ABSTRACT
Electrical impedance tomography (EIT) is a non-invasive inverse method which attempts to determine the electrical conductivity σ of a medium in a domain Ω, by making voltage and current measurements at the boundary ∂Ω of the medium. In mathematical terms, the EIT problem is the recovery of the coefficient σ of an elliptic partial differential equation, defined for x ∈ Ω, given knowledge of the Cauchy data, i.e., the Neumann-to-Dirichlet map or the Dirichlet-to-Neumann map. The EIT problem has important applications in fields such as medical imaging, nondestructive testing of materials, environmental cleaning and geophysics. In the last two decades, it has been the topic of many theoretical and numerical studies. However, there are still important questions, such as improving the stability of reconstruction algorithms, improving the resolution and reliability of reconstructions of σ, and increasing the speed of inversion algorithms so σ can be imaged in real time [55].
