Dejiao Zhang

Iterative online subspace learning for robust image alignment

Robust high-dimensional data processing has witnessed an exciting development in recent years, as theoretical results have shown that it is possible using convex programming to optimize data fit to a low-rank component plus a sparse outlier component. This problem is also known as Robust PCA, and it has found application in many areas of computer vision. In image and video processing and face recognition, an exciting opportunity for processing of massive image databases is emerging as people upload photo and video data online in unprecedented volumes. However, the data quality and consistency is not controlled in any way, and the massiveness of the data poses a serious computational challenge. In this paper we present t-GRASTA, or “Transformed GRASTA (Grassmannian Robust Adaptive Subspace Tracking Algorithm)”. t-GRASTA performs incremental gradient descent constrained to the Grassmann manifold of subspaces in order to simultaneously estimate a decomposition of a collection of images into a low-rank subspace, a sparse part of occlusions and foreground objects, and a transformation such as rotation or translation of the image. We show that t-GRASTA is 4× faster than state-of-the-art algorithms, has half the memory requirement, and can achieve alignment for face images as well as jittered camera surveillance images.

Matched subspace detection using compressively sampled data

We consider the problem of detecting whether a high dimensional signal lies in a given low dimensional subspace using only a few compressive measurements of it. By leveraging modern random matrix theory, we show that, even when we are short on information, a reliable detector can be constructed via a properly defined measure of energy of the signal outside the subspace. Our results extend those in [1] to a more general sampling framework. Moreover, the test statistic we define is much simpler than that required by [1], and it results in more efficient computation, which is crucial for high-dimensional data processing.