# Online multidimensional dictionary learning

arXiv: https://arxiv.org/abs/2503.09337 · HTML: https://mlsanity.com/paper/2503.09337/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 22 references that are in the map.
- First posted on arXiv 12 Mar 2025.

## Builds on (most cited first, 4 of 4)

- [Globally Convergent Type-I Anderson Acceleration for Non-Smooth Fixed-Point Iterations](https://mlsanity.com/paper/1808.03971/) (2018)
- [Exact Low Tubal Rank Tensor Recovery from Gaussian Measurements](https://mlsanity.com/paper/1806.02511/) (2018)
- [A Tensor-Based Dictionary Learning Approach to Tomographic Image Reconstruction](https://mlsanity.com/paper/1506.04954/) (2015)
- [Denoising and Completion of 3D Data via Multidimensional Dictionary Learning](https://mlsanity.com/paper/1512.09227/) (2015)

## Abstract (arXiv)

Dictionary learning is a widely used technique in signal processing and machine learning that aims to represent data as a linear combination of a few elements from an overcomplete dictionary. In this work, we propose a generalization of the dictionary learning technique using the t-product framework, enabling efficient handling of multidimensional tensor data. We address the dictionary learning problem through online methods suitable for tensor structures. To effectively address the sparsity problem, we utilize an accelerated Iterative Shrinkage-Thresholding Algorithm (ISTA) enhanced with an extrapolation technique known as Anderson acceleration. This approach significantly improves signal reconstruction results. Extensive experiments prove that our proposed method outperforms existing acceleration techniques, particularly in applications such as data completion. These results suggest that our approach can be highly beneficial for large-scale tensor data analysis in various domains.