Data driven regularization by projection

Andrea Aspri, Yury Korolev, Otmar Scherzer

Research output: Contribution to journalArticlepeer-review

2 Citations (SciVal)

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.

Original languageEnglish
Article number125009
JournalInverse Problems
Volume36
Issue number12
DOIs
Publication statusPublished - 3 Dec 2020

Keywords

  • Data driven regularization
  • Gram-Schmidt orthogonalization
  • Inverse problems
  • Regularization by projection
  • Variational regularization

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Signal Processing
  • Mathematical Physics
  • Computer Science Applications
  • Applied Mathematics

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