# Deep Gaussian Scale Mixture Prior for Spectral Compressive Imaging

arXiv: https://arxiv.org/abs/2103.07152 · HTML: https://mlsanity.com/paper/2103.07152/

## Key facts

- Cited by 58 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 49 references that are in the map.
- First posted on arXiv 12 Mar 2021.

## Builds on (most cited first, 11 of 11)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Enhanced Deep Residual Networks for Single Image Super-Resolution](https://mlsanity.com/paper/1707.02921/) (2017)
- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [Burst Denoising with Kernel Prediction Networks](https://mlsanity.com/paper/1712.02327/) (2017)
- [Rank Minimization for Snapshot Compressive Imaging](https://mlsanity.com/paper/1807.07837/) (2018)
- [Plug-and-Play Algorithms for Large-scale Snapshot Compressive Imaging](https://mlsanity.com/paper/2003.13654/) (2020)
- [GAP-net for Snapshot Compressive Imaging](https://mlsanity.com/paper/2012.08364/) (2020)
- [Compressive Hyperspectral Imaging with Side Information](https://mlsanity.com/paper/1502.06260/) (2015)

## Built on by (most cited first, 30 of 58)

- [Mask-guided Spectral-wise Transformer for Efficient Hyperspectral Image Reconstruction](https://mlsanity.com/paper/2111.07910/) (2021)
- [MST++: Multi-stage Spectral-wise Transformer for Efficient Spectral Reconstruction](https://mlsanity.com/paper/2204.07908/) (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)
- [Self-supervised Neural Networks for Spectral Snapshot Compressive Imaging](https://mlsanity.com/paper/2108.12654/) (2021)
- [Fusformer: A Transformer-based Fusion Approach for Hyperspectral Image Super-resolution](https://mlsanity.com/paper/2109.02079/) (2021)
- [HerosNet: Hyperspectral Explicable Reconstruction and Optimal Sampling Deep Network for Snapshot Compressive Imaging](https://mlsanity.com/paper/2112.06238/) (2021)
- [Binarized Spectral Compressive Imaging](https://mlsanity.com/paper/2305.10299/) (2023)
- [Residual Degradation Learning Unfolding Framework with Mixing Priors across Spectral and Spatial for Compressive Spectral Imaging](https://mlsanity.com/paper/2211.06891/) (2022)
- [Pixel Adaptive Deep Unfolding Transformer for Hyperspectral Image Reconstruction](https://mlsanity.com/paper/2308.10820/) (2023)
- [Spectral-wise Implicit Neural Representation for Hyperspectral Image Reconstruction](https://mlsanity.com/paper/2312.01061/) (2023)
- [MIPI 2022 Challenge on Under-Display Camera Image Restoration: Methods and Results](https://mlsanity.com/paper/2209.07052/) (2022)
- [Hyperspectral Image Reconstruction via Combinatorial Embedding of Cross-Channel Spatio-Spectral Clues](https://mlsanity.com/paper/2312.11119/) (2023)
- [In2SET: Intra-Inter Similarity Exploiting Transformer for Dual-Camera Compressive Hyperspectral Imaging](https://mlsanity.com/paper/2312.13319/) (2023)
- [Computational Imaging and Artificial Intelligence: The Next Revolution of Mobile Vision](https://mlsanity.com/paper/2109.08880/) (2021)
- [Aperture Diffraction for Compact Snapshot Spectral Imaging](https://mlsanity.com/paper/2309.16372/) (2023)
- [Progressive Content-aware Coded Hyperspectral Compressive Imaging](https://mlsanity.com/paper/2303.09773/) (2023)
- [DiffSCI: Zero-Shot Snapshot Compressive Imaging via Iterative Spectral Diffusion Model](https://mlsanity.com/paper/2311.11417/) (2023)
- [OTLRM: Orthogonal Learning-based Low-Rank Metric for Multi-Dimensional Inverse Problems](https://mlsanity.com/paper/2412.11165/) (2024)
- [Modeling Mask Uncertainty in Hyperspectral Image Reconstruction](https://mlsanity.com/paper/2112.15362/) (2021)
- [Spectral Compressive Imaging Reconstruction Using Convolution and Contextual Transformer](https://mlsanity.com/paper/2201.05768/) (2022)
- [Block Modulating Video Compression: An Ultra Low Complexity Image Compression Encoder for Resource Limited Platforms](https://mlsanity.com/paper/2205.03677/) (2022)
- [Cooperative Hardware-Prompt Learning for Snapshot Compressive Imaging](https://mlsanity.com/paper/2306.01176/) (2023)
- [A Simple Adaptive Unfolding Network for Hyperspectral Image Reconstruction](https://mlsanity.com/paper/2301.10208/) (2023)
- [RDFNet: Regional Dynamic FISTA-Net for Spectral Snapshot Compressive Imaging](https://mlsanity.com/paper/2302.02519/) (2023)
- [SST-ReversibleNet: Reversible-prior-based Spectral-Spatial Transformer for Efficient Hyperspectral Image Reconstruction](https://mlsanity.com/paper/2305.04054/) (2023)
- [A Compound Gaussian Least Squares Algorithm and Unrolled Network for Linear Inverse Problems](https://mlsanity.com/paper/2305.11120/) (2023)
- [Dual Hyperspectral Mamba for Efficient Spectral Compressive Imaging](https://mlsanity.com/paper/2406.00449/) (2024)
- [Exploiting Frequency Correlation for Hyperspectral Image Reconstruction](https://mlsanity.com/paper/2406.00683/) (2024)

## Abstract (arXiv)

In coded aperture snapshot spectral imaging (CASSI) system, the real-world hyperspectral image (HSI) can be reconstructed from the captured compressive image in a snapshot. Model-based HSI reconstruction methods employed hand-crafted priors to solve the reconstruction problem, but most of which achieved limited success due to the poor representation capability of these hand-crafted priors. Deep learning based methods learning the mappings between the compressive images and the HSIs directly achieved much better results. Yet, it is nontrivial to design a powerful deep network heuristically for achieving satisfied results. In this paper, we propose a novel HSI reconstruction method based on the Maximum a Posterior (MAP) estimation framework using learned Gaussian Scale Mixture (GSM) prior. Different from existing GSM models using hand-crafted scale priors (e.g., the Jeffrey's prior), we propose to learn the scale prior through a deep convolutional neural network (DCNN). Furthermore, we also propose to estimate the local means of the GSM models by the DCNN. All the parameters of the MAP estimation algorithm and the DCNN parameters are jointly optimized through end-to-end training. Extensive experimental results on both synthetic and real datasets demonstrate that the proposed method outperforms existing state-of-the-art methods. The code is available at https://see.xidian.edu.cn/faculty/wsdong/Projects/DGSM-SCI.htm.