2-Microlocal Analysis and Application in Signal Processing
Résumé
This paper introduces the use of 2-microlocal analysis in signal processing. 2-microlocal analysis is a powerful tool for studying the regularity of solutions of partial differential equations. It allows to track the evolution of the Hölder exponent under the action of pseudo-differential operators. We first prove theoretical results pertaining to the so-called 2-microlocal frontier, that allow to characterize and prescribe it at a given point. We then show how to combine 2-microlocal analysis with multifractal analysis in order to perform image denoising.
Domaines
Probabilités [math.PR]
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