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A central challenge in systems biology is the reconstruction of biological networks from high-throughput data sets. A particularly difficult case of this is the inference of dynamic cellular signaling networks. Within signaling networks, a common motif is that of many activators and inhibitors acting upon a small set of substrates. Here we present a novel technique for high-resolution inference of signaling networks from perturbation data based on parameterized modeling of biochemical rates. We also introduce a powerful new signal-processing method for reduction of batch effects in microarray data. We demonstrate the efficacy of these techniques on data from experiments we performed on the Drosophila Rho-signaling network, correctly identifying many known features of the network. In comparison to existing techniques, we are able to provide significantly improved prediction of signaling networks on simulated data, and higher robustness to the noise inherent in all high-throughput experiments. While previous methods have been effective at inferring biological networks in broad statistical strokes, this work takes the further step of modeling both specific interactions and correlations in the background to increase the resolution. The generality of our techniques should allow them to be applied to a wide variety of networks.