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.