A fast super-resolution reconstruction algorithm for pure translational motion and common space-invariant blur

TLDR

The paper tackles the challenge of reconstructing a super‑resolved image from a set of warped, blurred, and decimated observations, noting that many algorithms have already been proposed for this general problem. It focuses on the special case of pure translational warps, space‑invariant blur shared across all images, and white noise, aiming to devise a tailored solution. By leveraging prior results, the authors develop a highly efficient algorithm that separates de‑blurring from measurement fusion, yielding a non‑iterative, maximum‑likelihood optimal reconstruction. Simulations confirm that the simple fusion step preserves optimality and demonstrate the algorithm’s practical effectiveness.

Abstract

This paper addresses the problem of recovering a super-resolved image from a set of warped blurred and decimated versions thereof. Several algorithms have already been proposed for the solution of this general problem. In this paper, we concentrate on a special case where the warps are pure translations, the blur is space invariant and the same for all the images, and the noise is white. We exploit previous results to develop a new highly efficient super-resolution reconstruction algorithm for this case, which separates the treatment into de-blurring and measurements fusion. The fusion part is shown to be a very simple non-iterative algorithm, preserving the optimality of the entire reconstruction process, in the maximum-likelihood sense. Simulations demonstrate the capabilities of the proposed algorithm.