# Gaussian Splatting-based Low-Rank Tensor Representation for Multi-Dimensional Image Recovery

arXiv: https://arxiv.org/abs/2511.14270 · HTML: https://mlsanity.com/paper/2511.14270/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 48 references that are in the map.
- First posted on arXiv 18 Nov 2025.

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

- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [4D Gaussian Splatting for Real-Time Dynamic Scene Rendering](https://mlsanity.com/paper/2310.08528/) (2023)
- [LangSplat: 3D Language Gaussian Splatting](https://mlsanity.com/paper/2312.16084/) (2023)
- [A Survey on 3D Gaussian Splatting](https://mlsanity.com/paper/2401.03890/) (2024)
- [Tensor Robust Principal Component Analysis with A New Tensor Nuclear Norm](https://mlsanity.com/paper/1804.03728/) (2018)
- [GaussianImage: 1000 FPS Image Representation and Compression by 2D Gaussian Splatting](https://mlsanity.com/paper/2403.08551/) (2024)
- [DreamScene360: Unconstrained Text-to-3D Scene Generation with Panoramic Gaussian Splatting](https://mlsanity.com/paper/2404.06903/) (2024)
- [A Wasserstein-type distance in the space of Gaussian Mixture Models](https://mlsanity.com/paper/1907.05254/) (2019)
- [Exact tensor completion using t-SVD](https://mlsanity.com/paper/1502.04689/) (2015)
- [Efficient tensor completion for color image and video recovery: Low-rank tensor train](https://mlsanity.com/paper/1606.01500/) (2016)
- [Novel methods for multilinear data completion and de-noising based on tensor-SVD](https://mlsanity.com/paper/1407.1785/) (2014)
- [Pixel to Gaussian: Ultra-Fast Continuous Super-Resolution with 2D Gaussian Modeling](https://mlsanity.com/paper/2503.06617/) (2025)
- [Tensor Ring Decomposition with Rank Minimization on Latent Space: An Efficient Approach for Tensor Completion](https://mlsanity.com/paper/1809.02288/) (2018)
- [Guaranteed Tensor Recovery Fused Low-rankness and Smoothness](https://mlsanity.com/paper/2302.02155/) (2023)
- [Instant Gaussian Stream: Fast and Generalizable Streaming of Dynamic Scene Reconstruction via Gaussian Splatting](https://mlsanity.com/paper/2503.16979/) (2025)
- [GaussianSR: High Fidelity 2D Gaussian Splatting for Arbitrary-Scale Image Super-Resolution](https://mlsanity.com/paper/2407.18046/) (2024)
- [Controllable Text-to-3D Generation via Surface-Aligned Gaussian Splatting](https://mlsanity.com/paper/2403.09981/) (2024)
- [Tucker decomposition-based Temporal Knowledge Graph Completion](https://mlsanity.com/paper/2011.07751/) (2020)
- [Self-Supervised Nonlinear Transform-Based Tensor Nuclear Norm for Multi-Dimensional Image Recovery](https://mlsanity.com/paper/2105.14320/) (2021)
- [SurgicalGS: Dynamic 3D Gaussian Splatting for Accurate Robotic-Assisted Surgical Scene Reconstruction](https://mlsanity.com/paper/2410.09292/) (2024)
- [Progressively Deformable 2D Gaussian Splatting for Video Representation at Arbitrary Resolutions](https://mlsanity.com/paper/2503.05600/) (2025)

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

- [Pre-Trained Low-Rank Tensor Decomposition for Multi-Dimensional Image Recovery](https://mlsanity.com/paper/2609.12843/) (2026)

## Abstract (arXiv)

Tensor singular value decomposition (t-SVD) is a promising tool for multi-dimensional image representation, which decomposes a multi-dimensional image into a latent tensor and an accompanying transform matrix. However, two critical limitations of t-SVD methods persist: (1) the approximation of the latent tensor (e.g., tensor factorizations) is coarse and fails to accurately capture spatial local high-frequency information; (2) The transform matrix is composed of fixed basis atoms (e.g., complex exponential atoms in DFT and cosine atoms in DCT) and cannot precisely capture local high-frequency information along the mode-3 fibers. To address these two limitations, we propose a Gaussian Splatting-based Low-rank tensor Representation (GSLR) framework, which compactly and continuously represents multi-dimensional images. Specifically, we leverage tailored 2D Gaussian splatting and 1D Gaussian splatting to generate the latent tensor and transform matrix, respectively. The 2D and 1D Gaussian splatting are indispensable and complementary under this representation framework, which enjoys a powerful representation capability, especially for local high-frequency information. To evaluate the representation ability of the proposed GSLR, we develop an unsupervised GSLR-based multi-dimensional image recovery model. Extensive experiments on multi-dimensional image recovery demonstrate that GSLR consistently outperforms state-of-the-art methods, particularly in capturing local high-frequency information.