In this paper, we consider sparsity-driven change detection for short human motion indication in urban sensing and through-the-wall radar imaging applications. Stationary targets and clutter are removed via change detection, resulting in a sparse scene of a few human targets, undergoing sudden short movements of their limbs, heads, and/or torsos, inside enclosed structures and behind walls. We establish an appropriate change detection model that permits the scene reconstruction within the compressive sensing framework. Results based on Laboratory experiments show that a sizable reduction in the data volume is achieved using the proposed approach without a degradation in system performance.