Reconstruct Lame parameters of linear isotropic elasticity system

Transient Elastography enables detection and characterization of tissue abnormalities. In this paper we assume that the displacements are modeled by linear isotropic elasticity system and the tissue displacement has been obtained by the first step in hybrid methods. Then we reconstruct the Lam\'e parameters of this system from knowledge of tissue displacement. We show that for a sufficiently large number of solutions of the elasticity system and for an open set of the well-chosen boundary conditions, $(\lambda,\mu)$ can be uniquely and stably reconstructed. The set of well-chosen boundary conditions is characterized in terms of appropriate complex geometrical optics solutions.