Fast inversion method for electromagnetic imaging of cylindrical dielectric objects with optimal regularization parameter

This paper presents a fast inversion method for electromagnetic imaging of cylindrical dielectric objects with the optimal regularization parameter us ed in the Levenberg-Marquardt method. A novel procedure for choosing the op timal regularization parameter is proposed. The method of moments with puls e-basis functions and point matching is applied to discretize the equations for the scattered electric field and the total electric field inside the o bject. Then the inverse scattering problem is reduced to solving the matrix equation for the unknown expansion coefficients of a contrast function, wh ich is represented as a function of the relative permittivity of the object . The matrix equation may be solved in the least-squares sense with the Lev enberg-Marquardt method. Thus the contrast function can be reconstructed by the minimization of a functional, which is expressed as the sum of a stand ard error term on the scattered electric field and an additional regulariza tion term. While a regularization parameter is usually chosen according to the generalized cross-validation (GCV) method, the optimal one is now deter mined by minimizing the absolute value of the radius of curvature of the GC V function. This scheme is quite different from the GCV method. Numerical r esults are presented for a circular cylinder and a stratified circular cyli nder consisting of two concentric homogeneous layers. The convergence behav iors of the proposed method and the GCV method are compared with each other . It is confirmed from the numerical results that the proposed method provi des successful reconstructions with the property of much faster convergence than the conventional GCV method.