The ill-posedness of Calderon's inverse conductivity problem makes electrical impedance tomography (EIT) challenging to implement in ways that are useful in clinical or industrial settings. I will describe an approach (theoretical, so far) which might allow EIT to be used to locate and image interior singularities of the conductivity.

This method exploits the complex principal type structure which is well-known to underly the construction of so called Complex Geometrical Optics solutions, and has previously been used for the purpose of proofs of uniqueness.

Combining this point of view with the Astala-Paivarinta-Huhtanen-Peramaki solutions available in 2D, we show that one can efficiently image inclusions within inclusions.

This is joint work with M. Lassas, M. Santacesaria, S. Siltanen and G.

Uhlmann.