Statistical performance analysis of a fast super-resolution technique using noisy translations

TL;DR

This paper analyzes the statistical performance of a fast super-resolution method using noisy, precisely controlled image translations, providing bounds on the number of images needed for reliable resolution enhancement.

Contribution

It introduces a statistical analysis of super-resolution with noisy translations and derives bounds on the number of images required for desired accuracy.

Findings

Derived lower bounds on the number of images needed for specified error probability.

Analyzed the impact of spatial uncertainty on super-resolution accuracy.

Provided probabilistic guarantees for super-resolution reconstruction quality.

Abstract

It is well known that the registration process is a key step for super-resolution reconstruction. In this work, we propose to use a piezoelectric system that is easily adaptable on all microscopes and telescopes for controlling accurately their motion (down to nanometers) and therefore acquiring multiple images of the same scene at different controlled positions. Then a fast super-resolution algorithm \cite{eh01} can be used for efficient super-resolution reconstruction. In this case, the optimal use of $r^2$ images for a resolution enhancement factor $r$ is generally not enough to obtain satisfying results due to the random inaccuracy of the positioning system. Thus we propose to take several images around each reference position. We study the error produced by the super-resolution algorithm due to spatial uncertainty as a function of the number of images per position. We obtain a lower bound on the number of images that is necessary to ensure a given error upper bound with probability higher than some desired confidence level.