In this talk, we present an iterative RKHS + Heaviside framework to address the problem of image resolution enhancement, including single natural image super-resolution and remote sensing image pansharpening. We solve the problem from the image intensity function estimation perspective and assume the image contains smooth and edge components. We model the smooth components of an image using a thin-plate reproducing kernel Hilbert space (RKHS) and the edges using approximated Heaviside functions. The proposed method is applied to image patches, aiming to reduce computation and storage. Visual and quantitative comparisons with some competitive approaches show the effectiveness of the proposed framework. Additionally, we also present some attempts in pansharpening with the deep neural network.