# 3DeepRep: 3D Deep Low-rank Tensor Representation for Hyperspectral Image Inpainting

arXiv: https://arxiv.org/abs/2506.16735 · HTML: https://mlsanity.com/paper/2506.16735/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 51 references that are in the map.
- First posted on arXiv 20 Jun 2025.

## Builds on (most cited first, 18 of 18)

- [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)
- [Tensor Ring Decomposition](https://mlsanity.com/paper/1606.05535/) (2016)
- [Tensor Robust Principal Component Analysis with A New Tensor Nuclear Norm](https://mlsanity.com/paper/1804.03728/) (2018)
- [Exact tensor completion using t-SVD](https://mlsanity.com/paper/1502.04689/) (2015)
- [Novel methods for multilinear data completion and de-noising based on tensor-SVD](https://mlsanity.com/paper/1407.1785/) (2014)
- [Guaranteed Tensor Recovery Fused Low-rankness and Smoothness](https://mlsanity.com/paper/2302.02155/) (2023)
- [HIR-Diff: Unsupervised Hyperspectral Image Restoration Via Improved Diffusion Models](https://mlsanity.com/paper/2402.15865/) (2024)
- [Framelet Representation of Tensor Nuclear Norm for Third-Order Tensor Completion](https://mlsanity.com/paper/1909.06982/) (2019)
- [Tensor N-tubal rank and its convex relaxation for low-rank tensor recovery](https://mlsanity.com/paper/1812.00688/) (2018)
- [Dictionary Learning with Low-rank Coding Coefficients for Tensor Completion](https://mlsanity.com/paper/2009.12507/) (2020)
- [Low-tubal-rank Tensor Completion using Alternating Minimization](https://mlsanity.com/paper/1610.01690/) (2016)
- [Self-Supervised Nonlinear Transform-Based Tensor Nuclear Norm for Multi-Dimensional Image Recovery](https://mlsanity.com/paper/2105.14320/) (2021)
- [Combining Weighted Total Variation and Deep Image Prior for natural and medical image restoration via ADMM](https://mlsanity.com/paper/2009.11380/) (2020)
- [Nonlinear Transform Induced Tensor Nuclear Norm for Tensor Completion](https://mlsanity.com/paper/2110.08774/) (2021)
- [Tensor Q-Rank: New Data Dependent Definition of Tensor Rank](https://mlsanity.com/paper/1910.12016/) (2019)
- [Compressive Spectral Image Reconstruction using Deep Prior and Low-Rank Tensor Representation](https://mlsanity.com/paper/2101.07424/) (2021)
- [H2TF for Hyperspectral Image Denoising: Where Hierarchical Nonlinear Transform Meets Hierarchical Matrix Factorization](https://mlsanity.com/paper/2304.11141/) (2023)

## Abstract (arXiv)

Recent approaches based on transform-based tensor nuclear norm (TNN) have demonstrated notable effectiveness in hyperspectral image (HSI) inpainting by leveraging low-rank structures in latent representations. Recent developments incorporate deep transforms to improve low-rank tensor representation; however, existing approaches typically restrict the transform to the spectral mode, neglecting low-rank properties along other tensor modes. In this paper, we propose a novel 3-directional deep low-rank tensor representation (3DeepRep) model, which performs deep nonlinear transforms along all three modes of the HSI tensor. To enforce low-rankness, the model minimizes the nuclear norms of mode-i frontal slices in the corresponding latent space for each direction (i=1,2,3), forming a 3-directional TNN regularization. The outputs from the three directional branches are subsequently fused via a learnable aggregation module to produce the final result. An efficient gradient-based optimization algorithm is developed to solve the model in a self-supervised manner. Extensive experiments on real-world HSI datasets demonstrate that the proposed method achieves superior inpainting performance compared to existing state-of-the-art techniques, both qualitatively and quantitatively.