# Convergence Analysis of (Statistical) Inverse Problems under Conditional Stability Estimates

## TL;DR

This paper analyzes the convergence of Tikhonov regularization for nonlinear inverse problems with conditional stability estimates, providing theoretical results and practical insights for deterministic and stochastic noise scenarios.

## Contribution

It extends convergence analysis to inverse problems with general concave stability estimates, including stochastic noise, and discusses parameter choice rules.

## Key findings

- Convergence rates are established for regularized solutions.
- Validity of assumptions is demonstrated in various models.
- Both deterministic and stochastic noise cases are addressed.

## Abstract

Conditional stability estimates require additional regularization for obtaining stable approximate solutions if the validity area of such estimates is not completely known. In this context, we consider ill-posed nonlinear inverse problems in Hilbert scales satisfying conditional stability estimates characterized by general concave index functions. For that case, we exploit Tikhonov regularization and provide convergence and convergence rates of regularized solutions for both deterministic and stochastic noise. We further discuss a priori and a posteriori parameter choice rules and illustrate the validity of our assumptions in different model and real world situations.