Stability in Dynamic Elastographic Imaging
Presented by Mr. Thomas WIDLAK
Type: Oral presentation
Track: Numerical Methods for Partial Differential Equations
Hybrid imaging techniques couple different imaging modalities in order to maximize contrast and resolution. In general, a ground modality provides interior data, from which the material parameters are then reconstructed in a second step, given a PDE model. We treat the elastography problem, where the displacement vector field is given and the Lam\'e parameters are sought. The estimation of the elastic parameters is a nonlinear inverse problem. Recently, methods for proving stability of the linearized form of those problems were provided by Kuchment and Bal for conductivity imaging, using redundant elliptic systems. In this talk, we treat the elasticity problem by the method of Bal. The application of the stability results is in proving convergence of the iterative numerical solution for the elastographic imaging problem.