Title: Robust Kronecker-Decomposable Component Analysis for Low-Rank Modeling,
Abstract: Dictionary learning and component analysis are part of one of the most
well-studied and active research fields, at the intersection of signal and
image processing, computer vision, and statistical machine learning. In
dictionary learning, the current methods of choice are arguably K-SVD and its
variants, which learn a dictionary (i.e., a decomposition) for sparse coding
via Singular Value Decomposition. In robust component analysis, leading methods
derive from Principal Component Pursuit (PCP), which recovers a low-rank matrix
from sparse corruptions of unknown magnitude and support. However, K-SVD is
sensitive to the presence of noise and outliers in the training set.
Additionally, PCP does not provide a dictionary that respects the structure of
the data (e.g., images), and requires expensive SVD computations when solved by
convex relaxation. In this paper, we introduce a new robust decomposition of
images by combining ideas from sparse dictionary learning and PCP. We propose a
novel Kronecker-decomposable component analysis which is robust to gross
corruption, can be used for low-rank modeling, and leverages separability to
solve significantly smaller problems. We design an efficient learning algorithm
by drawing links with a restricted form of tensor factorization. The
effectiveness of the proposed approach is demonstrated on real-world
applications, namely background subtraction and image denoising, by performing
a thorough comparison with the current state of the art.