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Microwave imaging methods are useful for non-destructive inspection of dielectric targets. In this work, a numerical technique for solving the 3D Lippmann-Schwinger integral equation of the inverse scattering problem via Gauss-Newton linearization in Banach spaces is analysed. More specifically, two different approximations of the Fréchet derivative are proposed in order to speed up the computation. Indeed it is well known that the computation of the Fréchet derivative is generally quite expensive in three dimensional restorations. Numerical tests show that the approximations give a faster restoration without loosing accuracy

Nonlinear electromagnetic inverse scattering in via Frozen or Broyden update of the Fréchet derivative