Abstract
We study variational regularisation methods for inverse problems with imperfect forward operators whose errors can be modelled by order intervals in a partial order of a Banach lattice.We carry out analysis with respect to existence and convex duality for general data fidelity terms and regularisation functionals. Both forapriori and a posteriori parameter choice rules,we obtain convergence rates of the regularised solutions in terms of Bregman distances. Our results apply to fidelity terms such as Wasserstein distances, φ-divergences, norms, as well as sums and infimal convolutions of those.
Original language | English |
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Article number | 125014 |
Journal | Inverse Problems |
Volume | 36 |
Issue number | 12 |
DOIs | |
Publication status | Published - Dec 2020 |
Bibliographical note
Publisher Copyright:© 2020 The Author(s).
Keywords
- Banach lattices
- Bregman distances
- Discrepancy principle
- F -divergences
- Imperfect forward models
- Kullback-Leibler divergence
- Wasserstein distances
ASJC Scopus subject areas
- Theoretical Computer Science
- Signal Processing
- Mathematical Physics
- Computer Science Applications
- Applied Mathematics