We propose a new method for the blind deconvolution of a discrete linear system perturbed with additive noise. The method comes from a characterization of discrete variables when perturbed with additive noise with unknown variance together with a characterization of this variance through Hankel matrix. Based on this probabilistic description, an estimator is proposed for the inverse system and the variance of the noise. These estimators are shown to be consistent under weak assumptions, whatever the signal-to-noise ratio is. In particular, the input signal needs not be independently distributed. Numerical examples demonstrate the effectiveness of the method, even when nonstationary signals are used as inputs.