# Continuous Shearlet Frames and Resolution of the Wavefront Set - Mathematics > Functional Analysis

Abstract: In recent years directional multiscale transformations like the curvelet- orshearlet transformation have gained considerable attention. The reason for thisis that these transforms are - unlike more traditional transforms like wavelets- able to efficiently handle data with features along edges. The main result inG. Kutyniok, D. Labate. Resolution of the Wavefront Set using continuousShearlets, Trans. AMS 361 2009, 2719-2754 confirming this property forshearlets is due to Kutyniok and Labate where it is shown that for very specialfunctions $\psi$ with frequency support in a compact conical wegde the decayrate of the shearlet coefficients of a tempered distribution $f$ with respectto the shearlet $\psi$ can resolve the Wavefront Set of $f$. We demonstratethat the same result can be verified under much weaker assumptions on $\psi$,namely to possess sufficiently many anisotropic vanishing moments. We also showhow to build frames for $L^2\mathbb{R}^2$ from any such function. To proveour statements we develop a new approach based on an adaption of the Radontransform to the shearlet structure.

Author: Philipp Grohs

Source: https://arxiv.org/