  In this paper, we study the problem of matrix recovery, which aims to restore
a target matrix of authentic samples from grossly corrupted observations. Most
of the existing methods, such as the well-known Robust Principal Component
Analysis (RPCA), assume that the target matrix we wish to recover is low-rank.
However, the underlying data structure is often non-linear in practice,
therefore the low-rankness assumption could be violated. To tackle this issue,
we propose a novel method for matrix recovery in this paper, which could well
handle the case where the target matrix is low-rank in an implicit feature
space but high-rank or even full-rank in its original form. Namely, our method
pursues the low-rank structure of the target matrix in an implicit feature
space. By making use of the specifics of an accelerated proximal gradient based
optimization algorithm, the proposed method could recover the target matrix
with non-linear structures from its corrupted version. Comprehensive
experiments on both synthetic and real datasets demonstrate the superiority of
our method.
