Overview and Classification of Some Regularization Techniques for the Gauss-Newton Inversion Method Applied to Inverse Scattering Problems

Different regularization techniques used in conjunction with the Gauss-Newton inversion method for electromagnetic inverse scattering problems are studied and classified into two main categories. The first category attempts to regularize the quadratic form of the nonlinear data misfit cost-functional at different iterations of the Gauss-Newton inversion method. This can be accomplished by utilizing penalty methods or projection methods. The second category tries to regularize the nonlinear data misfit cost-functional before applying the Gauss-Newton inversion method. This type of regularization may be applied via additive, multiplicative or additive-multiplicative terms. We show that these two regularization strategies can be viewed from a single consistent framework.