Dynamic inverse problems: Online regularisation theory
Provides a theoretical foundation for online regularisation in dynamic inverse problems, which is important for practitioners in imaging and signal processing.
The paper develops regularisation theory for dynamic inverse problems solved with online methods over an infinite time horizon, proving that time-averaged reconstruction errors converge to zero as noise and errors vanish. The theory is illustrated with a dynamic electrical impedance tomography example.
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.