State estimation and inverse problems in electrical impedance tomography: observability, convergence and regularization

Solving electrical impedance tomography (EIT) inverse problems in real-time is a challenging task due to their dimension, the nonlinearities involved and the fact that they are ill-posed. Thus, efficient algorithms are required to address the application of tomographic technologies in process industry. In practical applications the EIT inverse problem is often linearized for fast and robust reconstruction. The aim of this paper is to analyse the solution of linearized EIT inverse problem from the perspective of a state estimation problem, providing links between regularization, observability and convergence of the algorithms. In addition, also a new way to define the fictitious outputs is proposed, leading to observers with fewer parameters than with the approach widely used in literature. Simulation of EIT examples illustrate the main ideas and algorithmic improvements of the proposed approaches.