# Superpixel-informed Continuous Low-Rank Tensor Representation for Multi-Dimensional Data Recovery

arXiv: https://arxiv.org/abs/2508.12261 · HTML: https://mlsanity.com/paper/2508.12261/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 32 references that are in the map.
- First posted on arXiv 17 Aug 2025.

## Builds on (most cited first, 13 of 13)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Nerfies: Deformable Neural Radiance Fields](https://mlsanity.com/paper/2011.12948/) (2020)
- [Learning Continuous Image Representation with Local Implicit Image Function](https://mlsanity.com/paper/2012.09161/) (2020)
- [NeRV: Neural Representations for Videos](https://mlsanity.com/paper/2110.13903/) (2021)
- [Rank Minimization for Snapshot Compressive Imaging](https://mlsanity.com/paper/1807.07837/) (2018)
- [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)
- [Low-Rank Tensor Function Representation for Multi-Dimensional Data Recovery](https://mlsanity.com/paper/2212.00262/) (2022)
- [Efficient Low Rank Tensor Ring Completion](https://mlsanity.com/paper/1707.08184/) (2017)
- [Guaranteed Tensor Recovery Fused Low-rankness and Smoothness](https://mlsanity.com/paper/2302.02155/) (2023)
- [Framelet Representation of Tensor Nuclear Norm for Third-Order Tensor Completion](https://mlsanity.com/paper/1909.06982/) (2019)
- [Low-rank tensor completion via tensor joint rank with logarithmic composite norm](https://mlsanity.com/paper/2309.16208/) (2023)

## Abstract (arXiv)

Low-rank tensor representation (LRTR) has emerged as a powerful tool for multi-dimensional data processing. However, classical LRTR-based methods face two critical limitations: (1) they typically assume that the holistic data is low-rank, this assumption is often violated in real-world scenarios with significant spatial variations; and (2) they are constrained to discrete meshgrid data, limiting their flexibility and applicability. To overcome these limitations, we propose a Superpixel-informed Continuous low-rank Tensor Representation (SCTR) framework, which enables continuous and flexible modeling of multi-dimensional data beyond traditional grid-based constraints. Our approach introduces two main innovations: First, motivated by the observation that semantically coherent regions exhibit stronger low-rank characteristics than holistic data, we employ superpixels as the basic modeling units. This design not only encodes rich semantic information, but also enhances adaptability to diverse forms of data streams. Second, we propose a novel asymmetric low-rank tensor factorization (ALTF) where superpixel-specific factor matrices are parameterized by a shared neural network with specialized heads. By strategically separating global pattern learning from local adaptation, this framework efficiently captures both cross-superpixel commonalities and within-superpixel variations. This yields a representation that is both highly expressive and compact, balancing model efficiency with adaptability. Extensive experiments on several benchmark datasets demonstrate that SCTR achieves 3-5 dB PSNR improvements over existing LRTR-based methods across multispectral images, videos, and color images.