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Imaging methods that are able to detect targets located behind a wall and monitor their motion have recently gained an increasing attention. To pursue this aim, we propose a qualitative inverse scattering approach based on the linear sampling method, which is a computationally effective nonapproximated shape-reconstruction strategy. In particular, we describe the formulation of the method for the through-the-wall scenario for both the case of static and dynamic targets. The results of a numerical analysis are reported as a preliminary assessment of the achievable performances.