# A convex formulation for hyperspectral image superresolution via subspace-based regularization

arXiv: https://arxiv.org/abs/1411.4005 · HTML: https://mlsanity.com/paper/1411.4005/

## Key facts

- Cited by 48 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Nov 2014.

## Built on by (most cited first, 30 of 48)

- [HyperTransformer: A Textural and Spectral Feature Fusion Transformer for Pansharpening](https://mlsanity.com/paper/2203.02503/) (2022)
- [Unsupervised Hyperspectral Image Super-Resolution via Self-Supervised Modality Decoupling](https://mlsanity.com/paper/2412.04802/) (2024)
- [Unsupervised Hyperspectral Pansharpening via Low-rank Diffusion Model](https://mlsanity.com/paper/2305.10925/) (2023)
- [Improving Misaligned Multi-modality Image Fusion with One-stage Progressive Dense Registration](https://mlsanity.com/paper/2308.11165/) (2023)
- [Fast and High-Quality Blind Multi-Spectral Image Pansharpening](https://mlsanity.com/paper/2103.09943/) (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)
- [Learning A 3D-CNN and Transformer Prior for Hyperspectral Image Super-Resolution](https://mlsanity.com/paper/2111.13923/) (2021)
- [Tensor Decompositions for Hyperspectral Data Processing in Remote Sensing: A Comprehensive Review](https://mlsanity.com/paper/2205.06407/) (2022)
- [A Spectral Diffusion Prior for Hyperspectral Image Super-Resolution](https://mlsanity.com/paper/2311.08955/) (2023)
- [Hyperspectral and multispectral image fusion with arbitrary resolution through self-supervised representations](https://mlsanity.com/paper/2405.17818/) (2024)
- [Hyperspectral Pansharpening: Critical Review, Tools and Future Perspectives](https://mlsanity.com/paper/2407.01355/) (2024)
- [Band-wise Hyperspectral Image Pansharpening using CNN Model Propagation](https://mlsanity.com/paper/2311.06510/) (2023)
- [A Generalized Tensor Formulation for Hyperspectral Image Super-Resolution Under General Spatial Blurring](https://mlsanity.com/paper/2409.18731/) (2024)
- [Tuning-free Plug-and-Play Hyperspectral Image Deconvolution with Deep Priors](https://mlsanity.com/paper/2211.15307/) (2022)
- [Hyperspectral and Multispectral Image Fusion Using the Conditional Denoising Diffusion Probabilistic Model](https://mlsanity.com/paper/2307.03423/) (2023)
- [Unsupervised Hyperspectral and Multispectral Image Blind Fusion Based on Deep Tucker Decomposition Network with Spatial-Spectral Manifold Learning](https://mlsanity.com/paper/2409.09670/) (2024)
- [Enhanced Hyperspectral Image Super-Resolution via RGB Fusion and TV-TV Minimization](https://mlsanity.com/paper/2106.07066/) (2021)
- [Neural Shr"odinger Bridge Matching for Pansharpening](https://mlsanity.com/paper/2404.11416/) (2024)
- [Hyperspectral Image Super-Resolution in Arbitrary Input-Output Band Settings](https://mlsanity.com/paper/2103.10614/) (2021)
- [Self-Regression Learning for Blind Hyperspectral Image Fusion Without Label](https://mlsanity.com/paper/2103.16806/) (2021)
- [Robust Hyperspectral Image Fusion with Simultaneous Guide Image Denoising via Constrained Convex Optimization](https://mlsanity.com/paper/2209.11979/) (2022)
- [Real HSI-MSI-PAN image dataset for the hyperspectral/multi-spectral/panchromatic image fusion and super-resolution fields](https://mlsanity.com/paper/2407.02387/) (2024)
- [Zero-Shot Hyperspectral Pansharpening Using Hysteresis-Based Tuning for Spectral Quality Control](https://mlsanity.com/paper/2505.16658/) (2025)
- [Bayesian Fully-Connected Tensor Network for Hyperspectral-Multispectral Image Fusion](https://mlsanity.com/paper/2510.18400/) (2025)
- [GEWDiff: Geometric Enhanced Wavelet-based Diffusion Model for Hyperspectral Image Super-resolution](https://mlsanity.com/paper/2511.07103/) (2025)
- [Unregistered Spectral Image Fusion: Unmixing, Adversarial Learning, and Recoverability](https://mlsanity.com/paper/2603.21510/) (2026)
- [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)
- [DiriNet: A network to estimate the spatial and spectral degradation functions](https://mlsanity.com/paper/2201.12346/) (2022)

## Abstract (arXiv)

Hyperspectral remote sensing images (HSIs) usually have high spectral resolution and low spatial resolution. Conversely, multispectral images (MSIs) usually have low spectral and high spatial resolutions. The problem of inferring images which combine the high spectral and high spatial resolutions of HSIs and MSIs, respectively, is a data fusion problem that has been the focus of recent active research due to the increasing availability of HSIs and MSIs retrieved from the same geographical area. We formulate this problem as the minimization of a convex objective function containing two quadratic data-fitting terms and an edge-preserving regularizer. The data-fitting terms account for blur, different resolutions, and additive noise. The regularizer, a form of vector Total Variation, promotes piecewise-smooth solutions with discontinuities aligned across the hyperspectral bands. The downsampling operator accounting for the different spatial resolutions, the non-quadratic and non-smooth nature of the regularizer, and the very large size of the HSI to be estimated lead to a hard optimization problem. We deal with these difficulties by exploiting the fact that HSIs generally "live" in a low-dimensional subspace and by tailoring the Split Augmented Lagrangian Shrinkage Algorithm (SALSA), which is an instance of the Alternating Direction Method of Multipliers (ADMM), to this optimization problem, by means of a convenient variable splitting. The spatial blur and the spectral linear operators linked, respectively, with the HSI and MSI acquisition processes are also estimated, and we obtain an effective algorithm that outperforms the state-of-the-art, as illustrated in a series of experiments with simulated and real-life data.