Robust L1 Norm Factorization in the Presence of Outliers and Missing Data by Alternative Convex Programming

Abstract

Matrix factorization has many applications in computer vision. Singular Value Decomposition (SVD) is the standard algorithm for factorization. When there are outliers and missing data, which often happen in real measurements, SVD is no longer applicable. For robustness Iteratively Re-weighted Least Squares (IRLS) is often used for factorization by assigning a weight to each element in the measurements. Because it uses L2 norm, good initialization in IRLS is critical for success, but is non-trivial. In this paper, we formulate matrix factorization as a L1 norm minimization problem that is solved efficiently by alternative convex programming. Our formulation 1) is robust without requiring initial weighting, 2) handles missing data straightforwardly, and 3) provides a framework in which constraints and prior knowledge (if available) can be conveniently incorporated. In the experiments we apply our approach to factorization-based structure from motion. It is shown that our approach achieves better results than other approaches (including IRLS) on both synthetic and real data.