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In this note we present a reconstructive algorithm for solving thecross-sectional pipe area from boundary measurements in a tree network with oneinaccessbile end. This is equivalent to reconstructing the first orderperturbation to a wave equation on a quantum graph from boundary measurementsat all network ends except one. The method presented here is based on a timereversal boundary control method originally presented by Sondhi and Gopinathfor one dimensional problems and later by Oksanen to higher dimensionalmanifolds. The algorithm is local, so is applicable to complicated networks ifwe are interested only in a part isomorphic to a tree. Moreover the numericalimplementation requires only one matrix inversion or least squares minimizationper discretization point in the physical network. We present a theoreticalsolution existence proof, a step-by-step algorithm, and a numericalimplementation applied to two numerical experiments.

Blockage detection in networks: the area reconstruction method