On the randomised stability constant for inverse problems

On the randomised stability constant for inverse problems

In this paper we introduce the randomised stability constant for abstract inverse problems, as a generalisation of the randomised observability constant, which was studied in the context of observability inequalities for the linear wave equation. We study the main properties of the randomised stabil...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Mathematics in engineering 2020-01, Vol.2 (2), p.264-286
Hauptverfasser: S. Alberti, Giovanni, Capdeboscq, Yves, Privat, Yannick
Format: Artikel
Sprache:eng
Schlagworte:
Analysis of PDEs
compressed sensing
deep learning
electrical impedance tomography
inverse problems
Mathematics
observability constant
passive imaging
Probability
randomisation
regularisation
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:In this paper we introduce the randomised stability constant for abstract inverse problems, as a generalisation of the randomised observability constant, which was studied in the context of observability inequalities for the linear wave equation. We study the main properties of the randomised stability constant and discuss the implications for the practical inversion, which are not straightforward.
ISSN:2640-3501
2640-3501
DOI:10.3934/mine.2020013