Denoising and Completion of 3D Data via Multidimensional Dictionary Learning

TL;DR

This paper introduces KTSVD, a novel tensor-based dictionary learning algorithm that directly handles multidimensional data for tasks like video completion and multispectral image denoising, extending traditional methods to higher dimensions.

Contribution

The paper proposes a new algebraic tensor-SVD approach and extends the K-SVD algorithm to K-TSVD for multidimensional data, enabling more effective denoising and completion.

Findings

Effective in video completion tasks

Improves multispectral image denoising quality

Demonstrates advantages over traditional vector/matrix methods

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 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.