  Robust principal component analysis (RPCA) is a critical tool in modern
machine learning, which detects outliers in the task of low-rank matrix
reconstruction. In this paper, we propose a scalable and learnable non-convex
approach for high-dimensional RPCA problems, which we call Learned Robust PCA
(LRPCA). LRPCA is highly efficient, and its free parameters can be effectively
learned to optimize via deep unfolding. Moreover, we extend deep unfolding from
finite iterations to infinite iterations via a novel
feedforward-recurrent-mixed neural network model. We establish the recovery
guarantee of LRPCA under mild assumptions for RPCA. Numerical experiments show
that LRPCA outperforms the state-of-the-art RPCA algorithms, such as ScaledGD
and AltProj, on both synthetic datasets and real-world applications.
