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We present an analysis of the exploitation of noise for signal reconstruction by an array of nonlinear threshold-based devices. This phenomenon has been described as a form of stochastic resonance known as suprathreshold stochastic resonance. It occurs when all devices in an array of size N have identical thresholds and are subject to independent additive noise. The original work showed that the mutual information between the input and output of the array has a maximum for a nonzero value of noise intensity, for a random input signal. In this paper, we extend the results on this phenomenon to the case of Laplacian signal and noise probability densities, and show conditions exist under which it is optimal.