Biologically inspired statistical matched filter receiver

How could human vision system differentiate a small misalignment of two short lines up to 1/10-th of photoreceptor size (better than the Nyquist rate) when the retina is moving constantly? Over the last twenty years, detection theory has played essential role in explaining this hyper-acuity phenomenon. These principles may be useful for us to develop new communication systems. In this paper, we investigate the optimal detection theory for a retinal-like device. We model the fixational eye movement and point spread as a two-dimensional first-order Markov process. Due to the movement and point spread, a single dot stimulus will produce a center-surround opponent reception field at the output of photoreceptor. We develop an optimal statistic matched filter receiver to detect the presence of the moving dot. We show that the movement and spread are essential to the eye hyper-acuity function. Our detector can differentiate a small mismatch (just 10% of the size of photoreceptor) between two short lines. The mean values of output from photoreceptor do not contribute to the optimal receiver. However, without the mean values, the ON-center and work OFF-center pathways are essential to differentiate a black object in a white background from a white object in a black background.