---
title: "Flexible Generalized Low-Rank Regularizer for Tensor RPCA"
authors:
  - "Zhiyang Gong"
  - "Jie Yu"
  - "Yutao Hu"
  - "Yulong Wang"
doi: "10.24963/ijcai.2025/583"
url: "https://ijcai.org/proceedings/2025/583"
pdf: "https://ijcai.org/proceedings/2025/0583.pdf"
venue: "Proceedings of the Thirty-Fourth International Joint Conference on Artificial Intelligence"
year: 2025
pages: "5235-5243"
track: "Main Track"
keywords:
  - "Machine Learning: ML: Robustness"
  - "Machine Learning: ML: Matrix/tensor methods"
---

# Flexible Generalized Low-Rank Regularizer for Tensor RPCA

Zhiyang Gong, Jie Yu, Yutao Hu, Yulong Wang

*Proceedings of the Thirty-Fourth International Joint Conference on Artificial Intelligence*, pages 5235-5243. DOI: [10.24963/ijcai.2025/583](https://doi.org/10.24963/ijcai.2025/583)

## Abstract

Tensor Robust Principal Component Analysis (TRPCA) has emerged as a powerful technique for low-rank tensor recovery.  To achieve better recovery performance, a variety of TNN (Tensor Nuclear Norm) based low-rank regularizers have been proposed case by case, lacking  a general and flexible framework. In this paper, we design a novel tensor low-rank regularization framework coined  FGTNN (Flexible Generalized Tensor Nuclear Norm). Equipped with FGTNN,  we develop the FGTRPCA (Flexible Generalized TRPCA) framework, which has two desirable properties. 1) Generalizability: Many existing TRPCA methods can be viewed as special cases of our framework; 2) Flexibility: Using FGTRPCA as a general platform, we derive a series of new TRPCA methods by tuning a continuous parameter to improve performance. In addition, we develop another novel smooth and low-rank regularizer coined t-FGJP and the resulting SFGTRPCA (Smooth FGTRPCA) method by leveraging the low-rankness and smoothness priors simultaneously. Experimental results on various tensor denoising and recovery tasks demonstrate the superiority of our methods.