This　paper　offers　a　new　perspective　on　the　vibrations　of　discrete　bearing　faults　by　focusing　on　the　micro-motion　states　of　rolling　elements　in　spall　fault　bearings　and　proposes　an　improved　matching　pursuit　algorithm　for　quantitative　diagnosis　with　a　high　accuracy　of　atom　selection　and　calculation　efficiency.　The　generation　mechanism　of　the　vibration　response　signal　is　explained　by　analyzing　the　micro-motion　status　when　rolling　elements　passing　through　the　spall.　A　concatenation　dictionary　composed　of　an　impact　dictionary　as　the　higher　level　and　step　dictionary　as　the　lower　level　is　constructed　based　on　the　acceleration　variation　analysis　of　the　rolling　elements.　The　information　output　by　the　higher-level　dictionary　is　used　as　the　input　information　for　the　lower-level　dictionary　to　extract　the　fault　features.　Only　one　iteration　on　the　higher-level　dictionary　is　necessary　to　extract　the　correct　impact　atoms,　with　all　subsequent　iterative　steps　assigned　to　the　lower-level　dictionary.　The　advantage　is　that　the　influence　of　high-energy　impact　components　on　the　extraction　of　step　atoms　can　be　removed.　Thereafter,　the　optimized　algorithm　based　on　the　concatenation　dictionary　is　applied　to　the　analysis　of　simulation　and　experimental　signals.　The　comparative　analysis　demonstrates　that　the　effective　quantitative　diagnosis　is　obtained,　while　the　diagnostic　precision　and　calculation　efficiency　are　improved.