Robust Autoencoders for Collective Corruption Removal
This work addresses the challenge of corruption removal in image data for applications like computer vision, representing an incremental advance over existing robust PCA methods by extending them to manifold settings.
The paper tackles the problem of robustly learning manifolds for natural data like images in the presence of sparse corruption, proposing robust autoencoders that outperform previous methods in removing corruption without needing clean training images, with significant improvements demonstrated on standard image datasets.
Robust PCA is a standard tool for learning a linear subspace in the presence of sparse corruption or rare outliers. What about robustly learning manifolds that are more realistic models for natural data, such as images? There have been several recent attempts to generalize robust PCA to manifold settings. In this paper, we propose $\ell_1$- and scaling-invariant $\ell_1/\ell_2$-robust autoencoders based on a surprisingly compact formulation built on the intuition that deep autoencoders perform manifold learning. We demonstrate on several standard image datasets that the proposed formulation significantly outperforms all previous methods in collectively removing sparse corruption, without clean images for training. Moreover, we also show that the learned manifold structures can be generalized to unseen data samples effectively.