Based on this model-based likelihood function, we construct an optimal (Bayesian) estimator for image velocity given the population spike train response. We implement two variants of this decoder. In the first, we assume the visual input is formed by translation of a known spatial intensity image. In the second, we assume only the (naturalistic) correlation structure of the intensity image is known, but do not know the image explicitly. Finally we explore a biologically-plausible ``motion energy'' method for decoding the velocity and show that, as with estimators based on spatio-temporal gradients, there is a close mathematical connection between this energy method and the optimal Bayesian decoder in the case that the image is not known.

Through simulations, we show that the performance of the Bayesian decoder is less accurate with decreasing prior image information. Simulations across several different speeds and contrasts of a moving bar stimulus reveal that the Bayesian decoder with full image information achieves an average speed estimation precision of 2.7%, while the motion energy method results in an average speed estimation precision of only 7.8% across the same set of conditions. For both methods, estimation precision is shown to be better for more slowly moving stimuli and for stimuli with higher contrast. Human psychophysical performance on short duration velocity estimation tasks seems to be much better represented by the performance of the model in the case that the image is not known exactly a priori. Finally, we show that estimation performance is shown to be rather insensitive to the details of the precise receptive field location, correlated activity between cells, and spike timing.