The　condition　monitoring　of　rolling　element　bearings　(REBs)　is　essential　to　maintain　the　reliable　operation　of　rotating　machinery,　and　the　difficulty　lies　in　how　to　estimate　fault　information　from　the　raw　signal　that　is　always　overwhelmed　by　severe　background　noise　and　other　interferences.　The　method　based　on　a　sparse　model　has　attracted　increasing　attention　because　it　can　capture　deep-level　fault　features.　However,　when　processing　a　signal　with　complex　components　and　weak　fault　features,　the　performance　of　sparse　model-based　methods　is　often　not　ideal.　In　this　work,　the　fault　information-based　sparse　low-rank　algorithm　(FISLRA)　is　proposed　to　abstract　the　fault　information　from　a　noisy　signal　interfered　with　by　background　noise　and　external　interference.　Concretely,　a　sparse　and　low-rank　model　is　formulated　in　the　time-frequency　domain.　Then,　a　fast-converging　algorithm　is　derived　based　on　the　alternating　direction　method　of　multipliers　(ADMM)　to　solve　the　formulated　model.　Moreover,　to　further　highlight　the　periodical　transients,　a　correlated　kurtosis-based　thresholding　(CKT)　scheme　proposed　in　this　paper　is　also　incorporated　to　solve　the　proposed　low-rank　spares　model.　The　superiority　of　the　proposed　FISLRA　over　the　traditional　sparse　low-rank　model　(TSLRM)　and　spectral　kurtosis　(SK)　is　proved　by　simulation　analysis.　In　addition,　two　experimental　signals　collected　from　a　bearing　test　rig　are　utilized　to　demonstrate　the　efficiency　of　the　proposed　FISLRA　in　fault　detection.　The　results　illustrate　that　compared　to　the　TSLRM　method,　FISLRA　can　effectively　extract　periodical　fault　transients　even　when　harmonic　components　(HCs)　are　present　in　the　noisy　signal.