The　sparse　decomposition　based　on　matching　pursuit　is　an　adaptive　sparse　expression　of　the　signals.　An　adaptive　matching　pursuit　algorithm　that　uses　an　impulse　dictionary　is　introduced　in　this　article　for　rolling　bearing　vibration　signal　processing　and　fault　diagnosis.　First,　a　new　dictionary　model　is　established　according　to　the　characteristics　and　mechanism　of　rolling　bearing　faults.　The　new　model　incorporates　the　rotational　speed　of　the　bearing,,　the　dimensions　of　the　bearing　and　the　bearing　fault　status,　among　other　parameters.　The　model　can　simulate　the　impulse　experienced　by　the　bearing　at　different　bearing　fault　levels.　A　simulation　experiment　suggests　that　a　new　impulse　dictionary　used　in　a　matching　pursuit　algorithm　combined　with　a　genetic　algorithm　has　a　more　accurate　effect　on　bearing　fault　diagnosis　than　using　a　traditional　impulse　dictionary.　However,　those　two　methods　have　some　weak　points,　namely,　poor　stability,　rapidity　and　controllability.　Each　key　parameter　in　the　dictionary　model　and　its　influence　on　the　analysis　results　are　systematically　studied,　and　the　impulse　location　is　determined　as　the　primary　model　parameter.　The　adaptive　impulse　dictionary　is　established　by　changing　characteristic　parameters　progressively.　The　dictionary　built　by　this　method　has　a　lower　redundancy　and　a　higher　relevance　between　each　dictionary　atom　and　the　analyzed　vibration　signal.　The　matching　pursuit　algorithm　of　an　adaptive　impulse　dictionary　is　adopted　to　analyze　the　simulated　signals.　The　results　indicate　that　the　characteristic　fault　components　could　be　accurately　extracted　from　the　noisy　simulation　fault　signals　by　this　algorithm,　and　the　result　exhibited　a　higher　efficiency　in　addition　to　an　improved　stability,　rapidity　and　controllability　when　compared　with　a　matching　pursuit　approach　that　was　based　on　a　genetic　algorithm.　We　experimentally　analyze　the　early-stage　fault　signals　and　composite　fault　signals　of　the　bearing.　The　results　further　demonstrate　the　effectiveness　and　superiority　of　the　matching　pursuit　algorithm　that　uses　the　adaptive　impulse　dictionary.　Finally,　this　algorithm　is　applied　to　the　analysis　of　engineering　data,　and　good　results　are　achieved.　(C)　2014　Elsevier　Ltd.　All　rights　reserved.