On the lifting of deterministic convergence rates for inverse problems with stochastic noise
For researchers in inverse problems, this provides a general framework to transfer deterministic convergence results to stochastic noise, reducing the need for separate stochastic analyses.
The paper bridges deterministic and stochastic noise models for inverse problems, showing that deterministic convergence rates can be lifted to stochastic settings, enabling the application of deterministic regularization methods without individual stochastic analysis.
Both for the theoretical and practical treatment of Inverse Problems, the modeling of the noise is a crucial part. One either models the measurement via a deterministic worst-case error assumption or assumes a certain stochastic behavior of the noise. Although some connections between both models are known, the communities develop rather independently. In this paper we seek to bridge the gap between the deterministic and the stochastic approach and show convergence and convergence rates for Inverse Problems with stochastic noise by lifting the theory established in the deterministic setting into the stochastic one. This opens the wide field of deterministic regularization methods for stochastic problems without having to do an individual stochastic analysis for each problem.