Single image super-resolution via low-rank tensor representation and hierarchical dictionary learning

Super-resolution (SR) has been widely studied due to its importance in real applications and scenarios. In this paper, we focus on generating an SR image from a single low-resolution (LR) input image by employing the multi-resolution structures of an input image. By taking the LR image and its downsampled resolution (DR) and upsampled resolution (UR) versions as inputs, we propose a hierarchical dictionary learning approach to learn the latent UR-LR dictionary pair by preserving the internal structure coherence with the LR-DR dictionary pair. Note that an imposed restriction involved in this process is that the pairwise resolution images are jointly trained to obtain more compact patterns of image patches. In particular, to better explore the underlying structures of tensor data spanned by image patches, we propose a low-rank tensor approximation (LRTA) algorithm based on nuclear-norm regularization to embed input image patches into a low-dimensional space. Experimental results from publicly used images show that our proposed method achieves performance comparable with that of other state-of-the-art SR algorithms, even without using any external training databases.