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

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SVD is no longer applicable.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.