1. A system for reconstructing a scene using an array of transmitters and receivers, comprising: a transmitter for transmitting pulses into the scene, wherein at any one time one pulse is transmitted by the transmitter; a set of receivers for receiving the one pulse after reflection by reflectors at locations in the scene as a set of signals, wherein the one transmitter and each receiver in the set of receivers form a sensing pair for an array instance; a processor, connected to the transmitter and the set of receivers, for sampling and decomposing each signal in the set of signals to produce frequency coefficients stacked in a set of linear system of equations modeling a reflectivity of the scene, wherein there is one linear system for each sensing pair, applying a reconstruction method to the set of linear system of equations, wherein the reconstruction method solves each linear system of equation separately to obtain a corresponding solution, while the corresponding solutions share information of a joint sparsity pattern of the scene during the solving, combines the solutions to reconstruct the scene, and determines a total energy of the solutions at each location.