# Low-Rank and Sparse Enhanced Tucker Decomposition for Tensor Completion

arXiv: https://arxiv.org/abs/2010.00359 · HTML: https://mlsanity.com/paper/2010.00359/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Oct 2020.

## Built on by (most cited first, 4 of 4)

- [Theoretical Guarantees for Low-Rank Compression of Deep Neural Networks](https://mlsanity.com/paper/2502.02766/) (2025)
- [Spatiotemporal Regularized Tucker Decomposition Approach for Traffic Data Imputation](https://mlsanity.com/paper/2305.06563/) (2023)
- [Tensor completion using geodesics on Segre manifolds](https://mlsanity.com/paper/2108.00735/) (2021)
- [An Interdisciplinary and Cross-Task Review on Missing Data Imputation](https://mlsanity.com/paper/2511.01196/) (2025)

## Abstract (arXiv)

Tensor completion refers to the task of estimating the missing data from an incomplete measurement or observation, which is a core problem frequently arising from the areas of big data analysis, computer vision, and network engineering. Due to the multidimensional nature of high-order tensors, the matrix approaches, e.g., matrix factorization and direct matricization of tensors, are often not ideal for tensor completion and recovery. In this paper, we introduce a unified low-rank and sparse enhanced Tucker decomposition model for tensor completion. Our model possesses a sparse regularization term to promote a sparse core tensor of the Tucker decomposition, which is beneficial for tensor data compression. Moreover, we enforce low-rank regularization terms on factor matrices of the Tucker decomposition for inducing the low-rankness of the tensor with a cheap computational cost. Numerically, we propose a customized ADMM with enough easy subproblems to solve the underlying model. It is remarkable that our model is able to deal with different types of real-world data sets, since it exploits the potential periodicity and inherent correlation properties appeared in tensors. A series of computational experiments on real-world data sets, including internet traffic data sets, color images, and face recognition, demonstrate that our model performs better than many existing state-of-the-art matricization and tensorization approaches in terms of achieving higher recovery accuracy.