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In this paper, we propose a kind of energy-efficient data aggregation scheme to reduce communication cost and to prolong network lifetime based on distributed compressed sensing theory. First, we introduce a distributed compressed sensing model for a cluster-based underwater acoustic sensor network in which spatial and temporal correlations are both considered. Second, two schemes, namely, BUTM-DCS (block upper triangular matrix DCS) and BDM-DCS (block diagonal matrix DCS), are proposed based on the design of observation matrix with strictly restricted isometric property. Both schemes take multihop underwater acoustic communication cost into account. Finally, a distributed compressed sensing reconstruction algorithm, DCS-SOMP (Simultaneous Orthogonal Matching Pursuit for DCS), is adopted to recover raw sensor readings at the fusion center. We performed simulation experiments on both the synthesized and real sensor readings. 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