SVD Framework

Tensor singular value decomposition (t-SVD) frameworks are used to analyze and process high-dimensional data, such as videos and hyperspectral images, by exploiting their underlying low-rank structure. Current research focuses on extending t-SVD to higher-order tensors, improving robustness to noise and outliers, and developing efficient algorithms, including Bayesian methods and those incorporating randomized techniques or deep learning architectures like unrolling networks. These advancements enable improved performance in tasks like tensor completion, denoising, and clustering, with significant implications for various fields including image processing, medical imaging, and data analysis.

Papers

January 3, 2025

Guaranteed Nonconvex Low-Rank Tensor Estimation via Scaled Gradient Descent
Tong Wu
Natural Gradient Tensor Recovery Tensor Singular Value SVD Framework

December 15, 2024

OTLRM: Orthogonal Learning-based Low-Rank Metric for Multi-Dimensional Inverse Problems
Xiangming Wang, Haijin Zeng, Jiaoyang Chen, Sheng Liu, Yongyong Chen, Guoqing Chao
Inverse Problem North Star Metric Post Hoc Orthogonalization Tensor Singular Value SVD Framework

November 10, 2023

Low-Multi-Rank High-Order Bayesian Robust Tensor Factorization
Jianan Liu, Chunguang Li
Tensor Factorization Low Rank Tensor Tensor Robust Principal Component Analysis SVD Framework

July 18, 2023

Robust Data Clustering with Outliers via Transformed Tensor Low-Rank Representation
Tong Wu
Individual Representation Tensor Data Tensor Based LOw Rank Robust Clustering Tensor Robust Principal Component Analysis Tensor Recovery Task SVD Framework

May 19, 2023

Nonconvex Robust High-Order Tensor Completion Using Randomized Low-Rank Approximation
Wenjin Qin, Hailin Wang, Feng Zhang, Weijun Ma, Jianjun Wang, Tingwen Huang
Average Approximation Order Tensor Tensor Approximation SVD Framework

April 21, 2023

H2TF for Hyperspectral Image Denoising: Where Hierarchical Nonlinear Transform Meets Hierarchical Matrix Factorization
Jiayi Li, Jinyu Xie, Yisi Luo, Xile Zhao, Jianli Wang
Hyperspectral Image Denoising Nonlinear Transform SVD Framework

September 8, 2022

T2LR-Net: An unrolling network learning transformed tensor low-rank prior for dynamic MR image reconstruction
Yinghao Zhang, Peng Li, Yue Hu
Low Rank Tensor Dynamic Magnetic Resonance SVD Framework

SVD Framework

Papers

Guaranteed Nonconvex Low-Rank Tensor Estimation via Scaled Gradient Descent

OTLRM: Orthogonal Learning-based Low-Rank Metric for Multi-Dimensional Inverse Problems

Low-Multi-Rank High-Order Bayesian Robust Tensor Factorization

Robust Data Clustering with Outliers via Transformed Tensor Low-Rank Representation

Nonconvex Robust High-Order Tensor Completion Using Randomized Low-Rank Approximation

H2TF for Hyperspectral Image Denoising: Where Hierarchical Nonlinear Transform Meets Hierarchical Matrix Factorization

T2LR-Net: An unrolling network learning transformed tensor low-rank prior for dynamic MR image reconstruction