Generalized cross-validation applied to a Newton-type algorithm for microwave tomography

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Abstract
The non-linear inverse scattering problem, occurring in the field of microwave tomography for biomedical applications, is solved with the Newton-type iterative algorithm. This method allows the reconstruction of the complex permittivity of strongly inhomogeneous objects. An ill-conditioned system of linear equations is obtained at each iteration and is regularized using Tikhonov's method. The choice of regularization is crucial, specially when random error is present in the data. We investigate the Generalized Cross Validation method for choosing the regularization parameter. Numerical examples are given in the case of 2D TM inverse problems.

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