Improved Robust PCA using low-rank denoising with optimal singular value shrinkage

We study the robust PCA problem of reliably recovering a low-rank signal matrix from a signal-plus-noise-plus-outliers matrix. We analytically characterize the extent to which the singular vectors of the signal-plus-noise-plus-outliers matrix can be degraded by outliers and discuss why a recently proposed method for robust PCA that exploits outlier sparsity to improve low-rank estimation will produce suboptimal low-rank matrix estimates in the presence of noise. Next, we propose a new iterative algorithm for robust PCA that utilizes an optimal, data-driven low-rank matrix estimator (OptShrink). Finally, we show that the proposed approach yields superior background subtraction on a computer vision dataset.