Online optimisation for dynamic electrical impedance tomography

TL;DR

This paper introduces a primal-dual online optimization method for real-time electrical impedance tomography, analyzing its convergence and demonstrating its effectiveness in monitoring moving bodies in fluids.

Contribution

It proposes a novel primal-dual online optimization approach for nonlinear inverse problems and proves second-order differentiability of the CEM solution operator.

Findings

Effective real-time monitoring of moving bodies using EIT

Convergence analysis via regret theory

Proof of second-order differentiability of the CEM operator

Abstract

Online optimisation studies the convergence of optimisation methods as the data embedded in the problem changes. Based on this idea, we propose a primal dual online method for nonlinear time-discrete inverse problems. We analyse the method through regret theory and demonstrate its performance in real-time monitoring of moving bodies in a fluid with Electrical Impedance Tomography (EIT). To do so, we also prove the second-order differentiability of the Complete Electrode Model (CEM) solution operator on $L^\infty$.