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Denoising and Completion of 3D Data via Multidimensional Dictionary Learning

Zemin Zhang, Shuchin Aeron

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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.

Zemin Zhang, and Shuchin Aeron. 2016. Denoising and Completion of 3D Data via Multidimensional Dictionary Learning. In Proceedings of the Twenty-Fifth International Joint Conference on Artificial Intelligence, IJCAI-16. IJCAI, 2371–2376. https://ijcai.org/proceedings/2016/338
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