The optimal synapse for sparse, binary signals in the rod pathway

The sparsity of photons at very low light levels necessitates a nonlinear synaptic transfer function between the rod photoreceptors and the rod-bipolar cells. We examine different ways to characterize the performance of the pathway: the error rate, two variants of the mutual information, and the signal-to-noise ratio. Simulation of the pathway shows that these approaches yield substantially different performance at very low light levels and that maximizing the signal-to-noise ratio yields the best performance when judged from simulated images. The results are compared to recent data.