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.

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]

Data driven regularization by projection

A. Aspri
Primo
;
2020

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.
Data driven regularization; Gram-Schmidt orthogonalization; Inverse problems; Regularization by projection; Variational regularization
Settore MAT/05 - Analisi Matematica
Article (author)
File in questo prodotto:
File Dimensione Formato  
8.Aspri_IP20.pdf

accesso aperto

Descrizione: Articolo principale
Tipologia: Publisher's version/PDF
Dimensione 640.96 kB
Formato Adobe PDF
640.96 kB Adobe PDF Visualizza/Apri
Pubblicazioni consigliate

Caricamento pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/898370
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 2
  • ???jsp.display-item.citation.isi??? 2
social impact