Denoising and Completion of 3D Data via Multidimensional Dictionary Learning
arXiv:1512.09227
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.
9 pages, submitted to Conference on Computer Vision and Pattern Recognition (CVPR) 2016
Cited by in corpus (5)
- Minimax Lower Bounds on Dictionary Learning for Tensor Data
- Learning Mixtures of Separable Dictionaries for Tensor Data: Analysis and Algorithms
- A Comprehensive Comparison of Multi-Dimensional Image Denoising Methods
- Tensor Low Rank Modeling and Its Applications in Signal Processing
- Randomized Kaczmarz for Tensor Linear Systems