Efficient Tensor Robust PCA under Hybrid Model of Tucker and Tensor Train

TL;DR

This paper introduces an efficient tensor robust PCA method combining Tucker and tensor train models, reducing computational complexity while maintaining recovery accuracy for large-scale tensor data.

Contribution

It proposes a hybrid Tucker-TT model that converts TT nuclear norm computation to a smaller tensor, significantly lowering computational costs in tensor recovery.

Findings

Reduces SVD computational cost via Tucker compression

Outperforms existing TRPCA models on synthetic data

Effective on real-world large-scale tensor data

Abstract

Tensor robust principal component analysis (TRPCA) is a fundamental model in machine learning and computer vision. Recently, tensor train (TT) decomposition has been verified effective to capture the global low-rank correlation for tensor recovery tasks. However, due to the large-scale tensor data in real-world applications, previous TRPCA models often suffer from high computational complexity. In this letter, we propose an efficient TRPCA under hybrid model of Tucker and TT. Specifically, in theory we reveal that TT nuclear norm (TTNN) of the original big tensor can be equivalently converted to that of a much smaller tensor via a Tucker compression format, thereby significantly reducing the computational cost of singular value decomposition (SVD). Numerical experiments on both synthetic and real-world tensor data verify the superiority of the proposed model.