Combining edge difference with nonlocal self-similarity constraints for single image super-resolution

Sparse representation based nonlocal self-similarity methods have been proved to be effective for single image super-resolution. However, as the noise level increases, these methods always lead to the aggravated blurring of image small scale structures, which means the failure to preserve the edge structures. In this paper, we propose a new single image super-resolution method by combining edge difference with nonlocal self-similarity constraints. In the proposed method, firstly, we extract the image texture feature in the main direction for dictionary learning with Principal Components Analysis (PCA) to ensure the learned subdictionaries contain the image texture structures. Then, we explore the one dimensional edge difference between LR image and degraded version (e.g., blurred, noisy, and down-sampled) of the image reconstructed by the sparse representation based nonlocal self-similarity method with the leaned PCA subdictionaries and utilize it as the edge difference constraint. Thirdly, we incorporate the edge difference constraint into the sparse representation model based nonlocal self-similarity to preserve the edge structures and nonlocal self-similarity structures simultaneously. Moreover, we propose a nonlocal structure tensor optimization model to further improve image quality, which can effectively mitigate the loss of image high-frequency texture and edge information. Experiments on natural images validate that our method outperforms other state-of-the-art methods, especially for the noise image.