Compressive　sensing　(CS)　provides　a　new　paradigm　for　correlated　data　processing　and　transmission　over　wireless　sensor　networks　(WSNs).　In　this　paper,　we　take　a　new　look　to　investigate　the　performance　of　CS　for　data　gathering　from　the　perspective　of　in-network　computation.　We　formulate　the　problem　of　computing　random　projections　for　CS　in　WSNs　as　in-network　function　computation　in　random　geometric　networks.　We　focus　on　the　design　and　performance　analysis　of　the　protocols　that　are　efficient　in　terms　of　computation　complexity.　We　first　propose　an　efficient　tree-based　computation　protocol　with　an　optimal　refresh　rate　and　characterize　the　scaling　laws　of　energy　and　latency　requirements,　which　show　that　it　can　reduce　energy　consumption　and　latency　compared　with　the　traditional　approach.　Then,　we　present　a　more　efficient　block　computation　protocol　by　considering　the　correlations　of　temporal　measurements　in　function　computation　to　improve　the　performance　in　terms　of　refresh　rate　and　energy　consumption.　We　also　devise　a　gossip-based　scheme　to　improve　the　robustness　of　function　computation,　which　is　able　to　distribute　computation　results　to　all　the　nodes　throughout　the　network.　We　show　that　the　proposed　protocol　can　improve　upon　the　existing　gossip-based　schemes　in　terms　of　energy　consumption.　Finally,　simulation　results　are　also　presented　to　demonstrate　the　effectiveness　of　the　proposed　protocols.　©　2017　IEEE.