# Iterative Low-rank Network for Hyperspectral Image Denoising

arXiv: https://arxiv.org/abs/2509.00356 · HTML: https://mlsanity.com/paper/2509.00356/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 69 references that are in the map.
- First posted on arXiv 30 Aug 2025.

## Builds on (most cited first, 23 of 23)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Training behavior of deep neural network in frequency domain](https://mlsanity.com/paper/1807.01251/) (2018)
- [Decorrelated Batch Normalization](https://mlsanity.com/paper/1804.08450/) (2018)
- [Degradation-Aware Unfolding Half-Shuffle Transformer for Spectral Compressive Imaging](https://mlsanity.com/paper/2205.10102/) (2022)
- [Hyperspectral Image Restoration via Total Variation Regularized Low-rank Tensor Decomposition](https://mlsanity.com/paper/1707.02477/) (2017)
- [GAP-net for Snapshot Compressive Imaging](https://mlsanity.com/paper/2012.08364/) (2020)
- [Hyperspectral Image Denoising Employing a Spatial-Spectral Deep Residual Convolutional Neural Network](https://mlsanity.com/paper/1806.00183/) (2018)
- [Image-to-Image Translation via Group-wise Deep Whitening-and-Coloring Transformation](https://mlsanity.com/paper/1812.09912/) (2018)
- [3D Quasi-Recurrent Neural Network for Hyperspectral Image Denoising](https://mlsanity.com/paper/2003.04547/) (2020)
- [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)
- [Spectral Enhanced Rectangle Transformer for Hyperspectral Image Denoising](https://mlsanity.com/paper/2304.00844/) (2023)
- [A Trainable Spectral-Spatial Sparse Coding Model for Hyperspectral Image Restoration](https://mlsanity.com/paper/2111.09708/) (2021)
- [Spatial-Spectral Transformer for Hyperspectral Image Denoising](https://mlsanity.com/paper/2211.14090/) (2022)
- [WaveletKernelNet: An Interpretable Deep Neural Network for Industrial Intelligent Diagnosis](https://mlsanity.com/paper/1911.07925/) (2019)
- [Pixel Adaptive Deep Unfolding Transformer for Hyperspectral Image Reconstruction](https://mlsanity.com/paper/2308.10820/) (2023)
- [Robust Differentiable SVD](https://mlsanity.com/paper/2104.03821/) (2021)
- [Hybrid Noise Removal in Hyperspectral Imagery With a Spatial-Spectral Gradient Network](https://mlsanity.com/paper/1810.00495/) (2018)
- [SMDS-Net: Model Guided Spectral-Spatial Network for Hyperspectral Image Denoising](https://mlsanity.com/paper/2012.01829/) (2020)
- [Hybrid Convolutional and Attention Network for Hyperspectral Image Denoising](https://mlsanity.com/paper/2403.10067/) (2024)
- [Degradation-Noise-Aware Deep Unfolding Transformer for Hyperspectral Image Denoising](https://mlsanity.com/paper/2305.04047/) (2023)

## Built on by (most cited first, 2 of 2)

- [High-Dimensional Noise to Low-Dimensional Manifolds: A Manifold-Space Diffusion Framework for Degraded Hyperspectral Image Classification](https://mlsanity.com/paper/2604.26279/) (2026)
- [A Study of the Limits of Collaborative DCT-Based Image Denoising via Interpretable Neural Networks](https://mlsanity.com/paper/2609.29334/) (2026)

## Abstract (arXiv)

Hyperspectral image (HSI) denoising is a crucial preprocessing step for subsequent tasks. The clean HSI usually reside in a low-dimensional subspace, which can be captured by low-rank and sparse representation, known as the physical prior of HSI. It is generally challenging to adequately use such physical properties for effective denoising while preserving image details. This paper introduces a novel iterative low-rank network (ILRNet) to address these challenges. ILRNet integrates the strengths of model-driven and data-driven approaches by embedding a rank minimization module (RMM) within a U-Net architecture. This module transforms feature maps into the wavelet domain and applies singular value thresholding (SVT) to the low-frequency components during the forward pass, leveraging the spectral low-rankness of HSIs in the feature domain. The parameter, closely related to the hyperparameter of the singular vector thresholding algorithm, is adaptively learned from the data, allowing for flexible and effective capture of low-rankness across different scenarios. Additionally, ILRNet features an iterative refinement process that adaptively combines intermediate denoised HSIs with noisy inputs. This manner ensures progressive enhancement and superior preservation of image details. Experimental results demonstrate that ILRNet achieves state-of-the-art performance in both synthetic and real-world noise removal tasks.