No abstract

Motivated by biological neural networks and distributed sensing networks, we study how pooling networks – or quantizers – with random thresholds can be used in detection tasks. We provide a brief overview of the use of deterministic quantizers in detection by presenting how quantizers can be optimally designed for detection purposes. We study the behavior of these networks when they are used in a problem for which they are not optimal (mismatching). We show that adding random fluctuations to the thresholds of the networks can then enhance the performance of the quantizers, thus helping in the recovery of "a kind of" optimality. We also show that (for a small number of thresholds) it suffices to use random uniform quantizers, for which we provide a study of the behavior as a function of several parameters (size, fluctuation nature, observation noise nature). The conclusion to these studies are the robustness of the uniform quantizer used as a detector with respect to fluctuations added on its thresholds.

This paper is devoted to a study of the role of the fluctuations that the eye is subject to, from the point of view of noise-enhanced processing. To this end, a basic model of the retina is considered, namely a regular sampler subject to space and time fluctuations that model the random sampling and the involuntary eye tremor respectively. The filtering that can be done by the photoreceptor is also taken into account and the study focuses on a stochastic model of a natural scene. To quantify the effect of the noise, a coefficient of correlation between the signal acquired by a given photoreceptor and a given point of the scene that the eye is looking at is considered. It is shown both for academic examples and for a more realistic case that the fluctuations which affect the retina can induce noise-enhanced processing effects. The observed effect is then interpreted as a stochastic control of the retina via the random tremor.

In this paper, we revisit the problem of detecting a known signal corrupted by an independent identically distributed α-stable noise. The implementation of the optimal receiver, i.e. the log-likelihood ratio, requires the explicit expression of the probability density function of the noise. In the general α-stable case, there exists no closed-form for the probability density function of the noise. To avoid the numerical evaluation of the probability density function of the noise, we propose to study a parametric suboptimal detector based on properties of α-stable noise and on implementation considerations. We focus our attention on several optimization criteria of the parameters, showing that our choice allows the optimization without using the explicit expression of the noise probability density function. The chosen detector allows to retrieve the optimal Gaussian detector (matched filter) as well as the locally optimal detector in the Cauchy context. The performance of the detector is studied and compared to usual detectors and to the optimal detector. The robustness of the detector against the signal amplitude and the stability index of the noise is discussed.