Quantitative control of the error bounds of a fast super-resolution technique for microscopy and astronomy

Pierre Chainais 1, 2, 3, 4 Pierre Pfennig 3, 4, 2 Aymeric Leray 5
1 CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
2 SEQUEL - Sequential Learning
LIFL - Laboratoire d'Informatique Fondamentale de Lille, Inria Lille - Nord Europe, LAGIS - Laboratoire d'Automatique, Génie Informatique et Signal
3 Ecole Centrale de Lille
4 LAGIS-SI
LAGIS - Laboratoire d'Automatique, Génie Informatique et Signal
5 IRI - Institut de Recherche Interdisciplinaire [Villeneuve d'Ascq]
Abstract : While the registration step is often problematic for super-resolution, many microscopes and telescopes are now equipped with a piezoelectric mechanical system which permits to ac-curately control their motion (down to nanometers). There-fore 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 r 2 images for a resolution enhancement factor r is generally not sufficient to obtain good results. We propose to take several images at po-sitions 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.
Keywords : confidence level error estimate Index Terms— microscopy super-resolution
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Pierre Chainais, Pierre Pfennig, Aymeric Leray. Quantitative control of the error bounds of a fast super-resolution technique for microscopy and astronomy. Int. Conf. on Acoustics, Speech and Signal Processing (ICASSP), May 2014, Florence, Italy. pp.2853 - 2857, ⟨10.1109/ICASSP.2014.6854121⟩. ⟨hal-01081402⟩

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