  Image super-resolution is a process to enhance image resolution. It is widely
used in medical imaging, satellite imaging, target recognition, etc. In this
paper, we conduct continuous modeling and assume that the unknown image
intensity function is defined on a continuous domain and belongs to a space
with a redundant basis. We propose a new iterative model for single image
super-resolution based on an observation: an image is consisted of smooth
components and non-smooth components, and we use two classes of approximated
Heaviside functions (AHFs) to represent them respectively. Due to sparsity of
the non-smooth components, a $L_{1}$ model is employed. In addition, we apply
the proposed iterative model to image patches to reduce computation and
storage. Comparisons with some existing competitive methods show the
effectiveness of the proposed method.
