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

arXiv: https://arxiv.org/abs/2304.11141 · HTML: https://mlsanity.com/paper/2304.11141/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 34 references that are in the map.
- First posted on arXiv 21 Apr 2023.

## Builds on (most cited first, 13 of 13)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Implicit Regularization in Deep Matrix Factorization](https://mlsanity.com/paper/1905.13655/) (2019)
- [Tensor Robust Principal Component Analysis with A New Tensor Nuclear Norm](https://mlsanity.com/paper/1804.03728/) (2018)
- [Hyperspectral Image Restoration via Total Variation Regularized Low-rank Tensor Decomposition](https://mlsanity.com/paper/1707.02477/) (2017)
- [Hyperspectral Image Denoising Employing a Spatial-Spectral Deep Residual Convolutional Neural Network](https://mlsanity.com/paper/1806.00183/) (2018)
- [Non-local Meets Global: An Iterative Paradigm for Hyperspectral Image Restoration](https://mlsanity.com/paper/2010.12921/) (2020)
- [Framelet Representation of Tensor Nuclear Norm for Third-Order Tensor Completion](https://mlsanity.com/paper/1909.06982/) (2019)
- [FastHyMix: Fast and Parameter-free Hyperspectral Image Mixed Noise Removal](https://mlsanity.com/paper/2109.08879/) (2021)
- [Low-tubal-rank Tensor Completion using Alternating Minimization](https://mlsanity.com/paper/1610.01690/) (2016)
- [Fast Noise Removal in Hyperspectral Images via Representative Coefficient Total Variation](https://mlsanity.com/paper/2211.01825/) (2022)
- [Tensor Q-Rank: New Data Dependent Definition of Tensor Rank](https://mlsanity.com/paper/1910.12016/) (2019)
- [Hyperspectral Image Denoising and Anomaly Detection Based on Low-rank and Sparse Representations](https://mlsanity.com/paper/2103.07437/) (2021)
- [Adaptive and Implicit Regularization for Matrix Completion](https://mlsanity.com/paper/2208.05640/) (2022)

## Built on by (most cited first, 3 of 3)

- [Hyperspectral Image Fusion via Logarithmic Low-rank Tensor Ring Decomposition](https://mlsanity.com/paper/2310.10044/) (2023)
- [3DeepRep: 3D Deep Low-rank Tensor Representation for Hyperspectral Image Inpainting](https://mlsanity.com/paper/2506.16735/) (2025)
- [An Interdisciplinary and Cross-Task Review on Missing Data Imputation](https://mlsanity.com/paper/2511.01196/) (2025)

## Abstract (arXiv)

Recently, tensor singular value decomposition (t-SVD) has emerged as a promising tool for hyperspectral image (HSI) processing. In the t-SVD, there are two key building blocks: (i) the low-rank enhanced transform and (ii) the accompanying low-rank characterization of transformed frontal slices. Previous t-SVD methods mainly focus on the developments of (i), while neglecting the other important aspect, i.e., the exact characterization of transformed frontal slices. In this letter, we exploit the potentiality in both building blocks by leveraging the underlinebf Hierarchical nonlinear transform and the underlinebf Hierarchical matrix factorization to establish a new underlinebf Tensor underlinebf Factorization (termed as H2TF). Compared to shallow counter partners, e.g., low-rank matrix factorization or its convex surrogates, H2TF can better capture complex structures of transformed frontal slices due to its hierarchical modeling abilities. We then suggest the H2TF-based HSI denoising model and develop an alternating direction method of multipliers-based algorithm to address the resultant model. Extensive experiments validate the superiority of our method over state-of-the-art HSI denoising methods.