A propagation-back-propagation algorithm for the solution of the inverse scattering problem for Maxwell's equations (Q2783522)

The dissertation is devoted to the numerical solution of an inverse problem in 3D microwave tomography, which consists in the reconstruction of the complex-valued index of refraction of an object from measurements of the scattered electric field. The initial value problem for Maxwell's equations leads to a nonlinear operator acting from the space of indices of refraction to the space of measured data. Using the Fréchet derivative of this operator, an iterative method for the inverse problem is proposed where in each iteration step a direct problem and an adjoint linearized direct problem have to be solved. The theoretical justification of the algorithm relies on an equivalent formulation of Maxwell's equations, a stability result for the initial value problem and a study of the Fréchet derivative of the mentioned nonlinear operator. Various numerical examples demonstrate the practicability of the method.