In　the　big　data　era,　data　often　comes　in　the　form　of　streams　and　fast　data　stream　analysis　has　recently　attracted　intensive　research　interest.　Submodular　optimization　naturally　appears　in　many　streaming　data　applications　such　as　social　network　influence　maximization　with　the　property　of　diminishing　returns.　However,　in　a　practical　setting,　streaming　data　frequently　comes　with　noises　that　are　small　but　significant　enough　to　impact　the　optimality　of　submodular　optimization　solutions.　Following　the　framework　of　differential　privacy　(DP),　this　paper　considers　a　streaming　model　with　DP　noise　that　is　small　by　construction.　Within　this　noisy　streaming　model,　the　paper　strives　to　address　the　general　problem　of　submodular　maximization　with　a　cardinality　constraint.　The　main　theoretical　result　we　obtained　is　a　streaming　algorithm　that　is　one-pass　and　has　an　approximation　guarantee　of　[Formula　presented]　for　any　δ＞0.　Finally,　we　implement　the　algorithm　and　evaluate　it　against　several　baseline　methods.　Numerical　results　support　the　practical　performance　of　our　algorithm　across　several　real　datasets.　©　2022