optimization approach to a multi-dimensional electromagnetic inverse problem in the time domain is considered. Wave-splitting is integrated in the optimization algorithm. An analysis based on energy estimates is given to show that the wave-splitting provides the best linear combination of the fields for use in this type of inverse problem. The permittivity, permeability and conductivity are reconstructed by minimizing an objective functional. An explicit expression for the gradient of the objective functional is derived by introducing some auxiliary functions and using the Gauss theorem. The parameters are reconstructed by an iterative conjugate gradient algorithm. Numerical results are presented.