Weighted Low Rank Approximation for Background Estimation Problems

2017/07/04 by Aritra Dutta, Xin Li, Dutta, Aritra +1
Computer Science · Engineering · #Blind Source Separation Techniques #Computer Vision and Pattern Recognition (cs.CV) #FOS: Computer and information sciences #FOS: Mathematics #Image and Signal Denoising Methods #Optimization and Control (math.OC) #Sparse and Compressive Sensing Techniques

paper · pdf · doi:10.48550/arxiv.1707.01753

openalex publication_date 2017/07/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Robust principal component analysis?

Cited by

• A Batch-Incremental Video Background Estimation Model using Weighted\n Low-Rank Approximation of Matrices

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