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The reconstruction process of two-dimensional and three-dimensional sound-soft obstacles from a set of scattered field measurements is formulated as a linear filtering problem. Under coherent and incoherent insonification, the impulse response of the equivalent filter completely characterizes the acoustical imaging process. An energy-based criterion is proposed to describe the impulse response features in both cases. Numerical simulations are also presented, showing the better performance of the incoherent insonification.