Stochastic resonance with colored noise for neural signal detection

Abstract

We analyze signal detection with nonlinear test statistics in the presence of colored noise. In the limits of small signal and weak noise correlation, the optimal test statistic and its performance are derived under general conditions, especially concerning the type of noise. We also analyze, for a threshold nonlinearity-a key component of a neural model, the conditions for noise-enhanced performance, establishing that colored noise is superior to white noise for detection. For a parallel array of nonlinear elements, approximating neurons, we demonstrate even broader conditions allowing noise-enhanced detection, via a form of suprathreshold stochastic resonance.

Figure 1. Eigenvector .

An illustration of the eigenvector of the variance matrix ().

Figure 2. Stochastic resonance of a single threshold neuron.

Detection efficacy of as a function of noise variance for the correlation coefficient and different values of (red), (blue) and (green). The resonant peaks of are marked by the square (▪), the star () and the down triangle (▾) for and , respectively. Here, the transfer function , and the noise distribution is Gaussian mixture model of Eq. (33).

Figure 3. Suprathreshold stochastic resonance in an array of threshold neurons.

Detection efficacy as a function of the internal uniform noise level and the neuron array size . From the bottom upwards, . Here, the initial Gaussian noise level , the transfer function , the correlation coefficient (a) and (b) .