# Deep Posterior Distribution-based Embedding for Hyperspectral Image Super-resolution

arXiv: https://arxiv.org/abs/2205.14887 · HTML: https://mlsanity.com/paper/2205.14887/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 65 references that are in the map.
- First posted on arXiv 30 May 2022.

## Builds on (most cited first, 21 of 21)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [DARTS: Differentiable Architecture Search](https://mlsanity.com/paper/1806.09055/) (2018)
- [Enhanced Deep Residual Networks for Single Image Super-Resolution](https://mlsanity.com/paper/1707.02921/) (2017)
- [Image Super-Resolution Using Very Deep Residual Channel Attention Networks](https://mlsanity.com/paper/1807.02758/) (2018)
- [Accurate Image Super-Resolution Using Very Deep Convolutional Networks](https://mlsanity.com/paper/1511.04587/) (2015)
- [Rethinking Spatiotemporal Feature Learning: Speed-Accuracy Trade-offs in Video Classification](https://mlsanity.com/paper/1712.04851/) (2017)
- [Graph Convolutional Networks for Hyperspectral Image Classification](https://mlsanity.com/paper/2008.02457/) (2020)
- [Learning Spatial-Spectral Prior for Super-Resolution of Hyperspectral Imagery](https://mlsanity.com/paper/2005.08752/) (2020)
- [Multispectral and Hyperspectral Image Fusion by MS/HS Fusion Net](https://mlsanity.com/paper/1901.03281/) (2019)
- [Cross-Attention in Coupled Unmixing Nets for Unsupervised Hyperspectral Super-Resolution](https://mlsanity.com/paper/2007.05230/) (2020)
- [Unsupervised Sparse Dirichlet-Net for Hyperspectral Image Super-Resolution](https://mlsanity.com/paper/1804.05042/) (2018)
- [Boosting of Image Denoising Algorithms](https://mlsanity.com/paper/1502.06220/) (2015)
- [Aerial Vehicle Tracking by Adaptive Fusion of Hyperspectral Likelihood Maps](https://mlsanity.com/paper/1707.03553/) (2017)
- [Unsupervised and Unregistered Hyperspectral Image Super-Resolution with Mutual Dirichlet-Net](https://mlsanity.com/paper/1904.12175/) (2019)
- [Hyperspectral Image Super-resolution via Deep Progressive Zero-centric Residual Learning](https://mlsanity.com/paper/2006.10300/) (2020)
- [Zero-order Reverse Filtering](https://mlsanity.com/paper/1704.04037/) (2017)
- [Deep Amended Gradient Descent for Efficient Spectral Reconstruction from Single RGB Images](https://mlsanity.com/paper/2108.05547/) (2021)
- [Semantic-embedded Unsupervised Spectral Reconstruction from Single RGB Images in the Wild](https://mlsanity.com/paper/2108.06659/) (2021)
- [Spatial-Spectral Residual Network for Hyperspectral Image Super-Resolution](https://mlsanity.com/paper/2001.04609/) (2020)

## Built on by (most cited first, 9 of 9)

- [HIR-Diff: Unsupervised Hyperspectral Image Restoration Via Improved Diffusion Models](https://mlsanity.com/paper/2402.15865/) (2024)
- [Deep Diversity-Enhanced Feature Representation of Hyperspectral Images](https://mlsanity.com/paper/2301.06132/) (2023)
- [Hyperspectral Image Super-Resolution via Dual-domain Network Based on Hybrid Convolution](https://mlsanity.com/paper/2304.04589/) (2023)
- [Towards Lightweight Hyperspectral Image Super-Resolution with Depthwise Separable Dilated Convolutional Network](https://mlsanity.com/paper/2505.00374/) (2025)
- [A Fusion-Guided Inception Network for Hyperspectral Image Super-Resolution](https://mlsanity.com/paper/2505.03431/) (2025)
- [DACN: Dual-Attention Convolutional Network for Hyperspectral Image Super-Resolution](https://mlsanity.com/paper/2506.05041/) (2025)
- [Hybrid Deep Learning for Hyperspectral Single Image Super-Resolution](https://mlsanity.com/paper/2510.00033/) (2025)
- [Equal is Not Always Fair: A New Perspective on Hyperspectral Representation Non-Uniformity](https://mlsanity.com/paper/2505.11267/) (2025)
- [A Dual-Domain Convolutional Network for Hyperspectral Single-Image Super-Resolution](https://mlsanity.com/paper/2512.09546/) (2025)

## Abstract (arXiv)

In this paper, we investigate the problem of hyperspectral (HS) image spatial super-resolution via deep learning. Particularly, we focus on how to embed the high-dimensional spatial-spectral information of HS images efficiently and effectively. Specifically, in contrast to existing methods adopting empirically-designed network modules, we formulate HS embedding as an approximation of the posterior distribution of a set of carefully-defined HS embedding events, including layer-wise spatial-spectral feature extraction and network-level feature aggregation. Then, we incorporate the proposed feature embedding scheme into a source-consistent super-resolution framework that is physically-interpretable, producing lightweight PDE-Net, in which high-resolution (HR) HS images are iteratively refined from the residuals between input low-resolution (LR) HS images and pseudo-LR-HS images degenerated from reconstructed HR-HS images via probability-inspired HS embedding. Extensive experiments over three common benchmark datasets demonstrate that PDE-Net achieves superior performance over state-of-the-art methods. Besides, the probabilistic characteristic of this kind of networks can provide the epistemic uncertainty of the network outputs, which may bring additional benefits when used for other HS image-based applications. The code will be publicly available at https://github.com/jinnh/PDE-Net.