# Compressive Spectral Image Reconstruction using Deep Prior and Low-Rank Tensor Representation

arXiv: https://arxiv.org/abs/2101.07424 · HTML: https://mlsanity.com/paper/2101.07424/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Jan 2021.

## Built on by (most cited first, 7 of 7)

- [DeepTensor: Low-Rank Tensor Decomposition with Deep Network Priors](https://mlsanity.com/paper/2204.03145/) (2022)
- [JR2net: A Joint Non-Linear Representation and Recovery Network for Compressive Spectral Imaging](https://mlsanity.com/paper/2205.07770/) (2022)
- [RDFNet: Regional Dynamic FISTA-Net for Spectral Snapshot Compressive Imaging](https://mlsanity.com/paper/2302.02519/) (2023)
- [Mixture-Net: Low-Rank Deep Image Prior Inspired by Mixture Models for Spectral Image Recovery](https://mlsanity.com/paper/2211.02973/) (2022)
- [mHealth hyperspectral learning for instantaneous spatiospectral imaging of hemodynamics](https://mlsanity.com/paper/2303.16205/) (2023)
- [SDIP: Self-Reinforcement Deep Image Prior Framework for Image Processing](https://mlsanity.com/paper/2404.12142/) (2024)
- [3DeepRep: 3D Deep Low-rank Tensor Representation for Hyperspectral Image Inpainting](https://mlsanity.com/paper/2506.16735/) (2025)

## Abstract (arXiv)

Compressive spectral imaging (CSI) has emerged as an alternative spectral image acquisition technology, which reduces the number of measurements at the cost of requiring a recovery process. In general, the reconstruction methods are based on hand-crafted priors used as regularizers in optimization algorithms or recent deep neural networks employed as an image generator to learn a non-linear mapping from the low-dimensional compressed measurements to the image space. However, these data-driven methods need many spectral images to obtain good performance. In this work, a deep recovery framework for CSI without training data is presented. The proposed method is based on the fact that the structure of some deep neural networks and an appropriated low-dimensional structure are sufficient to impose a structure of the underlying spectral image from CSI. We analyzed the low-dimension structure via the Tucker representation, modeled in the first net layer. The proposed scheme is obtained by minimizing the ℓ2-norm distance between the compressive measurements and the predicted measurements, and the desired recovered spectral image is formed just before the forward operator. Simulated and experimental results verify the effectiveness of the proposed method.