This paper presents a method for single-frame image superresolution using an unsupervised learning technique. The required prior knowledge about the high-resolution images is obtained from Kernel Principal Component Analysis (KPCA). The original form of KPCA, however, can be only applied to strongly restricted image classes due to the limited number of training examples that can be processed. We therefore propose a new iterative method for performing KPCA, the Kernel Hebbian Algorithm. By kernelizing the Generalized Hebbian Algorithm, one can iteratively estimate the Kernel Principal Components with only linear order memory complexity. The resulting super-resolution algorithm shows a comparable performance to the existing supervised methods on images containing faces and natural scenes.