- AutorIn
- Dr. Daniel Gerth
- Titel
- Tikhonov regularization with oversmoothing penalties
- Zitierfähige Url:
- https://nbn-resolving.org/urn:nbn:de:bsz:ch1-qucosa-216262
- Schriftenreihe
- Preprintreihe der Fakultät für Mathematik der TU Chemnitz, Preprint 2016-08
- Erstveröffentlichung
- 2016
- ISSN
- 1614-8835
- Abstract (EN)
- In the last decade l1-regularization became a powerful and popular tool for the regularization of Inverse Problems. While in the early years sparse solution were in the focus of research, recently also the case that the coefficients of the exact solution decay sufficiently fast was under consideration. In this paper we seek to show that l1-regularization is applicable and leads to optimal convergence rates even when the exact solution does not belong to l1 but only to l2. This is a particular example of over-smoothing regularization, i.e., the penalty implies smoothness properties the exact solution does not fulfill. We will make some statements on convergence also in this general context.
- Andere Ausgabe
- Preprint series
Link: https://www.tu-chemnitz.de/mathematik/preprint/ - Freie Schlagwörter (DE)
- Tikhonov Regularisierung, l1 Regularisierung, Überglätten, Konvergenzraten
- Freie Schlagwörter (EN)
- Tikhonov regularization, convergence rates, l1-regularization, oversmoothing
- Klassifikation (DDC)
- 510
- Normschlagwörter (GND)
- Mathematik
- Publizierende Institution
- Technische Universität Chemnitz, Chemnitz
- Version / Begutachtungsstatus
- eingereichte Version / Preprint
- URN Qucosa
- urn:nbn:de:bsz:ch1-qucosa-216262
- Veröffentlichungsdatum Qucosa
- 21.12.2016
- Dokumenttyp
- Preprint
- Sprache des Dokumentes
- Englisch