  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.
