The answer linked below discusses an outlier-tolerant PCA method. Is there a publicly available implementation?
Here's the paper:
Xu, H., Caramanis, C., & Mannor, S. (2013). Outlier-robust PCA: the high-dimensional case. IEEE transactions on information theory, 59(1), 546-572. http://users.ece.utexas.edu/~cmcaram/pubs/HRPCA_Journal.final.pdf
Readers may be interested the following discussions of multivariate outlier removal, sparse PCA, and robust covariance estimation, though they do not answer this specific question. (Sparse PCA with corrupted entries is different from outlier-robust PCA with corrupted columns, and OGK does not provide an actual list of outliers.)