Denoising and Completion of 3D Data via Multidimensional Dictionary Learning
This addresses the problem of handling 2D and 3D data for researchers in computer vision and signal processing, but it is incremental as it extends existing methods to higher dimensions.
The paper tackles the problem of denoising and completing 3D data by proposing KTSVD, a new dictionary learning algorithm for multidimensional data, which achieves results demonstrated on video completion and multispectral image denoising.
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.