Lam\'e Parameter Estimation from Static Displacement Field Measurements in the Framework of Nonlinear Inverse Problems

TL;DR

This paper addresses the inverse problem of estimating Lamé parameters in static elastography using nonlinear operator equations, verifying convergence conditions for iterative methods, and demonstrating numerical recovery from simulated data.

Contribution

It verifies a nonlinearity condition ensuring convergence of iterative regularization methods in infinite-dimensional spaces for Lamé parameter estimation.

Findings

Verification of a nonlinearity condition for convergence

Numerical demonstration of parameter recovery from simulated data

Analysis of Landweber iteration in elastography context

Abstract

We consider a problem of quantitative static elastography, the estimation of the Lam\'e parameters from internal displacement field data. This problem is formulated as a nonlinear operator equation. To solve this equation, we investigate the Landweber iteration both analytically and numerically. The main result of this paper is the verification of a nonlinearity condition in an infinite dimensional Hilbert space context. This condition guarantees convergence of iterative regularization methods. Furthermore, numerical examples for recovery of the Lam\'e parameters from displacement data simulating a static elastography experiment are presented.