Modified gradient method and modified Born method for solving a two-dimensional inverse scattering problem

This paper concerns the reconstruction of the complex relative permittivity of an inhomogeneous object from the measured scattered field. The parameter of interest is retrieved using iterative techniques. Four methods are considered, in which the permittivity is updated along the standard Polak-Ribiere conjugate gradient directions of a cost functional. The difference lies in the update direction for the field, and the determination of the expansion coefficients. In the modified gradient method, the search direction is the conjugate gradient direction for the field, and the expansion coefficients for field and profile are determined simultaneously. In the Born method (BM) the field is considered as the fixed solution of the forward problem with the available estimate of the unknown permittivity, and only the profile coefficients are determined from the cost function. In the modified Born method, we use the same field direction as in the BM, but determine the coefficients for field and profile simultaneously. In the modified(2) gradient method, we use both field directions, and again update all coefficients simultaneously. Examples of the reconstruction of either metal or dielectric cylinders from experimental data are presented and the methods are compared for a range of frequencies.