Proposes single-loop online methods for PDE-constrained dynamic inverse problems that replace exact gradients with estimates having summable errors to retain standard regret bounds.
Online optimisation for dynamic electrical impedance tomography
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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 $L^\infty$.
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2026 2verdicts
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Proves time-averaged reconstruction errors converge to zero in online dynamic inverse problems as noise, algorithmic errors, and regularization vanish with growing horizon.
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Dynamic inverse problems: Online regularisation theory
Proves time-averaged reconstruction errors converge to zero in online dynamic inverse problems as noise, algorithmic errors, and regularization vanish with growing horizon.