Microlocal analysis of singularities from directional multiscale representations

Abstract

The classical wavelet transform is a remarkably effective tool for the analysis of pointwise regularity of functions and distributions.During the last decade, the emergence of a new generation of multiscale representations has extended the classical wavelet approach leading to the introduction of a class of generalized wavelet transforms—most notably the shearlet transform—which offers amuch more powerful framework for microlocal analysis. In this paper, we show that the shearlet transform enables a precise geometric characterization of the set of singularities of a large class of multidimensional functions and distributions, going far beyond the capabilities of the classical wavelet transform. This paper generalizes and extends several results that previously appeared in the literature and provides the theoretical underpinning for advanced applications from image processing and pattern recognition including edge detection, shape classification, and feature extraction.

Department(s)

Mathematics

Document Type

Conference Proceeding

DOI

https://doi.org/10.1007/978-3-319-06404-8_10

Keywords

Analysis of singularities, Continuous wavelet transform, Edge detection, Shearlets, Wavefront set, Wavelets

Publication Date

1-1-2014

Journal Title

Springer Proceedings in Mathematics and Statistics

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