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A noisy input signal is observed by means of a parallel array of one-bit threshold quantizers, in which all the quantizer outputs are added to produce the array output. This parsimonious signal representation is used to implement an optimal Bayesian estimation from the output of the array. Such conditions can be relevant for fast real-time processing in large-scale sensor networks. We demonstrate that, for input signals of arbitrary amplitude, the performance in the estimation can be improved by the addition of independent noises onto the thresholds in the array. These results constitute a novel instance of the phenomenon of suprathreshold stochastic resonance in arrays, by which nonlinear transmission or processing of signals with arbitrary amplitude can be improved through cooperative coupling with noise.