Iterative inversion reconstructs the object from the measured scattered fields by minimizing the cost function which is defined as the squared magnitude of the difference between the angular mode of the measured fields and that of the fields calculated from the assumed profile of the scatterer. The fields scattered by the object of assumed shape and profiles may be calculated by the method of moments(MOM). The MOM discretizes the object into cells smaller than $0.2\lambda /\sqrt{ \epsilon_r} \times 0.2\lambda $ /$\sqrt{\epsilon_r}$ such that the total field and the permittivity in the cell may be approximated as constants, respectively, and are taken out of the integral representation of scattered fields, where \lambda and $\epsilon_r$ are respectively the wavelength in the free space and the relative permittivity of the object.
The cost function as a function of $\epsilon_r$ of the object has a lot of extremes and one global minimum for sufficiently many data points. The Levenberg-Marquardt algorithm(LMA) alone finds the nearest minimum of the cost function from the initially chosen profile. This is useful for the reconstruction of a small and low contrast target. For a large and high-contrast object, it is shown here that the original profile is reconstructed by using the genetic algorithm(GA) or the hybrid algorithm combining the LMA and GA. Computing time efficiency of the conventional GA is improved by introducing the 2N-parent parameter-wise crossover rather than the conventional crossover, where N is the number of parameters to be optimized.
The size of the reconstructed object via the iterative inversion is limited by computing capability of the forward fields, because the iterative inversion needs calculation of scattered fields so many times. The size of matrix to calculate the total field inside the scatterer becomes N × N for given distribution of permittivities,$\epsilon_n$ of N cells. This size of the matrix is limited approximately by 100×100 in the iterative inversion due to the capability of the modern computer calculating the inverse of this matrix and it limits the size of the two-dimensional square object by $2.0\lambda/\sqrt{\epsilon_r} \times 2.0 \lambda/\sqrt {\epsilon_r}$, since the size of the cell is smaller than $0.2 \lambda/\sqrt{\epsilon_r} \times 0.2 \lambda/\sqrt{\epsilon_r}$ for the MOM and N becomes which means 10 by 10 cells. If the relative dielectric constant equals 4.0, an object of 1.0\lambda by 1.0\lambda may be reconstructed by the iterative inversion.
It is shown here that the size of the discretized cell may be enlarged up to $0.5\lambda/\sqrt{\epsilon_r} \times 0.5 \lambda / \sqrt{\epsilon_r}$ without incurring large errors in its reconstructed permittivities(less than 10 percent). Numerical reconstruction of the dielectric object of 3.0\lambda by 3.0\lambda with $\epsilon_r=4.0$ is shown to be successful when 10 percent Gaussian noise is added to the scattered fields.
