  An inverse boundary value problem for a 1+1 dimensional wave equation with
wave speed $c(x)$ is considered. We give a regularisation strategy for
inverting the map $\mathcal A:c\mapsto \Lambda,$ where $\Lambda$ is the
hyperbolic Neumann-to-Dirichlet map corresponding to the wave speed $c$. More
precisely, we consider the case when we are given a perturbation of the
Neumann-to-Dirichlet map $\tilde \Lambda=\Lambda +\mathcal E $, where $\mathcal
E$ corresponds to the measurement errors, and reconstruct an approximate wave
speed $\tilde c$. We emphasize that $\tilde \Lambda$ may not not be in the
range of the map $\mathcal A$. We show that the reconstructed wave speed
$\tilde c$ satisfies $\| \tilde c-c\|_{L^\infty}<C \|E\|^{1/18}$. Our
regularization strategy is based on a new formula to compute $c$ from
$\Lambda$.
