Convergence Analysis of Ensemble Kalman Inversion: The Linear, Noisy Case
Provides theoretical guarantees for a widely used algorithm in inverse problems, extending prior work to the noisy case, but is incremental as it focuses on linear problems.
The paper analyzes ensemble Kalman inversion for linear inverse problems with noisy data, proving well-posedness and convergence for fixed ensemble size, and investigates the influence of noise on convergence both theoretically and numerically.
We present an analysis of ensemble Kalman inversion, based on the continuous time limit of the algorithm. The analysis of the dynamical behaviour of the ensemble allows us to establish well-posedness and convergence results for a fixed ensemble size. We will build on the results presented in [26] and generalise them to the case of noisy observational data, in particular the influence of the noise on the convergence will be investigated, both theoretically and numerically. We focus on linear inverse problems where a very complete theoretical analysis is possible.