Lamé Parameter Estimation from Static Displacement Field Measurements in the Framework of Nonlinear Inverse Problems

Simon Hubmer, Ekaterina Sherina, Andreas Neubauer, Otmar Scherzer

Published 2017-10-28Version 1

The problem of estimating Lam\'e parameters from full internal static displacement field measurements is formulated as a nonlinear operator equation. The Fr\'echet derivative and the adjoint of the nonlinear operator are derived. The main theoretical result is the verification of a nonlinearity condition guaranteeing convergence of iterative regularization methods, which is proven in an infinite dimensional context. Furthermore, numerical examples for recovery of the Lam\'e parameters from simulated displacement data are presented, simulating a static elastography experiment.