Noise Benefits in Quantizer-Array Correlation Detection and Watermark Decoding

Quantizer noise can improve statistical signal detection in array-based nonlinear correlators in Neyman-Pearson and maximum-likelihood (ML) detection. This holds even for infinite-variance symmetric alpha-stable channel noise and for generalized-Gaussian channel noise. Noise-enhanced correlation detection leads to noise-enhanced watermark extraction based on such nonlinear detection at the pixel or bit level. This yields a noise-based algorithm for digital watermark decoding using two new noise-benefit theorems. The first theorem gives a necessary and sufficient condition for quantizer noise to increase the detection probability of a constant signal for a fixed false-alarm probability if the channel noise is symmetric and if the sample size is large. The second theorem shows that the array must contain more than one quantizer for such a stochastic-resonance noise benefit if the symmetric channel noise is unimodal. It also shows that the noise-benefit rate improves in the small-quantizer noise limit as the number of array quantizers increases. The second theorem further shows that symmetric uniform quantizer noise gives the optimal rate for an initial noise benefit among all finite-variance symmetric scale-family noise. Two corollaries give similar results for stochastic-resonance noise benefits in ML detection of a signal sequence with known shape but unknown amplitude.