Online optimisation for dynamic electrical impedance tomography
Neil Dizon, Jyrki Jauhiainen, Tuomo Valkonen
TL;DR
This work tackles real-time dynamic inverse problems by embedding online optimisation into nonlinear time-discrete EIT via an online primal-dual proximal splitting scheme. The method handles nonconvex framewise objectives, uses a predictor to model temporal coupling, and accommodates inexact PDE solves, with regret bounds guaranteeing performance relative to the best time-varying reference. A key theoretical contribution is the second-order differentiability of the CEM solution operator on $L^\infty$, enabling rigorous smoothness-based analysis in the online setting. Numerical experiments on moving inclusions in EIT demonstrate real-time reconstructions (about 12 ms per frame) and substantial improvements over uninformed predictions, while remaining competitive with, and significantly faster than, static reconstructions like RIPGN.
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 $L^\infty$.