One-step iterative reconstruction of conductivity inclusion via the concept of topological derivative

We consider an inverse problem of location identification of small conductivity inhomogeneity inside a conductor via boundary measurements which occurs in the EIT (Electrical Impedance Tomography). For this purpose, we derive topological derivative by applying the asymptotic formula for steady state voltage potentials in the existence of conductivity inclusion of small diameter. Using this derivative, we design only one-step iterative location search algorithm of small conductivity inhomogeneity completely embedded in the homogeneous domain by solving an adjoint problem. Numerical experiments presented for showing the feasibility of proposed algorithm.