On the randomised stability constant for inverse problems

Abstract

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.

Keywords

• inverse problems
• observability constant
• compressed sensing
• passive imaging
• regularisation
• randomisation
• deep learning
• electrical impedance tomography