High　data　quality　and　low　sensing　cost　are　two　primary　goals　in　large-scale　mobile　crowdsensing　applications.　The　oversampling　and　the　undersampling　are　common　problems　which　always　result　in　a　high　cost　or　low　data　quality　that　can　not　satisfy　the　system　requirement.　To　address　this　problem,　taking　into　account　low-rank　latent　structure,　we　propose　a　compressive　and　adaptive　data　sampling　scheme　(CAS)　which　exploits　adaptivity　to　identify　locations　which　are　highly　informative　for　learning　the　low-dimensional　space　of　the　data　matrix.　In　contrast　to　existing　random　sampling　methods,　it　involves　a　three-pass　sampling　procedure　that　firstly　assigns　a　fraction　of　samples　to　estimate　general　information,　then　samples　those　more　informative　locations　for　exact　recovery　and　finally　estimates　the　values　of　the　unsensing　locations.　Evaluations　on　synthetic　datasets　and　real　datasets　for　air　quality　monitoring　show　the　effectiveness　of　CAS.　The　experimental　results　demonstrate　that　the　proposed　scheme　is　able　to　not　only　significantly　improve　the　sensing　data　quality　but　also　reduce　the　computation　complexity　comparing　with　the　state-of-the-art　matrix　completion　methods.　©　2017　IEEE.