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