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Data collection is a crucial operation in wireless sensor networks. The design of data collection schemes is challenging due to the limited energy supply and the hot spot problem. Leveraging empirical observations that sensory data possess strong spatiotemporal compressibility, this paper proposes a novel compressive data collection scheme for wireless sensor networks. We adopt a power-law decaying data model verified by real data sets and then propose a random projection-based estimation algorithm for this data model. Our scheme requires fewer compressed measurements, thus greatly reduces the energy consumption. It allows simple routing strategy without much computation and control overheads, which leads to strong robustness in practical applications. Analytically, we prove that it achieves the optimal estimation error bound. Evaluations on real data sets (from the GreenOrbs, IntelLab and NBDC …