The registration process is a key step for super-resolution (SR) reconstruction. More and more devices permit to overcome this bottleneck using a controlled positioning system, e.g., sensor shifting using a piezoelectric stage. This makes possible to acquire multiple images of the same scene at different controlled positions. Then, a fast SR algorithm can be used for efficient SR 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 SR 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. Such results give precious hints to the design of SR systems.

While the registration step is often problematic for superresolution, many microscopes and telescopes are now equipped with a piezoelectric mechanical system which permits to accurately control their motion (down to nanometers). Therefore one can use such devices to acquire multiple images of the same scene at various controlled positions. Then a fast super-resolution algorithm [1] can be used for efficient super-resolution. However the minimal use of r2images for a resolution enhancement factor r is generally not sufficient to obtain good results. We propose to take several images at positions randomly distributed close to each reference position. We study the number of images necessary to control the error resulting from the super-resolution algorithm by [1] due to the uncertainty on positions. The main result is a lower bound on the number of images to respect a given error upper bound with probability higher than a desired confidence level.