Robust PCA is a widely used statistical procedure to recover a underlying
low-rank matrix with grossly corrupted observations. This work considers the
problem of robust PCA as a nonconvex optimization problem on the manifold of
low-rank matrices, and proposes two algorithms (for two versions of
retractions) based on manifold optimization...
It is shown that, with a proper
designed initialization, the proposed algorithms are guaranteed to converge to
the underlying low-rank matrix linearly. Compared with a previous work based on
the Burer-Monterio decomposition of low-rank matrices, the proposed algorithms
reduce the dependence on the conditional number of the underlying low-rank
matrix theoretically. Simulations and real data examples confirm the
competitive performance of our method.