Elastic shear modulus and density profiles inversion: Lipschitz stability results

Abstract

In this paper, we consider the inverse coefficients problem of recovering a shear modulus μ and density ρ of a medium from the Neumann-to-Dirichlet map. This inverse problem is motivated by the reconstruction of mechanical properties of tissues in non-destructive testing. We prove Lipschitz stability results for any dimension $d\ge 2$, provided that the parameters μ and ρ have upper and lower bounds and belong to a known finite dimensional subspace. The proofs rely on monotonicity relations between the parameters and the Neumann-to-Dirichlet operator, combined with the techniques of localized potentials.

Keywords:

• Shear modulus
• inverse problems
• monotonicity
• localized potentials
• stability

Maths:

• 35R30
• 34K20
• 74B05

Disclosure statement

No potential conflict of interest was reported by the author(s).