Weighted Low Rank Approximation for Background Estimation Problems

Classical principal component analysis (PCA) is not robust to the presence of sparse outliers in the data. The use of the ℓ1 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 ℓ1 norm. As a proof of concept, a background estimation model has been presented and compared with two ℓ1 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.