Addendum on data driven regularization by projection

TL;DR

This paper investigates the stability of data-driven projection-based regularization methods for linear inverse problems, especially when the operator is known indirectly through noisy, possibly dependent training data.

Contribution

It extends previous work to handle noisy, linearly dependent data pairs, enhancing the robustness of data-driven regularization techniques.

Findings

Demonstrates stability under noisy, dependent data conditions

Provides theoretical extension of previous regularization methods

Improves applicability to real-world inverse problems

Abstract

We study the stability of regularization by projection for solving linear inverse problems if the forward operator is given indirectly but specified via some input-output training pairs. We extend the approach in "Data driven regularization by projection" (Aspri, Korolev, and Scherzer; Inverse Problems; 36 (2020), 125009) to data pairs, which are noisy and, possibly, linearly dependent.