# A Range-Null Space Decomposition Approach for Fast and Flexible Spectral Compressive Imaging

arXiv: https://arxiv.org/abs/2305.09746 · HTML: https://mlsanity.com/paper/2305.09746/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 38 references that are in the map.
- First posted on arXiv 16 May 2023.

## Builds on (most cited first, 12 of 12)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Mask-guided Spectral-wise Transformer for Efficient Hyperspectral Image Reconstruction](https://mlsanity.com/paper/2111.07910/) (2021)
- [Rank Minimization for Snapshot Compressive Imaging](https://mlsanity.com/paper/1807.07837/) (2018)
- [Conv2Former: A Simple Transformer-Style ConvNet for Visual Recognition](https://mlsanity.com/paper/2211.11943/) (2022)
- [Coarse-to-Fine Sparse Transformer for Hyperspectral Image Reconstruction](https://mlsanity.com/paper/2203.04845/) (2022)
- [HDNet: High-resolution Dual-domain Learning for Spectral Compressive Imaging](https://mlsanity.com/paper/2203.02149/) (2022)
- [Degradation-Aware Unfolding Half-Shuffle Transformer for Spectral Compressive Imaging](https://mlsanity.com/paper/2205.10102/) (2022)
- [Deep Gaussian Scale Mixture Prior for Spectral Compressive Imaging](https://mlsanity.com/paper/2103.07152/) (2021)
- [GAP-net for Snapshot Compressive Imaging](https://mlsanity.com/paper/2012.08364/) (2020)
- [Deep Decomposition Learning for Inverse Imaging Problems](https://mlsanity.com/paper/1911.11028/) (2019)
- [GAN Prior based Null-Space Learning for Consistent Super-Resolution](https://mlsanity.com/paper/2211.13524/) (2022)
- [A Simple Adaptive Unfolding Network for Hyperspectral Image Reconstruction](https://mlsanity.com/paper/2301.10208/) (2023)

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

- [NukesFormers: Unpaired Hyperspectral Image Generation with Non-Uniform Domain Alignment](https://mlsanity.com/paper/2503.07004/) (2025)

## Abstract (arXiv)

We present RND-SCI, a novel framework for compressive hyperspectral image (HSI) reconstruction. Our framework decomposes the reconstructed object into range-space and null-space components, where the range-space part ensures the solution conforms to the compression process, and the null-space term introduces a deep HSI prior to constraining the output to have satisfactory properties. RND-SCI is not only simple in design with strong interpretability but also can be easily adapted to various HSI reconstruction networks, improving the quality of HSIs with minimal computational overhead. RND-SCI significantly boosts the performance of HSI reconstruction networks in retraining, fine-tuning or plugging into a pre-trained off-the-shelf model. Based on the framework and SAUNet, we design an extremely fast HSI reconstruction network, RND-SAUNet, which achieves an astounding 91 frames per second while maintaining superior reconstruction accuracy compared to other less time-consuming methods. Code and models are available at https://github.com/hustvl/RND-SCI.