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On the randomised stability constant for inverse problems

1 MaLGa Center, Department of Mathematics, University of Genoa, Via Dodecaneso 35, 16146 Genova, Italy
2 Université de Paris, Laboratoire Jacques-Louis Lions (LJLL), F-75013 Paris, France
3 Sorbonne Université, CNRS, LJLL, F-75005 Paris, France
4 IRMA, Université de Strasbourg, CNRS UMR 7501, 7 rue René Descartes, 67084 Strasbourg, France

This contribution is part of the Special Issue: Inverse problems in imaging and engineering science
Guest Editors: Lauri Oksanen; Mikko Salo
Link: https://www.aimspress.com/newsinfo/1270.html

Special Issues: Inverse problems in imaging and engineering science

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.
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Keywords inverse problems; observability constant; compressed sensing; passive imaging; regularisation; randomisation; deep learning; electrical impedance tomography

Citation: Giovanni S. Alberti, Yves Capdeboscq, Yannick Privat. On the randomised stability constant for inverse problems. Mathematics in Engineering, 2020, 2(2): 264-286. doi: 10.3934/mine.2020013

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