This paper considers the problem of reconstructing raw signals from random projections in the context of time-of-flight imaging with an array of sensors. It presents a new signal model, coined as multi-channel pulse-stream model, which exploits pulse-stream models and accounts for additional structure induced by inter-sensor dependencies. We propose a sampling theorem and a reconstruction algorithm, based on l1-minimization, for signals belonging to such a model. We demonstrate the benefits of the proposed approach by means of numerical simulations and on a real nondestructive- evaluation application where the peak-signal-to-noise ratio is increased by 3 dB compared to standard compressed-sensing strategies.