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