The　sparse　decomposition　based　on　matching　pursuit　is　an　adaptive　sparse　expression　method　for　signals.　This　paper　proposes　an　idea　concerning　a　composite　dictionary　multi-atom　matching　decomposition　and　reconstruction　algorithm,　and　the　introduction　of　threshold　de-noising　in　the　reconstruction　algorithm.　Based　on　the　structural　characteristics　of　gear　fault　signals,　a　composite　dictionary　combining　the　impulse　time-frequency　dictionary　and　the　Fourier　dictionary　was　constituted,　and　a　genetic　algorithm　was　applied　to　search　for　the　best　matching　atom.　The　analysis　results　of　gear　fault　simulation　signals　indicated　the　effectiveness　of　the　hard　threshold,　and　the　impulse　or　harmonic　characteristic　components　could　be　separately　extracted.　Meanwhile,　the　robustness　of　the　composite　dictionary　multi-atom　matching　algorithm　at　different　noise　levels　was　investigated.　Aiming　at　the　effects　of　data　lengths　on　the　calculation　efficiency　of　the　algorithm,　an　improved　segmented　decomposition　and　reconstruction　algorithm　was　proposed,　and　the　calculation　efficiency　of　the　decomposition　algorithm　was　significantly　enhanced.　In　addition　it　is　shown　that　the　multi-atom　matching　algorithm　was　superior　to　the　single-atom　matching　algorithm　in　both　calculation　efficiency　and　algorithm　robustness.　Finally,　the　above　algorithm　was　applied　to　gear　fault　engineering　signals,　and　achieved　good　results.