  An inverse boundary value problem for the 1+1 dimensional wave equation
$(\partial_t^2 - c(x)^2 \partial_x^2)u(x,t)=0,\quad x\in\mathbb{R}_+$ is
considered. We give a discrete regularization strategy to recover wave speed
$c(x)$ when we are given the boundary value of the wave, $u(0,t)$, that is
produced by a single pulse-like source. The regularization strategy gives an
approximative wave speed $\widetilde c$, satisfying a H\"older type estimate
$\| \widetilde c-c\|\leq C \epsilon^{\gamma}$, where $\epsilon$ is the noise
level.
