This analysis extends the data driven regularization method, assessing performance with noisy data pairs, indicating robustness in applications.
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.
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Hanke et al. (2025) studied this question.
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