On the identification of Lame parameters in linear isotropic elasticity via a weighted self-guided TV-regularization method

Recently in [V. Markaki, D. Kourounis and A. Charalambopoulos, A dual self-monitored reconstruction scheme on the TV \mathrm{TV} -regularized inverse conductivity problem, IMA J. Appl. Math. 86 2021, 3, 604-630], a novel reconstruction scheme has been developed for the solution of the inclusion problem in the inverse conductivity problem on the basis of a weighted self-guided regularization process generalizing the total variation approach. The present work extends this concept by implementing and investigating its applicability in the two-dimensional elasticity setting. To this end, we employ the framework of the reconstruction of linear and isotropic elastic structures described by their Lame parameters. Numerical examples of increasingly challenging geometric complexities illustrate the enhanced accuracy and efficiency of the method.