Abstract
We introduce an iterative algorithm for the reconstruction of dielectric profile functions from scattered field data, in which each step corresponds to the solution of a quadratic inversion problem. This means that, at each iteration, we perform a second-order approximation of the scattering operator connecting the unknown profile to the data about a reference profile function. This procedure is then compared with a linear iterative inversion algorithm, and it is pointed out that, within a prescribed class of profile functions, the linear iterative inversion does not converge to the actual solution, whereas the proposed approach does. This feature can be explained by reference not only to the improved approximation provided by the addition of a further term for profile functions of a larger norm but also to the different classes of functions that can be reconstructed by either the linear or the quadratic model. Numerical examples of profile reconstruction in the scalar two-dimensional geometry, with far-zone scattered field data at a fixed frequency, confirm the theoretical analysis.
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