Dual-Enhanced High-Order Self-Learning Tensor Singular Value Decomposition for Robust Principal Component Analysis
Honghui Xu, Chuangjie Fang, Renfang Wang, Shengyong Chen, Jianwei Zheng
Abstract
Recently, tensor singular value decomposition (TSVD) within high-order (Ho) algebra framework has shed new light on Tensor Robust Principal Component Analysis (TRPCA) problem. However, HoTSVD lacks flexibility in handling the hidden correlations along different modes of large-scale multi-dimensional data. Moreover, the utilization of fixed or data-independent transformations in HoTSVD may result in suboptimality. For a relief, we propose a dual-enhanced self-learning TSVD along all modes to address computational flaws and learn a lossless transformation that induces a lower average-rank tensor. Specifically, we multiply the learnable semi-orthogonal matrices obtained through Tucker compression with the original tensor along all modes, thus obtaining a core tensor with more inherent low rankness. Building upon this foundation, a new TNN is introduced by generalizing HoTSVD to Mode-k TSVD, followed by the facilitation to the core tensor, achieving dual-enhancement. Moreover, a reweighting scheme is imposed on the Mode-k HoTSVD to learn the global low-rank correlation and provide an efficient numerical solution. Finally, an alternating direction method of multipliers (ADMM)-based algorithm is developed as a solver. Experimental results on several types of multi-dimensional visual data, including Light Field Images (LFI) and color videos, demonstrate the superiority of the proposal over previous state-of-the-art methods.