“…The data for our recovery are the matrix elements s k j ( x, t 0 ; 0, t), and their first three derivatives with respect to t, for 0 < t < t 0 and t not conjugate to 0 along γ t0 x . In [8], we obtain the following result: It is possible to uniquely determine the Riemannian metric g in a neighborhood of γ x0,η0 ([0, t 0 )) in Riemannian normal coordinates having origin at the point y t0 (this can be done for general metrics, not just ones which are conformally Euclidean). Here, we cast this result into an algorithm, and construct a conversion from the mentioned coordinates to Cartesian coordinates, which is the main contribution of this paper.…”