# Under-Sampled High-Dimensional Data Recovery via Symbiotic Multi-Prior Tensor Reconstruction

arXiv: https://arxiv.org/abs/2504.05992 · HTML: https://mlsanity.com/paper/2504.05992/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 46 references that are in the map.
- First posted on arXiv 8 Apr 2025.

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

- [FFDNet: Toward a Fast and Flexible Solution for CNN based Image Denoising](https://mlsanity.com/paper/1710.04026/) (2017)
- [Masked Autoencoders As Spatiotemporal Learners](https://mlsanity.com/paper/2205.09113/) (2022)
- [Exact tensor completion using t-SVD](https://mlsanity.com/paper/1502.04689/) (2015)
- [Bayesian CP Factorization of Incomplete Tensors with Automatic Rank Determination](https://mlsanity.com/paper/1401.6497/) (2014)
- [Efficient tensor completion for color image and video recovery: Low-rank tensor train](https://mlsanity.com/paper/1606.01500/) (2016)
- [Low-Rank Tensor Function Representation for Multi-Dimensional Data Recovery](https://mlsanity.com/paper/2212.00262/) (2022)
- [Tensor-based formulation and nuclear norm regularization for multi-energy computed tomography](https://mlsanity.com/paper/1307.5348/) (2013)
- [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)
- [Deep Plug-and-play Prior for Low-rank Tensor Completion](https://mlsanity.com/paper/1905.04449/) (2019)
- [Non-local tensor completion for multitemporal remotely sensed images inpainting](https://mlsanity.com/paper/1801.10240/) (2018)

## Abstract (arXiv)

The advancement of sensing technology has driven the widespread application of high-dimensional data. However, issues such as missing entries during acquisition and transmission negatively impact the accuracy of subsequent tasks. Tensor reconstruction aims to recover the underlying complete data from under-sampled observed data by exploring prior information in high-dimensional data. However, due to insufficient exploration, reconstruction methods still face challenges when sampling rate is extremely low. This work proposes a tensor reconstruction method integrating multiple priors to comprehensively exploit the inherent structure of the data. Specifically, the method combines learnable tensor decomposition to enforce low-rank constraints of the reconstructed data, a pre-trained convolutional neural network for smoothing and denoising, and block-matching and 3D filtering regularization to enhance the non-local similarity in the reconstructed data. An alternating direction method of the multipliers algorithm is designed to decompose the resulting optimization problem into three subproblems for efficient resolution. Extensive experiments on color images, hyperspectral images, and grayscale videos datasets demonstrate the superiority of our method in extreme cases as compared with state-of-the-art methods.