# Hyperspectral Image Fusion via Logarithmic Low-rank Tensor Ring Decomposition

arXiv: https://arxiv.org/abs/2310.10044 · HTML: https://mlsanity.com/paper/2310.10044/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 56 references that are in the map.
- First posted on arXiv 16 Oct 2023.

## Builds on (most cited first, 14 of 14)

- [Tensor Ring Decomposition](https://mlsanity.com/paper/1606.05535/) (2016)
- [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)
- [Wide Compression: Tensor Ring Nets](https://mlsanity.com/paper/1802.09052/) (2018)
- [A convex formulation for hyperspectral image superresolution via subspace-based regularization](https://mlsanity.com/paper/1411.4005/) (2014)
- [Efficient Low Rank Tensor Ring Completion](https://mlsanity.com/paper/1707.08184/) (2017)
- [Tensor Ring Decomposition with Rank Minimization on Latent Space: An Efficient Approach for Tensor Completion](https://mlsanity.com/paper/1809.02288/) (2018)
- [Fast Fusion of Multi-Band Images Based on Solving a Sylvester Equation](https://mlsanity.com/paper/1502.03121/) (2015)
- [Hyperspectral Super-Resolution: A Coupled Tensor Factorization Approach](https://mlsanity.com/paper/1804.05307/) (2018)
- [Hyperspectral Super-Resolution via Coupled Tensor Ring Factorization](https://mlsanity.com/paper/2001.01547/) (2020)
- [Multi-Band Image Fusion Based on Spectral Unmixing](https://mlsanity.com/paper/1603.08720/) (2016)
- [Invariant Attribute Profiles: A Spatial-Frequency Joint Feature Extractor for Hyperspectral Image Classification](https://mlsanity.com/paper/1912.08847/) (2019)
- [Tensor completion via nonconvex tensor ring rank minimization with guaranteed convergence](https://mlsanity.com/paper/2005.09674/) (2020)
- [H2TF for Hyperspectral Image Denoising: Where Hierarchical Nonlinear Transform Meets Hierarchical Matrix Factorization](https://mlsanity.com/paper/2304.11141/) (2023)

## Abstract (arXiv)

Integrating a low-spatial-resolution hyperspectral image (LR-HSI) with a high-spatial-resolution multispectral image (HR-MSI) is recognized as a valid method for acquiring HR-HSI. Among the current fusion approaches, the tensor ring (TR) decomposition-based method has received growing attention owing to its superior performance on preserving the spatial-spectral correlation. Furthermore, the low-rank property in some TR factors has been exploited via the matrix nuclear norm regularization along mode-2. On the other hand, the tensor nuclear norm (TNN)-based approaches have recently demonstrated to be more efficient on keeping high-dimensional low-rank structures in tensor recovery. Here, we study the low-rankness of TR factors from the TNN perspective and consider the mode-2 logarithmic TNN (LTNN) on each TR factor. A novel fusion model is proposed by incorporating this LTNN regularization and the weighted total variation which is to promote the continuity of HR-HSI in the spatial-spectral domain. Meanwhile, we have devised a highly efficient proximal alternating minimization algorithm to solve the proposed model. The experimental results indicate that our method improves the visual quality and exceeds the existing state-of-the-art fusion approaches with respect to various quantitative metrics.