LAUSR

In this paper, we present a uniform mathematical framework based on a robust kernel-based regression for the task of simultaneous single-image super-resolution and denoising. The given model is formulated as a convex $\ell _{1}$ sparse optimization problem, which can be efficiently solved by the alternating direction method of multipliers (ADMM). Especially, the proposed method is applied to image patches to reduce computational time. Additionally, an iterative strategy is also incorporated into the approach to refine more image details. The extensive experiments on simulated natural images with additional sparse noise and real time-of-flight (ToF) images demonstrate the ability of simultaneously removing sparse noise and enhancing image resolution.