In　the　imaging　process　of　optical　remote　sensing　platforms,　clouds　are　an　inevitable　barrier　to　the　effective　observation　of　sensors.　To　recover　the　original　information　covered　by　the　clouds　and　the　accompanying　shadows,　a　nonnegative　matrix　factorization　(NMF)　and　error　correction　method　(S-NMF-EC)　is　proposed　in　this　paper.　Firstly,　a　cloud-free　fused　reference　image　is　obtained　by　a　reference　image　and　two　or　more　low-resolution　images　using　the　spatial　and　temporal　nonlocal　filter-based　data　fusion　model　(STNLFFM).　Secondly,　the　cloud-free　fused　reference　image　is　used　to　remove　the　cloud　cover　of　the　cloud-contaminated　image　based　on　NMF.　Finally,　the　cloud　removal　result　is　further　improved　by　error　correction.　It　is　worth　noting　that　cloud　detection　is　not　required　by　S-NMF-EC,　and　the　cloud-free　information　of　the　cloud-contaminated　image　is　maximally　retained.　Both　simulated　and　real-data　experiments　were　conducted　to　validate　the　proposed　S-NMF-EC　method.　Compared　with　other　cloud　removal　methods,　the　results　demonstrate　that　S-NMF-EC　is　visually　and　quantitatively　effective　(correlation　coefficients　≥　0.99)　for　the　removal　of　thick　clouds,　thin　clouds,　and　shadows.　©　2018　International　Society　for　Photogrammetry　and　Remote　Sensing,　Inc.　(ISPRS)