Robust PCA via Alternating Iteratively Reweighted Low-Rank Matrix Factorization

Nowadays, many modern imaging applications generate large-scale and high-dimensional data. In order to efficiently handle these data, statistical tools amenable to exploiting their intrisic low-dimensional nature are needed. PCA is a ubiquitous method which has been widely applied in a variety of applications. However a major shortcoming of PCA is its sensitivity to gross errors - outliers. In light of this, robust PCA has been recently proposed. Robust PCA accounts for gross errors by assuming that the data matrix is the superposition of a low-rank matrix and a sparse matrix. In this work, a matrix factorization-based formulation of robust PCA which can efficiently handle large scale data is proposed. Low-rankness is imposed via a novel low-rank promoting term applied on the matrix factors, which can be viewed as a weighted version of the variational form of the nuclear norm. The newly formulated robust PCA problem is addressed via an alternating iteratively reweighted least squares-type algorithm. Simulated and real data experiments verify the effectiveness of the proposed algorithm as compared to other state-of-the-art robust PCA algorithms.