Efficient Two-Dimensional Sparse Coding Using Tensor-Linear Combination
This work addresses image processing inefficiencies for researchers and practitioners by offering an incremental improvement in sparse coding methods.
The paper tackles the problem of conventional sparse coding vectorizing images, which disrupts local pixel structures, by proposing a two-dimensional sparse coding (2DSC) scheme using tensor-linear combinations. It demonstrates that 2DSC learns more concise dictionaries and reduces computational costs for multi-spectral image denoising with competitive performance compared to state-of-the-art algorithms.
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.