Recent progress on the factorization method for electrical impedance tomography

The Factorization Method is a noniterative method to detect the shape and position of conductivity anomalies inside an object. The method was introduced by Kirsch for inverse scattering problems and extended to electrical impedance tomography (EIT) by Brühl and Hanke. Since these pioneering works, substantial progress has been made on the theoretical foundations of the method. The necessary assumptions have been weakened, and the proofs have been considerably simplified. In this work, we aim to summarize this progress and present a state-of-the-art formulation of the Factorization Method for EIT with continuous data. In particular, we formulate the method for general piecewise analytic conductivities and give short and self-contained proofs.