Data di Pubblicazione:
2020
Citazione:
Data driven regularization by projection / A. Aspri, Y. Korolev, O. Scherzer. - In: INVERSE PROBLEMS. - ISSN 0266-5611. - 36:12(2020), pp. 125009.1-125009.35. [10.1088/1361-6420/abb61b]
Abstract:
We study linear inverse problems under the premise that the forward operator is not at hand but given indirectly through some input-output training pairs. We demonstrate that regularization by projection and variational regularization can be formulated by using the training data only and without making use of the forward operator. We study convergence and stability of the regularized solutions in view of Seidman (1980 J. Optim. Theory Appl. 30 535), who showed that regularization by projection is not convergent in general, by giving some insight on the generality of Seidman's nonconvergence example. Moreover,we show, analytically and numerically, that regularization by projection is indeed capable of learning linear operators, such as the Radon transform.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Data driven regularization; Gram-Schmidt orthogonalization; Inverse problems; Regularization by projection; Variational regularization
Elenco autori:
A. Aspri, Y. Korolev, O. Scherzer
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