K-CPD: Learning of overcomplete dictionaries for tensor sparse coding

Recently sparse coding has received expressions of interest in the field of pattern recognition. Most existing methods take the data-as-vector formulation, and deal with images (the second order tensor) or volumes (the third order tensor) by vectorization. However, such kind of vectorization will lose the original structure of the data and reduce the reliability of post processing, leading a poor representation. In this paper, we propose a new algorithm of overcomplete dictionary learning for tensor sparse coding, named K-CPD, by extension of K-SVD [8] from vector formulation to tensor formulation. A multilinear orthogonal matching pursuit (MOMP) algorithm is also developed for calculating sparse representation of tensor signal. We evaluate the performance of K-CPD for image denoising, and the results demonstrate that the proposed method surpasses the conventional methods.