# Denoising and Completion of 3D Data via Multidimensional Dictionary Learning

arXiv: https://arxiv.org/abs/1512.09227 · HTML: https://mlsanity.com/paper/1512.09227/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Dec 2015.

## Built on by (most cited first, 3 of 3)

- [A Comparison of Image Denoising Methods](https://mlsanity.com/paper/2304.08990/) (2023)
- [Online multidimensional dictionary learning](https://mlsanity.com/paper/2503.09337/) (2025)
- [Quantile-Based Randomized Kaczmarz for Corrupted Tensor Linear Systems](https://mlsanity.com/paper/2503.18190/) (2025)

## Abstract (arXiv)

In this paper a new dictionary learning algorithm for multidimensional data is proposed. Unlike most conventional dictionary learning methods which are derived for dealing with vectors or matrices, our algorithm, named KTSVD, learns a multidimensional dictionary directly via a novel algebraic approach for tensor factorization as proposed in [3, 12, 13]. Using this approach one can define a tensor-SVD and we propose to extend K-SVD algorithm used for 1-D data to a K-TSVD algorithm for handling 2-D and 3-D data. Our algorithm, based on the idea of sparse coding (using group-sparsity over multidimensional coefficient vectors), alternates between estimating a compact representation and dictionary learning. We analyze our KTSVD algorithm and demonstrate its result on video completion and multispectral image denoising.