Sparse Regularization of Inverse Problems by Operator-Adapted Frame Thresholding
- We analyze sparse frame based regularization of inverse problems by means of a diagonal frame decomposition (DFD) for the forward operator, which generalizes the SVD. The DFD allows to define a non-iterative (direct) operator-adapted frame thresholding approach which we show to provide a convergent regularization method with linear convergence rates. These results will be compared to the well-known analysis and synthesis variants of sparse ℓ1-regularization which are usually implemented thorough iterative schemes. If the frame is a basis (non-redundant case), the three versions of sparse regularization, namely synthesis and analysis variants of ℓ1-regularization as well as the DFD thresholding are equivalent. However, in the redundant case, those three approaches are pairwise different.
Author: | Jürgen FrikelORCiD, Markus HaltmeierORCiD |
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DOI: | https://doi.org/10.1007/978-3-030-47174-3_10 |
ISBN: | 978-3-030-47173-6 |
ISBN: | 978-3-030-47174-3 |
Parent Title (English): | Mathematics of Wave Phenomena |
Publisher: | Birkhäuser; Springer International Publishing |
Place of publication: | Cham |
Editor: | Willy Dörfler, Marlis Hochbruck, Dirk Hundertmark, Wolfgang Reichel, Andreas Rieder |
Document Type: | Part of a Book |
Language: | English |
Year of first Publication: | 2020 |
Release Date: | 2022/01/27 |
Edition: | 1st ed. |
First Page: | 163 |
Last Page: | 178 |
Institutes: | Fakultät Informatik und Mathematik |
Begutachtungsstatus: | peer-reviewed |
research focus: | Digitalisierung |
Licence (German): | Keine Lizenz - Es gilt das deutsche Urheberrecht: § 53 UrhG |