We investigate architectures for time encoding and time decoding of visual stimuli such as natural and synthetic video streams (movies, animation). The architecture for time encoding is akin to models of the early visual system. It consists of a bank of filters in cascade with single-input multi-output neural circuits. Neuron firing is based on either a threshold-and-fire or an integrate-and-fire spiking mechanism with feedback. We show that analog information is represented by the neural circuits as projections on a set of band-limited functions determined by the spike sequence. Under Nyquist-type and frame conditions, the encoded signal can be recovered from these projections with arbitrary precision. For the video time encoding machine architecture, we demonstrate that band-limited video streams of finite energy can be faithfully recovered from the spike trains and provide a stable algorithm for perfect recovery. The key condition for recovery calls for the number of neurons in the population to be above a threshold value.