The detection of abandoned objects in videos from moving cameras is of great importance to automatic surveillance systems that monitor large and visually complex areas. This paper proposes a new method based on sparse decompositions to identify video anomalies associated with abandoned objects. The proposed scheme inherently incorporates synchronization between the reference (anomaly-free) and target (under analysis) sequences thus reducing the implementation complexity of the overall surveillance system. Results indicate that the proposed video-processing scheme can lead to 95% complexity reduction while maintaining excellent detection capability of foreground objects.