Full Newton method for electromagnetic inverse scattering, utilizing 
explicit second order derivatives
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The full Newton's method is considered as an optimisation approach to the 
inverse electromagnetic scattering problem in the frequency-domain. For the 
sake of accuracy and computational efficiency, the gradient and the Hessian 
of the cost-functional, with respect to parameter functions in the 
L2-space, are derived explicitly by means of the adjoint scattering problem 
and the first and second order Frechet differentials of the cost-functional.
The theory is presented for the general case involving a three-dimensional 
scatterer consisting of general linear media, so called bianisotropic 
media. Numerical results are presented for a non-uniform transmission line 
problem. The numerical implementation, when reducing to a finite 
dimensional parameter space, and a regularization technique, for the 
resulting ill-conditioned Hessian matrix, are presented.
For the reconstruction of one or two parameters, the algorithm is tested on 
synthetic reflection data contaminated with Gaussian noise. The algorithm 
is also tested on measured reflection data to reconstruct a piecewise 
constant shunt-capacitance.