This　paper　presents　a　new　method　for　a　composite　dictionary　matching　pursuit　algorithm,　which　is　applied　to　vibration　sensor　signal　feature　extraction　and　fault　diagnosis　of　a　gearbox.　Three　advantages　are　highlighted　in　the　new　method.　First,　the　composite　dictionary　in　the　algorithm　has　been　changed　from　multi-atom　matching　to　single-atom　matching.　Compared　to　non-composite　dictionary　single-atom　matching,　the　original　composite　dictionary　multi-atom　matching　pursuit　(CD-MaMP)　algorithm　can　achieve　noise　reduction　in　the　reconstruction　stage,　but　it　cannot　dramatically　reduce　the　computational　cost　and　improve　the　efficiency　in　the　decomposition　stage.　Therefore,　the　optimized　composite　dictionary　single-atom　matching　algorithm　(CD-SaMP)　is　proposed.　Second,　the　termination　condition　of　iteration　based　on　the　attenuation　coefficient　is　put　forward　to　improve　the　sparsity　and　efficiency　of　the　algorithm,　which　adjusts　the　parameters　of　the　termination　condition　constantly　in　the　process　of　decomposition　to　avoid　noise.　Third,　composite　dictionaries　are　enriched　with　the　modulation　dictionary,　which　is　one　of　the　important　structural　characteristics　of　gear　fault　signals.　Meanwhile,　the　termination　condition　of　iteration　settings,　sub-feature　dictionary　selections　and　operation　efficiency　between　CD-MaMP　and　CD-SaMP　are　discussed,　aiming　at　gear　simulation　vibration　signals　with　noise.　The　simulation　sensor-based　vibration　signal　results　show　that　the　termination　condition　of　iteration　based　on　the　attenuation　coefficient　enhances　decomposition　sparsity　greatly　and　achieves　a　good　effect　of　noise　reduction.　Furthermore,　the　modulation　dictionary　achieves　a　better　matching　effect　compared　to　the　Fourier　dictionary,　and　CD-SaMP　has　a　great　advantage　of　sparsity　and　efficiency　compared　with　the　CD-MaMP.　The　sensor-based　vibration　signals　measured　from　practical　engineering　gearbox　analyses　have　further　shown　that　the　CD-SaMP　decomposition　and　reconstruction　algorithm　is　feasible　and　effective.