Data driven regularization by projection
Publication Date
2020Journal Title
Inverse Problems
ISSN
0266-5611
Publisher
IOP Publishing
Volume
36
Issue
12
Language
en
Type
Article
This Version
VoR
Metadata
Show full item recordCitation
Aspri, A., Korolev, Y., & Scherzer, O. (2020). Data driven regularization by projection. Inverse Problems, 36 (12) https://doi.org/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 T. I. Seidman. "Nonconvergence Results for the Application
of Least-Squares Estimation to Ill-Posed Problems". Journal of Optimization
Theory and Applications 30.4 (1980), pp. 535-547, 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.
Keywords
Paper, data driven regularization, variational regularization, regularization by projection, inverse problems, Gram–Schmidt orthogonalization
Sponsorship
Royal Society (NF170045)
Austrian Science Fund (I3661-N27 SFB F68 F6807-N36)
Identifiers
ipabb61b, abb61b, ip-102693.r1
External DOI: https://doi.org/10.1088/1361-6420/abb61b
This record's URL: https://www.repository.cam.ac.uk/handle/1810/333000
Rights
Licence:
https://creativecommons.org/licenses/by/4.0/
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