Resolution Guarantees for the Reconstruction of Inclusions in Linear Elasticity Based on Monotonicity Methods

TL;DR

This paper establishes resolution guarantees for reconstructing inclusions in elastic bodies using monotonicity methods, highlighting the influence of Lamé parameters and accounting for measurement noise.

Contribution

It provides new conditions for resolution guarantees in elastic inclusion reconstruction, emphasizing the roles of Lamé parameters and noise considerations.

Findings

Resolution depends heavily on Lamé parameter μ.

Guarantees are marginally affected by λ.

Conditions incorporate background error and measurement noise.

Abstract

We deal with the reconstruction of inclusions in elastic bodies based on monotonicity methods and construct conditions under which a resolution for a given partition can be achieved. These conditions take into account the background error as well as the measurement noise. As a main result, this shows us that the resolution guarantees depend heavily on the Lam\'e parameter $\mu$ and only marginally on $\lambda$.