This paper introduces a novel method for single-image super-resolution, which aims to recover a high-resolution image from a low-resolution input using training examples. The method is inspired by manifold learning, particularly locally linear embedding (LLE), where small image patches in both low- and high-resolution images form manifolds with similar local geometry in distinct feature spaces. Each patch's reconstruction is characterized by its neighbors in the feature space, and local compatibility and smoothness constraints are enforced through overlapping patches in the target high-resolution image. The method is flexible and can handle arbitrary magnification factors, requiring fewer training examples due to its ability to generalize over the training set. Experimental results demonstrate the method's effectiveness, showing superior performance compared to median filtering and cubic spline interpolation, especially with small training sets. The use of first-order and second-order gradients as features helps preserve high-contrast intensity changes while satisfying smoothness constraints. Future work may explore extending the method with primal sketch priors to handle image primitives more effectively.This paper introduces a novel method for single-image super-resolution, which aims to recover a high-resolution image from a low-resolution input using training examples. The method is inspired by manifold learning, particularly locally linear embedding (LLE), where small image patches in both low- and high-resolution images form manifolds with similar local geometry in distinct feature spaces. Each patch's reconstruction is characterized by its neighbors in the feature space, and local compatibility and smoothness constraints are enforced through overlapping patches in the target high-resolution image. The method is flexible and can handle arbitrary magnification factors, requiring fewer training examples due to its ability to generalize over the training set. Experimental results demonstrate the method's effectiveness, showing superior performance compared to median filtering and cubic spline interpolation, especially with small training sets. The use of first-order and second-order gradients as features helps preserve high-contrast intensity changes while satisfying smoothness constraints. Future work may explore extending the method with primal sketch priors to handle image primitives more effectively.