In　order　to　extract　the　weak　fault　feature　mixed　in　the　background　noise　and　escape　the　constraints　of　traditional　sampling　theorems　on　large-capacity　data　collection,　transmission　and　storage,　an　improved　compressed　sensing　(CS)　algorithm,　in　which　an　adaptive　sparse　representation　based　on　learning　dictionary　and　an　improved　reconstruction　scheme　are　integrated,　is　presented　in　this　paper.　The　adaptive　sparse　representation　method　includes　the　K-singular　value　decomposition　based　dictionary　learning　algorithm,　and　the　stagewise　weak　orthogonal　matching　pursuit　reconstruction　is　improved　by　the　regularization　principle,　backtracking　mechanism,　adaptive　mechanism　and　relevant　stop　criteria.　The　compressive　measurement　was　completed　through　Gaussian　random　matrix.　One　simulation　signal　and　two　different　experimental　data　sets　of　rolling　bearing　are　utilized　to　validate　the　effectiveness　of　the　proposed　method,　and　the　results　have　shown　that　the　reconstruction　accuracy　and　calculation　efficiency　can　be　improved　simultaneously.　Most　importantly,　the　weak　fault　feature　shaded　by　strong　background　noise　can　be　effectively　identified,　which　cannot　be　obtained　by　traditional　CS　method.