Online Tensor Robust Principal Component Analysis

Abstract

Tensor Robust Principal Component Analysis (TRPCA) is a procedure for recovering a data structure that has been corrupted by noise. In this thesis, a proof (inspired by Lu et al. (2018)) is given that TRPCA successfully performs this operation. An online optimisation algorithm to perform this procedure for p-dimensional tensors is proposed (based on a similar algorithm for the 3-dimensional case from Z. Zhang, Liu, Aeron, & Vetro (2016)). The required tensor identities to apply a proof of convergence (similar to the approach of Feng, Xu, & Yan (2013) for the matrix case) are derived and then applied. Examples using satellite image data and synthetic data are provided throughout to demonstrate the utility of the theoretical work and examine hypotheses.