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Classical principal component analysis (PCA) is not robust to the presence ofsparse outliers in the data. The use of the $\ell_1$ norm in the Robust PCA(RPCA) method successfully eliminates the weakness of PCA in separating thesparse outliers. In this paper, by sticking a simple weight to the Frobeniusnorm, we propose a weighted low rank (WLR) method to avoid the oftencomputationally expensive algorithms relying on the $\ell_1$ norm. As a proofof concept, a background estimation model has been presented and compared withtwo $\ell_1$ norm minimization algorithms. We illustrate that as long as asimple weight matrix is inferred from the data, one can use the weightedFrobenius norm and achieve the same or better performance.

Weighted Low Rank Approximation for Background Estimation Problems