Higher order error estimates for regularization of inverse problems under non-additive noise

TL;DR

This paper develops higher order error estimates for inverse problems affected by non-additive noise using a novel source condition, enhancing understanding of variational regularization with complex data fidelities.

Contribution

It introduces a new source condition inspired by the dual problem, extending error analysis to non-additive noise and general convex data fidelities in variational regularization.

Findings

Derived higher order error estimates using Bregman distances.

Interpreted the new source condition within a variational framework.

Extended the approach to general convex data fidelities.

Abstract

In this work we derive higher order error estimates for inverse problems distorted by non-additive noise, in terms of Bregman distances. The results are obtained by means of a novel source condition, inspired by the dual problem. Specifically, we focus on variational regularization having the Kullback-Leibler divergence as data-fidelity, and a convex penalty term. In this framework, we provide an interpretation of the new source condition, and present error estimates also when a variational formulation of the source condition is employed. We show that this approach can be extended to variational regularization that incorporates more general convex data fidelities.