A combined finite element-nonlinear conjugate gradient spatial method for the reconstruction of unknown scatterer profiles

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Abstract
The inversion of microwave imaging data is treated by means of a novel iterative spatial domain reconstruction technique. The latter combines the Finite Element Method and a Nonlinear Conjugate Gradient optimization scheme. The method is applied to the reconstruction of the complex permittivity profile of cylindrical inhomogeneous objects, that are illuminated by transverse magnetic incident waves, and is based on scattered far field measurements. Starting from an initial guess of the scatterer profile, the finite element method is used to solve the forward problem, resulting in an estimate of the scattered field. The inverse process of updating the constitutive parameters of the scatterer is performed by the Polak-Ribiere algorithm by the use of which the difference between the measured and the estimated scattered data is minimized. The minimization procedure is carried out by a sensitivity analysis scheme based on the finite element method and the introduction of the adjoint state vector. The proposed method is applied to various cases of scatterer profiles.