  In this note we present a reconstructive algorithm for solving the
cross-sectional pipe area from boundary measurements in a tree network with one
inaccessbile end. This is equivalent to reconstructing the first order
perturbation to a wave equation on a quantum graph from boundary measurements
at all network ends except one. The method presented here is based on a time
reversal boundary control method originally presented by Sondhi and Gopinath
for one dimensional problems and later by Oksanen to higher dimensional
manifolds. The algorithm is local, so is applicable to complicated networks if
we are interested only in a part isomorphic to a tree. Moreover the numerical
implementation requires only one matrix inversion or least squares minimization
per discretization point in the physical network. We present a theoretical
solution existence proof, a step-by-step algorithm, and a numerical
implementation applied to two numerical experiments.
