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

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 the existing algorithms with the advantage of significantly decreasing the computational complexity of these algorithms.

• Publication year

  2015

• Venue

  IEEE Transactions on Image Processing

• Publication date

  2015-02-10

• Fields of study

  Medicine, Computer Science, Engineering, Environmental Science

• Identifiers
  DOI 10.1109/TIP.2015.2458572arXiv 1502.03121PMID 26208345
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar, PubMed

• No claims are published for this paper.

• No concepts are published for this paper.

• Signal and Image Processing for Remote Sensing

  2017cited by this paper
• Bayesian fusion of multispectral and hyperspectral images using a block coordinate descent method

  2015influential reference
• Hyperspectral Pansharpening: A Review

  2015cited by this paper
• Bayesian fusion of hyperspectral and multispectral images

  2014cited by this paper
• A Convex Formulation for Hyperspectral Image Superresolution via Subspace-Based Regularization

  2014influential reference
• Hyperspectral and Multispectral Image Fusion Based on a Sparse Representation

  2014influential reference
• Hyperspectral and multispectral data fusion mission on hyperspectral imager suite (HISUI)

  2013cited by this paper
• Bayesian Fusion of Multi-Band Images

  2013cited by this paper
• Cross-Calibration for Data Fusion of EO-1/Hyperion and Terra/ASTER

  2013cited by this paper
• Medical Image Fusion: A survey of the state of the art

  2013cited by this paper
• Coupled Nonnegative Matrix Factorization Unmixing for Hyperspectral and Multispectral Data Fusion

  2012cited by this paper
• Change Detection in Synthetic Aperture Radar Images based on Image Fusion and Fuzzy Clustering

  2012cited by this paper
• A Bayesian Restoration Approach for Hyperspectral Images

  2012cited by this paper
• A survey of classical methods and new trends in pansharpening of multispectral images

  2011cited by this paper
• Bayesian data analysis.

  2010cited by this paper
• Proximal Splitting Methods in Signal Processing

  2009cited by this paper
• Noise-Resistant Wavelet-Based Bayesian Fusion of Multispectral and Hyperspectral Images

  2009cited by this paper
• An Augmented Lagrangian Approach to the Constrained Optimization Formulation of Imaging Inverse Problems

  2009cited by this paper
• Image Fusion: Algorithms and Applications

  2008cited by this paper
• Model-Based Satellite Image Fusion

  2008cited by this paper
• Hyperspectral Subspace Identification

  2008cited by this paper
• Variational posterior distribution approximation in Bayesian super resolution reconstruction of multispectral images

  2008cited by this paper
• Hyperspectral Data Exploitation

  2007cited by this paper
• The Bayesian choice : from decision-theoretic foundations to computational implementation

  2007cited by this paper
• Stochastic methods for joint registration, restoration, and interpolation of multiple undersampled images

  2006cited by this paper
• Multispectral Image Analysis Using the Object-Oriented Paradigm

  2006cited by this paper
• Effect of relative spectral response on multi-spectral measurements and NDVI from different remote sensing systems

  2006cited by this paper
• Application of the stochastic mixing model to hyperspectral resolution enhancement

  2004cited by this paper
• MAP estimation for hyperspectral image resolution enhancement using an auxiliary sensor

  2004cited by this paper
• Fusion of multispectral and panchromatic images using improved IHS and PCA mergers based on wavelet decomposition

  2004cited by this paper
• Solution Of Matrix Equation

  2003cited by this paper
• Monthly Notices of the Royal Astronomical Society

  2003cited by this paper
• Super-resolution image reconstruction: a technical overview

  2003cited by this paper
• Hyperspectral image data analysis

  2002cited by this paper
• Economic inequality and burden-sharing in the provision of local environmental quality

  2002cited by this paper
• The SAURON project – I. The panoramic integral-field spectrograph

  2001cited by this paper
• A fast super-resolution reconstruction algorithm for pure translational motion and common space-invariant blur

  2000cited by this paper
• Bayesian and regularization methods for hyperparameter estimation in image restoration

  1999cited by this paper
• Least squares subspace projection approach to mixed pixel classification for hyperspectral images

  1998cited by this paper
• Imaging Spectroscopy and the Airborne Visible/Infrared Imaging Spectrometer (AVIRIS)

  1998cited by this paper
• Joint MAP registration and high-resolution image estimation using a sequence of undersampled images

  1997cited by this paper
• Restoration of a single superresolution image from several blurred, noisy, and undersampled measured images

  1997cited by this paper
• The Bayesian choice

  1994cited by this paper
• Iterative identification and restoration of images

  1993cited by this paper
• Iterative identification and restoration of images

  1990cited by this paper
• Solution of the matrix equation AX-XB=C

  1986cited by this paper
• Solutions of ill-posed problems

  1977cited by this paper
• Solving least squares problems

  1976cited by this paper
• Solution of the matrix equation AX− XB = C

  1976cited by this paper
• Algorithm 432 [C2]: Solution of the matrix equation AX + XB = C [F4]

  1972cited by this paper

• Spatial-X fusion for multi-source satellite imageries

  2026cites this paper
• SCIAU-Net: A Spatial-Spectral Cross-Modal Interaction ADMM Unfolding Network for Hyperspectral and Multispectral Image Fusion

  2026cites this paper
• Fusion of EnMAP/PRISMA hyperspectral and Sentinel-2 multispectral imagery for estimating crop traits

  2026influential citation
• Subspace-Frequency Regularization for Hyperspectral Image Super-Resolution

  2026cites this paper
• Spatial–spectral fusion under highly dynamic ocean conditions based on optical water classification

  2026cites this paper
• RAMSF: A Novel Generic Framework for Optical Remote Sensing Multimodal Spatial-Spectral Fusion

  2025cites this paper
• A Parametric Non-Negative Coupled Canonical Polyadic Decomposition Algorithm for Hyperspectral Super-Resolution

  2025cites this paper
• Hyperspectral and multispectral image fusion: When model-driven meet data-driven strategies

  2025cites this paper
• Nonlinear Learnable Triple-Domain Transform Tensor Nuclear Norm for Hyperspectral Image Super-Resolution

  2025cites this paper
• Pointwise fuzzy mutual information based multi-label feature selection via feature low-rank regularization

  2025cites this paper
• Efficient image reconstruction via regularized variable s-step conjugate gradient method for Sylvester matrix equations

  2025cites this paper
• Deep unsupervised adaptive attention network for hyperspectral image cross-region reconstruction

  2025cites this paper
• Building Non-Uniform Degradation Model for Position-Aware Hyperspectral Image Fusion

  2025cites this paper
• An Image Fusion Algorithm Utilizing Coupled Non-Negative Matrix Factorization in Conjunction with a Total Variation Approach

  2025cites this paper
• Hyperspectral and Multispectral Image Fusion With Functional Data Analysis Techniques

  2025cites this paper
• Dual-Cross Transformer based on the Frequency Domain for Hyperspectral Image Super-resolution

  2025cites this paper
• Spectrotemporal fusion: Generation of frequent hyperspectral satellite imagery

  2025cites this paper
• A Multistage Semi-Supervised Network for Hyperspectral Super-Resolution

  2025cites this paper
• Unsupervised Model-Embedded Two-Stage Diffusion Method for Multispectral and Hyperspectral Image Fusion

  2025cites this paper
• A Comprehensive Benchmarking Framework for Sentinel-2 Sharpening: Methods, Dataset, and Evaluation Metrics

  2025cites this paper
• A Novel Spectral-Spatial Attention Network for Zero-Shot Pansharpening

  2025cites this paper
• Robust Anomaly Detection of Multivariate Time Series Data via Adversarial Graph Attention BiGRU

  2025cites this paper
• Perceptive spectral transformer unfolding network with multiscale mixed training for arbitrary-scale hyperspectral and multispectral image fusion

  2025cites this paper
• CGNet: Classification-Guided Multi-Task Interactive Network for Hyperspectral and Multispectral Image Fusion

  2025cites this paper
• Integrated Fusion Network for Hyperspectral, Multispectral and Panchromatic Data Fusion

  2025cites this paper
• SSDT: Multiscale Spatial–Spectral Dilated Transformer for Hyperspectral and Multispectral Image Fusion

  2025cites this paper
• Full-Scale Regression Modeling of Spatial Details for Single-/Multiplatform Hypersharpening

  2025cites this paper
• A Fast Fusion Method for Multi- and Hyperspectral Images via Subpixel-Shift Decomposition

  2025cites this paper
• AHMNet: SSM-Based Antinoise Hyperspectral and Multispectral Image Fusion

  2025cites this paper
• Hyperspectral and Multispectral Image Fusion Via Multi-Scale CNN-Mamba Network

  2025cites this paper
• Deep Learning in Remote Sensing Image Fusion: Methods, protocols, data, and future perspectives

  2025cites this paper
• Asymptotic Spectral Mapping for Hyperspectral Image Fusion

  2025cites this paper
• IGFNet: An Interactive-Guided Fusion Network for Hyperspectral Pansharpening

  2025cites this paper
• Low-rankness and Smoothness Meet Subspace: A Unified Tensor Regularization for Hyperspectral Image Super-resolution

  2025cites this paper
• Multiscale common-private feature adversarial decoupling network for hyperspectral pansharpening

  2025cites this paper
• Multi-modal consistent loss diffusion model for Sentinel-3 single image super resolution

  2025cites this paper
• Joint Tensor and Inter-View Low-Rank Recovery for Incomplete Multiview Clustering

  2025cites this paper
• A Grouping Strategy-Based Progressive Fusion Network for Hyperspectral Image Super-Resolution

  2025cites this paper
• Integrated Fusion for Panchromatic, Multispectral, Hyperspectral Remote Sensing Images: Insights From Multispectral Images

  2025cites this paper
• S3-Net: Learning spectral-spatio self-similarity for hyperspectral image super-resolution

  2025cites this paper
• A Progressive Spatial–Spectral Interactive Network for Integrated Fusion of Panchromatic, Multispectral, and Hyperspectral Images

  2025cites this paper
• Enhanced Spatial-Frequency Synergistic Network for Multispectral and Hyperspectral Image Fusion

  2025cites this paper
• Tensor decompositions for signal processing: Theory, advances, and applications

  2025cites this paper
• ISGM-Fus: Internal structure-guided model for multispectral and hyperspectral image fusion

  2025cites this paper
• Hyperspectral super-resolution via nonlinear unmixing

  2025cites this paper
• An Iterative Networks Based on Homogeneous and Heterogeneous Local-Global Interaction Modules for Multispectral Image Panchromatic Sharpening

  2025cites this paper
• Cross-domain correspondence intensity modulation based on Bayesian-decision for remote sensing image pansharpening

  2025cites this paper
• Progressive Synergistic Registration and Fusion Diffusion Network for Unregistered Hyperspectral and Multispectral Image Fusion

  2025cites this paper
• A Progressive Registration-Fusion Co-Optimization A-Mamba Network: Toward Deep Unregistered Hyperspectral and Multispectral Fusion

  2025cites this paper
• Multispectral and Hyperspectral Image Fusion With Spectrally Varying Blurs and MM Algorithm

  2025influential citation
• Adaptive Gradient Neural Networks for Solving the Time-Varying Sylvester Equation

  2025cites this paper
• An Arbitrarily Predefined-Time Convergent RNN for Dynamic LMVE With Its Applications in UR3 Robotic Arm Control and Multiagent Systems

  2025cites this paper
• Spectral Correlation-Based Fusion Network for Hyperspectral Image Super-Resolution

  2025cites this paper
• HyDeFuse: provably convergent denoiser-driven hyperspectral fusion

  2025cites this paper
• Rethinking Coupled Tensor Analysis for Hyperspectral Super-Resolution: Recoverable Modeling Under Endmember Variability

  2025cites this paper
• Compact Multi-level-prior Tensor Representation for Hyperspectral Image Super-resolution

  2025cites this paper
• Mapping the spatial distribution of species using airborne and spaceborne imaging spectroscopy: A case study of invasive plants

  2025cites this paper
• Simulation Comparison Between Nonlinear GNN and ZNN for Online Complex Sylvester Equation Solving

  2025cites this paper
• Cycle-Consistent Mamba-Based Registration-Fusion Joint Network for Unregistered Hyperspectral Image Super-Resolution

  2025cites this paper
• From classical image fusion to deep representation learning: A survey of the advances in hyperspectral image pan-sharpening

  2025cites this paper
• Progressive Structure Preservation and Detail Refinement for Remote Sensing Single-Image Super-Resolution

  2025cites this paper
• Dual-Path Interactive U-Net for Unsupervised Hyperspectral Image Super-Resolution

  2025cites this paper
• Unsupervised Hyperspectral and Multispectral Image Fusion With Deep Spectral-Spatial Collaborative Constraint

  2024cites this paper
• A Generalized Tensor Formulation for Hyperspectral Image Super-Resolution Under General Spatial Blurring

  2024cites this paper
• Multispectral and hyperspectral image fusion via multi-model deep prior regularization

  2024cites this paper
• A modified Fuvar fusion algorithm based on adaptive end-member selection for hyperspectral remote sensing images

  2024cites this paper
• CroDoSR: Tensor Cross-Domain Rank for Hyperspectral Image Super-Resolution

  2024cites this paper
• Multispectral and Hyperspectral Image Fusion Via Joint Low-Rank and Smooth Tensor Prior

  2024cites this paper
• Spectral-Enhanced Sparse Transformer Network for Hyperspectral Super-Resolution Reconstruction

  2024cites this paper
• Hyperspectral Super-Resolution Using Nonlinear Unmixing and Nonnegative Tensor Factorization

  2024cites this paper
• HSR-KAN: Efficient Hyperspectral Image Super-Resolution via Kolmogorov-Arnold Networks

  2024cites this paper
• Extended alternating structure-adapted proximal gradient algorithm for nonconvex nonsmooth problems

  2024cites this paper
• Hyperspectral Pansharpening: Critical review, tools, and future perspectives

  2024cites this paper
• A Hybrid Registration and Fusion Method for Hyperspectral Super-resolution

  2024cites this paper
• All in One: A Unified Network for Hyperspectral Image Fusion

  2024cites this paper
• NGST-Net: A N-Gram based Swin Transformer Network for improving multispectral and hyperspectral image fusion

  2024cites this paper
• Hyperspectral and Multispectral Image Fusion via Logarithmic Low-Rank Tensor Ring Decomposition

  2024cites this paper
• AMSIN: An adaptive multi-scale input network for hyperspectral image fusion

  2024cites this paper
• A Principle Design of Registration-Fusion Consistency: Toward Interpretable Deep Unregistered Hyperspectral Image Fusion

  2024cites this paper
• Advancing Hyperspectral and Multispectral Image Fusion: An Information-Aware Transformer-Based Unfolding Network

  2024influential citation
• MDC-FusFormer: Multiscale Deep Cross-Fusion Transformer Network for Hyperspectral and Multispectral Image Fusion

  2024cites this paper
• A Deep Unfolding Network for Multispectral and Hyperspectral Image Fusion

  2024cites this paper
• Multi-task multi-objective evolutionary network for hyperspectral image classification and pansharpening

  2024cites this paper
• S2CycleDiff: Spatial-Spectral-Bilateral Cycle-Diffusion Framework for Hyperspectral Image Super-resolution

  2024cites this paper
• Pansharpening and spatiotemporal image fusion method for remote sensing

  2024cites this paper
• A Coupled Tensor Double-Factor Method for Hyperspectral and Multispectral Image Fusion

  2024cites this paper
• SSCAConv: Self-Guided Spatial-Channel Adaptive Convolution for Image Fusion

  2024cites this paper
• Crossed Dual-Branch U-Net for Hyperspectral Image Super-Resolution

  2024cites this paper
• MMIF: Interpretable Hyperspectral and Multispectral Image Fusion via Maximum Mutual Information

  2024cites this paper
• Coupled Matrix Factorization Constrained Deep Hyperspectral and Multispectral Image Fusion

  2024cites this paper
• Domain Transform Model Driven by Deep Learning for Anti-Noise Hyperspectral and Multispectral Image Fusion

  2024cites this paper
• Two Spectral–Spatial Implicit Neural Representations for Arbitrary-Resolution Hyperspectral Pansharpening

  2024cites this paper
• A No-Reference Quality Assessment Method for Hyperspectral Sharpened Images via Benford's Law

  2024cites this paper
• Subspace Dynamic Combined Sparsity-Based Hyper-Sharpening for Diverse Auxiliary Images

  2024cites this paper
• Deep interpolation based hyperspectral-multispectral image fusion via anisotropic dependent principal component analysis

  2024cites this paper
• Hyperspectral Image Super-Resolution Based on Frequency Characteristics

  2024influential citation
• Hyperspectral Image Fusion via a Novel Generalized Tensor Nuclear Norm Regularization

  2024cites this paper
• MFT-GAN: A Multiscale Feature-Guided Transformer Network for Unsupervised Hyperspectral Pansharpening

  2024cites this paper
• Graph Low-Rank Non-Negative Matrix Factorization with Auto-Encoders for Fault Detection

  2024cites this paper
• Progressive fusion of hyperspectral and multispectral images based on joint bilateral filtering

  2024cites this paper