Reconstruction of a high contrast and large object by using the hybrid algorithm combining a Levenberg-Marquardt algorithm and a genetic algorithm

An iterative inverse scattering technique (IIST) is proposed for reconstructing the permittivity of a two dimensional object with large size and high contrast. The IIST uses the FEM for calculating the electric fields and uses the hybrid algorithm for minimizing the cost function where the hybrid algorithm (HGLMA) is composed of a Levenberg-Marquardt algorithm (LMA) that is a kind of gradient algorithm and genetic algorithm (GA). Numerical results show that the IISTs based on the HGLMA and the GA can all reconstruct the permittivity of the high-contrast and large object, in contrast the IIST based on the LMA can't reconstruct the desired permittivity due to trapping in local minima of the cost function. Numerical results also show that the quality of the permittivity reconstructed by the HGLMA is better than that of the permittivity by GA and the convergence of HGLMA is faster than that of GA. When the noise is present, the characteristics of the cost function show that multiple incident waves are needed for the stable inversion.