This paper describes a neural network model of the retinal responses to stimuli whose architecture is inspired by neurophysiological data. Suitable assumptions are identified which enable the development of a simple model for an individual X-type ganglion cell using backpropagation. This is then used to make a model of retinal processing. We present here our model of the individual ganglion cells and the underlying assumptions. We show that backpropagation leads to a model which is similar to the mathematical descriptions of retinal processing advanced by Marr. We present the results obtained when our model is used to simulate the effect of retinal processing on images. Empirical results about the speedups obtained when this model is implemented on parallel architectures are also reported.