Motivated　by　the　need　for　analyzing　the　rapidly　producing　data　streams,　such　as　images,　videos,　sensor　data,　etc,　in　a　timely　manner,　the　study　on　the　streaming　algorithms　to　extract　representative　information　from　massive　data　to　maximize　some　objective　function　is　therefore　important　and　urgent.　Most　of　previous　works　are　assumed　under　a　noise-free　environment,　while　in　many　realistic　applications　obtaining　the　exact　function　value　is　hard　or　computing　the　function　value　may　cost　much,　which　brings　the　noisy　version.　Hence　in　this　paper,　we　address　a　more　general　problem　to　select　a　subset　of　at　most　k　elements　from　the　stream　to　maximize　a　noisy　set　function　(not　necessarily　submodular).　To　be　specific,　we　cast　our　problem　as　the　streaming　submodular　maximization　problem　under　multiplicative　and　additive　noise　models.　We　develop　an　efficient　thresholding　streaming　algorithm,　which　calls　several　copies　of　a　subroutine　in　parallel.　Therefore,　this　algorithm　only　requires　two　passes　over　data　and　has　a　memory　independent　of　data　size.　For　both　of　noisy　models,　its　approximation　guarantee　approaches　2/k.　In　our　numerical　experiments,　we　extensively　evaluate　the　effectiveness　of　our　thresholding　streaming　algorithm　on　some　applications　in　real　data　set.