Single image super-resolution by approximated Heaviside functions

• Recover high resolution images with arbitrary upscaling factors from one single low resolution image.
• The unknown image can be viewed as consisting of smooth components and edges.
• Conduct continuous modeling by two sets of approximated Heaviside functions.
• One of the two sets represents smooth components and the other represents edges of images.
• The new method is fast and gets better numerical results than some competitive methods.

Image super-resolution involves the estimation of a high-resolution image from one or multiple low resolution images. It is widely used in medical imaging, satellite imaging, target recognition, etc. In this paper, we solve the problem of single image super-resolution from an image intensity function estimation perspective. We assume that the unknown image intensity function is defined on a continuous domain and belongs to a space with a redundant basis. The selection of the redundant basis is based on an observation: an image is composed of smooth and non-smooth components, and we use two classes of approximated Heaviside functions (AHFs) to represent them respectively. The coefficients of the redundant basis are computed iteratively from a given low-resolution image. In addition, we apply the proposed iterative scheme to image patches to reduce computation and storage size. Comparisons with some existing competitive methods show the effectiveness of the proposed method.