# Self-supervised Deep Hyperspectral Inpainting with the Plug and Play and Deep Image Prior Models

arXiv: https://arxiv.org/abs/2501.08195 · HTML: https://mlsanity.com/paper/2501.08195/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 56 references that are in the map.
- First posted on arXiv 14 Jan 2025.

## Builds on (most cited first, 23 of 23)

- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Regularisation of Neural Networks by Enforcing Lipschitz Continuity](https://mlsanity.com/paper/1804.04368/) (2018)
- [Plug-and-Play Methods Provably Converge with Properly Trained Denoisers](https://mlsanity.com/paper/1905.05406/) (2019)
- [Deep Decoder: Concise Image Representations from Untrained Non-convolutional Networks](https://mlsanity.com/paper/1810.03982/) (2018)
- [DeepRED: Deep Image Prior Powered by RED](https://mlsanity.com/paper/1903.10176/) (2019)
- [Plug-and-Play Priors for Bright Field Electron Tomography and Sparse Interpolation](https://mlsanity.com/paper/1512.07331/) (2015)
- [Image Restoration using Total Variation Regularized Deep Image Prior](https://mlsanity.com/paper/1810.12864/) (2018)
- [Early Stopping for Deep Image Prior](https://mlsanity.com/paper/2112.06074/) (2021)
- [Fast Hyperspectral Image Denoising and Inpainting Based on Low-Rank and Sparse Representations](https://mlsanity.com/paper/2103.06842/) (2021)
- [Deep Hyperspectral Prior: Denoising, Inpainting, Super-Resolution](https://mlsanity.com/paper/1902.00301/) (2019)
- [Self-supervised Neural Networks for Spectral Snapshot Compressive Imaging](https://mlsanity.com/paper/2108.12654/) (2021)
- [DDS2M: Self-Supervised Denoising Diffusion Spatio-Spectral Model for Hyperspectral Image Restoration](https://mlsanity.com/paper/2303.06682/) (2023)
- [Cross-Attention in Coupled Unmixing Nets for Unsupervised Hyperspectral Super-Resolution](https://mlsanity.com/paper/2007.05230/) (2020)
- [Deep Plug-and-Play Prior for Hyperspectral Image Restoration](https://mlsanity.com/paper/2209.08240/) (2022)
- [Fixed-Point and Objective Convergence of Plug-and-Play Algorithms](https://mlsanity.com/paper/2104.10348/) (2021)
- [Solving Inverse Problems with Hybrid Deep Image Priors: the challenge of preventing overfitting](https://mlsanity.com/paper/2011.01748/) (2020)
- [Decoupled-and-Coupled Networks: Self-Supervised Hyperspectral Image Super-Resolution with Subpixel Fusion](https://mlsanity.com/paper/2205.03742/) (2022)
- [Lyapunov Theory for Discrete Time Systems](https://mlsanity.com/paper/1809.05289/) (2018)
- [Self-Supervised Nonlinear Transform-Based Tensor Nuclear Norm for Multi-Dimensional Image Recovery](https://mlsanity.com/paper/2105.14320/) (2021)
- [Adaptive Deep PnP Algorithm for Video Snapshot Compressive Imaging](https://mlsanity.com/paper/2201.05483/) (2022)
- [Image Reconstruction for MRI using Deep CNN Priors Trained without Groundtruth](https://mlsanity.com/paper/2204.04771/) (2022)
- [Self-Supervised Hyperspectral Inpainting with the Optimisation inspired Deep Neural Network Prior](https://mlsanity.com/paper/2306.07308/) (2023)

## Built on by (most cited first, 1 of 1)

- [Hyperspectral Diffusion Equivariant Imaging (HyDiff-EI): A Self-supervised Framework for Hyperspectral Image Inpainting](https://mlsanity.com/paper/2608.26812/) (2026)

## Abstract (arXiv)

Hyperspectral images are typically composed of hundreds of narrow and contiguous spectral bands, each containing information regarding the material composition of the imaged scene. However, these images can be affected by various sources of noise, distortions, or data loss, which can significantly degrade their quality and usefulness. This paper introduces a convergent guaranteed algorithm, LRS-PnP-DIP(1-Lip), which successfully addresses the instability issue of DHP that has been reported before. The proposed algorithm extends the successful joint low-rank and sparse model to further exploit the underlying data structures beyond the conventional and sometimes restrictive unions of subspace models. A stability analysis guarantees the convergence of the proposed algorithm under mild assumptions , which is crucial for its application in real-world scenarios. Extensive experiments demonstrate that the proposed solution consistently delivers visually and quantitatively superior inpainting results, establishing state-of-the-art performance.