# Convergence Analysis of Ensemble Kalman Inversion: The Linear, Noisy Case

## TL;DR

This paper analyzes the convergence of ensemble Kalman inversion in linear, noisy settings, providing theoretical and numerical insights into its behavior and robustness.

## Contribution

It extends existing analysis to noisy data, establishing well-posedness and convergence results for ensemble Kalman inversion in linear inverse problems.

## Key findings

- Convergence is established for fixed ensemble size.
- Noise impacts the convergence behavior.
- Numerical experiments confirm theoretical predictions.

## Abstract

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.