Iterative methods for an inverse scattering problem of a three-dimensional flaw in anisotropic slab

A rigorous and efficient scheme based on coupled integral equations is proposed to circumvent the limitation of the Born and Rytov approximations. In this scheme, one forward and one inverse problem will be solved at each iteration. During the forward-phase, one updates the unknown electric field within the object, while during the inverse-phase the estimate of the conductivity of the object will be updated. The inversion algorithm for this scheme is based on conjugate gradients and the fast Fourier transform. This method is suitable for least-squares, overdetermined problems with many unknowns (i.e. several thousand).<>