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Researchers familiar with the state of the art are aware that the developmentof close-formed solutions for the EIT problem was not able to overpass the caseof once-time differentiable conductivities beside the well known particularAstala-P\"aiv\"arinta result for zero frequency. In this paper, we introducesome new techniques for the inverse conductivity problem combined with atransmission problem and achieve a reconstruction result based on an adaptationof the scattering data. The idea for these techniques, in particular theconcept of admissible points is coming from E. Lakshtanov and B. Vainberg.Moreover, we are going to establish the necessary footwork for working withadmissible points which will be required in any further research in thisdirection.

CGO-Faddeev approach for Complex Conductivities with Regular Jumps