Low-rank tensor completion via tensor tri-factorization and sparse transformation

Abstract

Low-rank tensor factorization techniques have gained significant attention in low-rank tensor completion (LRTC) tasks due to their ability to reduce computational costs while maintaining the tensor’s low-rank structure. However, existing methods often overlook the significance of tensor singular values and the sparsity of the tensor’s third-mode fibers in the transformation domain, leading to an incomplete capture of both the low-rank structure and the inherent sparsity, which limits recovery accuracy. To address these issues, we propose a novel tensor tri-factorization logarithmic norm (TTF-LN) that more effectively captures the low-rank structure by emphasizing the significance of tensor singular values. Building on this, we introduce the tensor tri-factorization with sparse transformation (TTF-ST) model for LRTC, which integrates both low-rank and sparse priors to improve accuracy of incomplete tensor recovery. The TTF-ST model incorporates a sparse transformation that represents the tensor as the product of a low-dimensional sparse representation tensor and a compact orthogonal matrix, which extracts sparsity while reducing computational complexity. To solve the proposed model, we design an optimization algorithm based on the alternating direction method of multipliers (ADMM) and provide a rigorous theoretical analysis. Extensive experiments demonstrate that the proposed method outperforms state-of-the-art methods in both recovery accuracy and computational efficiency.