# Fast Fusion of Multi-Band Images Based on Solving a Sylvester Equation

arXiv: https://arxiv.org/abs/1502.03121 · HTML: https://mlsanity.com/paper/1502.03121/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Feb 2015.

## Built on by (most cited first, 25 of 25)

- [Fusformer: A Transformer-based Fusion Approach for Hyperspectral Image Super-resolution](https://mlsanity.com/paper/2109.02079/) (2021)
- [Hyperspectral Pansharpening Based on Improved Deep Image Prior and Residual Reconstruction](https://mlsanity.com/paper/2107.02630/) (2021)
- [Model Inspired Autoencoder for Unsupervised Hyperspectral Image Super-Resolution](https://mlsanity.com/paper/2110.11591/) (2021)
- [Hyperspectral Pansharpening: Critical Review, Tools and Future Perspectives](https://mlsanity.com/paper/2407.01355/) (2024)
- [A Triple-Double Convolutional Neural Network for Panchromatic Sharpening](https://mlsanity.com/paper/2112.02237/) (2021)
- [DDRF: Denoising Diffusion Model for Remote Sensing Image Fusion](https://mlsanity.com/paper/2304.04774/) (2023)
- [LADMM-Net: An Unrolled Deep Network For Spectral Image Fusion From Compressive Data](https://mlsanity.com/paper/2103.00940/) (2021)
- [A Generalized Tensor Formulation for Hyperspectral Image Super-Resolution Under General Spatial Blurring](https://mlsanity.com/paper/2409.18731/) (2024)
- [Hyperspectral Image Super-resolution with Deep Priors and Degradation Model Inversion](https://mlsanity.com/paper/2201.09851/) (2022)
- [CD-GAN: a robust fusion-based generative adversarial network for unsupervised remote sensing change detection with heterogeneous sensors](https://mlsanity.com/paper/2203.00948/) (2022)
- [HSR-KAN: Efficient Hyperspectral Image Super-Resolution via Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2409.06705/) (2024)
- [Automated and Autonomous Experiment in Electron and Scanning Probe Microscopy](https://mlsanity.com/paper/2103.12165/) (2021)
- [LAConv: Local Adaptive Convolution for Image Fusion](https://mlsanity.com/paper/2107.11617/) (2021)
- [Identity-Preserving Pose-Robust Face Hallucination Through Face Subspace Prior](https://mlsanity.com/paper/2111.10634/) (2021)
- [mHealth hyperspectral learning for instantaneous spatiospectral imaging of hemodynamics](https://mlsanity.com/paper/2303.16205/) (2023)
- [Rethinking Coupled Tensor Analysis for Hyperspectral Super-Resolution: Recoverable Modeling Under Endmember Variability](https://mlsanity.com/paper/2512.19489/) (2025)
- [Subspace-Based Feature Fusion From Hyperspectral And Multispectral Image For Land Cover Classification](https://mlsanity.com/paper/2102.11228/) (2021)
- [Interpretable Hyperspectral AI: When Non-Convex Modeling meets Hyperspectral Remote Sensing](https://mlsanity.com/paper/2103.01449/) (2021)
- [Guided Deep Generative Model-based Spatial Regularization for Multiband Imaging Inverse Problems](https://mlsanity.com/paper/2306.17197/) (2023)
- [Unsupervised Hyperspectral and Multispectral Images Fusion Based on the Cycle Consistency](https://mlsanity.com/paper/2307.03413/) (2023)
- [ADASR: An Adversarial Auto-Augmentation Framework for Hyperspectral and Multispectral Data Fusion](https://mlsanity.com/paper/2310.07255/) (2023)
- [Hyperspectral Image Fusion via Logarithmic Low-rank Tensor Ring Decomposition](https://mlsanity.com/paper/2310.10044/) (2023)
- [A Hybrid Registration and Fusion Method for Hyperspectral Super-resolution](https://mlsanity.com/paper/2407.05279/) (2024)
- [Joint Tensor and Inter-View Low-Rank Recovery for Incomplete Multiview Clustering](https://mlsanity.com/paper/2503.02449/) (2025)
- [Compact Multi-level-prior Tensor Representation for Hyperspectral Image Super-resolution](https://mlsanity.com/paper/2510.06098/) (2025)

## Abstract (arXiv)

This paper proposes a fast multi-band image fusion algorithm, which combines a high-spatial low-spectral resolution image and a low-spatial high-spectral resolution image. The well admitted forward model is explored to form the likelihoods of the observations. Maximizing the likelihoods leads to solving a Sylvester equation. By exploiting the properties of the circulant and downsampling matrices associated with the fusion problem, a closed-form solution for the corresponding Sylvester equation is obtained explicitly, getting rid of any iterative update step. Coupled with the alternating direction method of multipliers and the block coordinate descent method, the proposed algorithm can be easily generalized to incorporate prior information for the fusion problem, allowing a Bayesian estimator. Simulation results show that the proposed algorithm achieves the same performance as existing algorithms with the advantage of significantly decreasing the computational complexity of these algorithms.