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Works in the last decades have shown that a large class of parametric non-bandlimited signals can be exactly re-constructed from samples of their filtered versions. In particular, signals x(t) that are linear combinations of a finite number of Diracs per unit of time can be acquired by linear filtering followed by uniform sampling. Nevertheless, when the samples are distorted by noise, many of the early proposed schemes can become ill-conditioned. Recently, a stochastic algorithm that recovers the filtered signal z(t) of x(t), but which fails in the reconstruction of x(t) has been presented. In the present paper, a novel stochastic algorithm which blends together concepts of evolutionary algorithms with those of Gibbs sampling and which successes in recovering x(t) is proposed. This algorithm is adapted to the case where the samples are distorted by quantization noise.