---
title: "Denoising and Completion of 3D Data via Multidimensional Dictionary Learning"
authors:
  - "Zemin Zhang"
  - "Shuchin Aeron"
doi: ""
url: "https://ijcai.org/proceedings/2016/338"
pdf: "https://ijcai.org/proceedings/2016/0338.pdf"
venue: "Proceedings of the Twenty-Fifth International Joint Conference on Artificial Intelligence"
year: 2016
pages: "2371-2376"
track: ""
keywords:
---

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

Zemin Zhang, Shuchin Aeron

*Proceedings of the Twenty-Fifth International Joint Conference on Artificial Intelligence*, pages 2371-2376.

## Abstract

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 K-TSVD, learns a multidimensional dictionary directly via a novel algebraic approach for tensor factorization as proposed in [Braman, 2010; Kilmer et al., 2011; Kilmer and Martin, 2011]. 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 K-TSVD algorithm and demonstrate its result on video completion and video/multispectral image denoising.