This paper proposes a novel method for single-image super-resolution, which uses neighbor embedding inspired by manifold learning, particularly locally linear embedding (LLE). The method aims to recover a high-resolution image from a low-resolution input using a set of training examples. The key idea is that small image patches in low- and high-resolution images form manifolds with similar local geometry in two distinct feature spaces. Local geometry is characterized by how a feature vector corresponding to a patch can be reconstructed by its neighbors in the feature space. The method uses training image pairs to estimate the high-resolution embedding and enforces local compatibility and smoothness constraints between patches in the target high-resolution image through overlapping. The method is flexible and gives good empirical results. Single-image super-resolution is the problem of generating a high-resolution image from a single low-resolution image, using a set of training images. It has applications in image enlargement, web page image display, and old photograph restoration. Previous methods include simple smoothing and interpolation techniques, as well as learning-based methods that use training sets or strong image priors. However, these methods often rely on only one nearest neighbor in the training set for generating each image patch. The proposed method is based on the assumption that small patches in low- and high-resolution images form manifolds with similar local geometry in two distinct feature spaces. The method uses the training examples to estimate the high-resolution embedding while preserving local geometry and enforcing local compatibility and smoothness constraints between patches. The method is flexible and can be used for super-resolution problems with arbitrary magnification factors. The method uses first-order and second-order gradients of the luminance as features to better preserve high-contrast intensity changes while satisfying smoothness constraints. The method is evaluated on several examples, showing superior performance compared to other methods. The results demonstrate that the method is effective in generating high-resolution images from low-resolution inputs.This paper proposes a novel method for single-image super-resolution, which uses neighbor embedding inspired by manifold learning, particularly locally linear embedding (LLE). The method aims to recover a high-resolution image from a low-resolution input using a set of training examples. The key idea is that small image patches in low- and high-resolution images form manifolds with similar local geometry in two distinct feature spaces. Local geometry is characterized by how a feature vector corresponding to a patch can be reconstructed by its neighbors in the feature space. The method uses training image pairs to estimate the high-resolution embedding and enforces local compatibility and smoothness constraints between patches in the target high-resolution image through overlapping. The method is flexible and gives good empirical results. Single-image super-resolution is the problem of generating a high-resolution image from a single low-resolution image, using a set of training images. It has applications in image enlargement, web page image display, and old photograph restoration. Previous methods include simple smoothing and interpolation techniques, as well as learning-based methods that use training sets or strong image priors. However, these methods often rely on only one nearest neighbor in the training set for generating each image patch. The proposed method is based on the assumption that small patches in low- and high-resolution images form manifolds with similar local geometry in two distinct feature spaces. The method uses the training examples to estimate the high-resolution embedding while preserving local geometry and enforcing local compatibility and smoothness constraints between patches. The method is flexible and can be used for super-resolution problems with arbitrary magnification factors. The method uses first-order and second-order gradients of the luminance as features to better preserve high-contrast intensity changes while satisfying smoothness constraints. The method is evaluated on several examples, showing superior performance compared to other methods. The results demonstrate that the method is effective in generating high-resolution images from low-resolution inputs.