Title: Weighted Low Rank Approximation for Background Estimation Problems,
Abstract: Classical principal component analysis (PCA) is not robust to the presence of
sparse 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 the
sparse outliers. In this paper, by sticking a simple weight to the Frobenius
norm, we propose a weighted low rank (WLR) method to avoid the often
computationally expensive algorithms relying on the $\ell_1$ norm. As a proof
of concept, a background estimation model has been presented and compared with
two $\ell_1$ norm minimization algorithms. We illustrate that as long as a
simple weight matrix is inferred from the data, one can use the weighted
Frobenius norm and achieve the same or better performance.