Summary: We propose some computational methods for extracting static backgrounds from surveillance videos corrupted by noise, blur, or both. The new methods are constructed based on the fact that the matrix representation of a static background consists of identical columns; hence the idea of median filtering is embedded in these methods. These new methods significantly differ from existing methods originating from the robust principal component analysis (RPCA) in that no nuclear-norm term is involved; thus the computation of singular value decomposition can be completely avoided when solving these new models iteratively. This is an important feature because usually the dimensionality of a surveillance video is large and so the involved singular value decomposition (which is inevitable for RPCA-based models) is very expensive computationally. We show that these methods can be easily solved by well-developed operator splitting methods in optimization literature such as the alternating direction method of multipliers. We compare the new methods with their RPCA-based counterparts via testing some synthetic and real videos. Our numerical results show that compared with RPCA-based models, these median filtering-based variational models can extract more accurate backgrounds when the background in a surveillance video is static, and numerically, they can be solved much more efficiently.