A scene is reconstructed by receiving pulses transmitted by a virtual array of transducers. The pulses are reflected by the scene. The virtual array has a set of configurations subject to positioning errors. Each received pulse is sampled and decomposed to produce frequency coefficients stacked in a set of linear systems modeling a reflectivity of the scene. There is one linear system for each configuration. A reconstruction method is applied to the set of linear systems. The reconstruction method solves each linear system separately to obtain a corresponding solution. The corresponding solutions share information during the solving. Then, the solutions are combined to reconstruct the scene.