An iterative reconstruction algorithm of accelerating the estimation of the complex relative permittivity of a cylindrical dielectric object based on the multigrid optimization method (MGOM) is presented. A cost functional is defined by the norm of a difference between the scattered electric fields measured and calculated for an estimated contrast function, which is expressed as a function of the complex relative permittivity of the object. Then the electromagnetic inverse scattering problem can be treated as an optimization problem where the contrast function is determined by minimizing the cost functional. We apply the conjugate gradient method (CGM) and the frequency-hopping technique (FHT) to the minimization of the cost functional, and also employ the multigrid method (MGM) with a V-cycle to accelerate the rate of convergence for getting the reconstructed profile. The reconstruction scheme is called the multigrid optimization method. Computer simulations are performed for lossy and inhomogeneous dielectric circular cylinders by using single-frequency or multifrequency scattering data. The numerical results demonstrate that the rate of convergence of the proposed metod is much faster than that of the conventional CGM for both noise-free and noisy cases.

This paper presents a fast inversion method for electromagnetic imaging of cylindrical dielectric objects with the optimal regularization parameter used in the Levenberg-Marquardt method. A novel procedure for choosing the optimal regularization parameter is proposed. The method of moments with pulse-basis functions and point matching is applied to discretize the equations for the scattered electric field and the total electric field inside the object. Then the inverse scattering problem is reduced to solving the matrix equation for the unknown expansion coefficients of a contrast function, which 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 Levenberg-Marquardt method. Thus the contrast function can be reconstructed by the minimization of a functional, which is expressed as the sum of a standard error term on the scattered electric field and an additional regularization term. While a regularization parameter is usually chosen according to the generalized cross-validation (GCV) method, the optimal one is now determined by minimizing the absolute value of the radius of curvature of the GCV function. This scheme is quite different from the GCV method. Numerical results are presented for a circular cylinder and a stratified circular cylinder consisting of two concentric homogeneous layers. The convergence behaviors of the proposed method and the GCV method are compared with each other. It is confirmed from the numerical results that the proposed method provides successful reconstructions with the property of much faster convergence than the conventional GCV method.