Iterative forward and inverse algorithms based on domain integral equations for three-dimensional electric and magnetic objects

An iterative approach to full vector three-dimensional inverse scattering problems, where the unknown objects can have conductivity, permittivity and permeability different from the known background medium, is discussed. Since this problem involves a large number of unknowns, it has to be solved effectively and efficiently so that the results can be obtained in timely manner. The forward modeling is based on a domain integral equation approach formulated in terms of the electric and magnetic contrast sources normalized with the characteristic impedance of the background medium. Our numerical tests indicate that this formulation is prerequisite in order to arrive at a forward solution within an acceptable number of iterations, and hence it is also of significant importance in the optimization process of the inverse problem. The inverse scattering problem is attacked using the Multiplicative Regularized Contrast Source Inversion method as known in the literature. The complexity of this inverse method is approximately equal to the complexity of two equivalent forward algorithms of the conjugate gradient type. Furthermore, this inverse method has been armed with a weighted L 2-norm regularizer which has been included as a multiplicative constraint. Some representative numerical testings will be presented to illustrate the ability of the our numerical algorithms.