  Sparse coding (SC) is an automatic feature extraction and selection technique
that is widely used in unsupervised learning. However, conventional SC
vectorizes the input images, which breaks apart the local proximity of pixels
and destructs the elementary object structures of images. In this paper, we
propose a novel two-dimensional sparse coding (2DSC) scheme that represents the
input images as the tensor-linear combinations under a novel algebraic
framework. 2DSC learns much more concise dictionaries because it uses the
circular convolution operator, since the shifted versions of atoms learned by
conventional SC are treated as the same ones. We apply 2DSC to natural images
and demonstrate that 2DSC returns meaningful dictionaries for large patches.
Moreover, for mutli-spectral images denoising, the proposed 2DSC reduces
computational costs with competitive performance in comparison with the
state-of-the-art algorithms.
