Interpolation Models for Image Super-resolution

Image super-resolution involves interpolating a non-uniformly sampled composite image at uniform locations of a high-resolution image. Interpolation methods used in the literature are generally based on arbitrary functions. Optimal (in least squares sense) interpolation kernels can be derived if the ground-truth high-resolution data is known, this is obviously impractical. An observation that the optimal kernels for very different images are similar suggests that a kernel derived on one image can interpolate another image with good results. This paper extends this idea by developing two image models that capture the important characteristics of an image and uses the models to derive optimal kernels. One of the models results in linear interpolation and the other one results in a piece-wise cubic kernel similar to that of cubic spline. This later model is experimentally shown to be near optimal for three different images. The notion of deriving optimal interpolators from the image model and the model of image capturing process provides a unifying framework that brings together linear and cubic interpolators and gives them a theoretic backing.