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Addendum on data driven regularization by projection

Published: August 11, 2025 | arXiv ID: 2508.07709v1

By: Martin Hanke, Otmar Scherzer

Potential Business Impact:

Teaches computers to fix blurry pictures from examples.

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.

Country of Origin
🇩🇪 🇦🇹 Germany, Austria

Page Count
12 pages

Category
Mathematics:
Numerical Analysis (Math)