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Robust high-dimensional data processing has witnessed an exciting developmentin recent years, as theoretical results have shown that it is possible usingconvex programming to optimize data fit to a low-rank component plus a sparseoutlier component. This problem is also known as Robust PCA, and it has foundapplication in many areas of computer vision. In image and video processing andface recognition, the opportunity to process massive image databases isemerging as people upload photo and video data online in unprecedented volumes.However, data quality and consistency is not controlled in any way, and themassiveness of the data poses a serious computational challenge. In this paperwe present t-GRASTA, or "Transformed GRASTA (Grassmannian Robust AdaptiveSubspace Tracking Algorithm)". t-GRASTA iteratively performs incrementalgradient descent constrained to the Grassmann manifold of subspaces in order tosimultaneously estimate a decomposition of a collection of images into alow-rank subspace, a sparse part of occlusions and foreground objects, and atransformation such as rotation or translation of the image. We show thatt-GRASTA is 4 $\times$ faster than state-of-the-art algorithms, has half thememory requirement, and can achieve alignment for face images as well asjittered camera surveillance images.

Iterative Grassmannian Optimization for Robust Image Alignment