Lamé Parameter Estimation from Static Displacement Field Measurements in the Framework of Nonlinear Inverse Problems
For researchers in quantitative elastography, this work provides theoretical convergence guarantees for iterative regularization methods applied to a nonlinear inverse problem, though it is incremental as it extends existing theory to a specific application.
This paper addresses the estimation of Lamé parameters from static displacement field data in elastography, formulated as a nonlinear inverse problem. The authors verify a nonlinearity condition ensuring convergence of Landweber iteration and present numerical examples demonstrating recovery of parameters.
We consider a problem of quantitative static elastography, the estimation of the Lamé 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 Lamé parameters from displacement data simulating a static elastography experiment are presented.