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The observations gathered by the individual nodes of a sensor network may be unreliable due to malfunctioning, observation noise or low battery level. Global reliability is typically recovered by collecting all the measurements in a fusion center which takes proper decisions. However, centralized networks are more vulnerable and prone to congestion around the sink nodes. To relax the congestion problem, decrease the network vulnerability and improve the network efficiency, it is appropriate to bring the decisions at the lowest possible level. In this paper, we propose a distributed algorithm allowing each node to improve the reliability of its own reading thanks to the interaction with the other nodes, assuming that the field monitored by the network is a smooth function. In mathematical terms, this only requires that the useful field belongs to a subspace of dimension smaller than the number of nodes. Although fully decentralized, the proposed algorithm is globally optimal, in the sense that it performs the projection of the overall set of observations onto the signal subspace through an iterative decentralized algorithms, that requires minimum convergence time, for any given node coverage.