Does eye tremor provide the hyperacuity phenomenon?

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.