  In this paper, we present an analytic non-iterative approach for recovering a
planar isotropic elastic inclusion embedded in an unbounded medium from the
elastic moment tensors (EMTs), which are coefficients for the multipole
expansion of field perturbation caused by the inclusion. EMTs contain
information about the inclusion's material and geometric properties and, as is
well known, the inclusion can be approximated by a disk from leading-order
EMTs. We define the complex contracted EMTs as the linear combinations of EMTs
where the expansion coefficients are given from complex-valued background
polynomial solutions. By using the layer potential technique for the Lam\'{e}
system and the theory of conformal mapping, we derive explicit asymptotic
formulas in terms of the complex contracted EMTs for the shape of the
inclusion, treating the inclusion as a perturbed disk. These formulas lead us
to an analytic non-iterative algorithm for elastic inclusion reconstruction
using EMTs. We perform numerical experiments to demonstrate the validity and
limitations of our proposed method.
