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.
Dynamic inverse problems: Online regularisation theory
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abstract
We develop regularisation theory for dynamic inverse problems, solved using online methods with an infinite time horizon. Using concepts of subregularity to treat nonsmooth regularisers, we prove that time-averaged reconstruction errors converge to zero as noise, algorithmic errors, and regularisation vanish as the horizon grows. We illustrate the theory numerically with a dynamic electrical impedance tomography example.
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math.OC 1years
2026 1verdicts
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Dynamic inverse problems: Single-loop online algorithms
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.