A direct sampling method for electrical impedance tomography

This work investigates the electrical impedance tomography (EIT) problem in the case when only one or two pairs of Cauchy data is available, which is known to be very difficult in achieving high reconstruction quality owing to its severely ill-posed nature. We propose a simple and efficient direct sampling method (DSM) to locate inhomogeneous inclusions. A new probing function based on the dipole potential is introduced to construct an indicator function for imaging the inclusions. Explicit formulae for the probing and indicator functions are derived in the case when the sampling domain is of spherical geometry in (n = 2, 3). This new method is easy to implement and computationally cheap. Numerical experiments are presented to demonstrate the robustness and effectiveness of the DSM, which provides a new numerical approach for solving the EIT problem.