On the randomised stability constant for inverse problems

Giovanni S. Alberti (1) , Yves Capdeboscq (2) , Yannick Privat (3, 4)

1 UniGe - Università degli studi di Genova = University of Genoa
2 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions
3 IRMA - Institut de Recherche Mathématique Avancée
4 TONUS - TOkamaks and NUmerical Simulations

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.

Mots clés: regularisation; deep learning; electrical impedance tomography; passive imaging; randomisation; inverse problems; compressed sensing; observability constant

Domaines: Equations aux dérivées partielles [math.AP]; Probabilités [math.PR]

Giovanni S. Alberti, Yves Capdeboscq, Yannick Privat. On the randomised stability constant for inverse problems. Mathematics in Engineering, 2020, 2 (2), pp.264-286. ⟨10.3934/mine.2020013⟩. ⟨hal-02077786v2⟩