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The monogenic synchrosqueezed wavelet transform: a tool for the decomposition/demodulation of AM–FM images

Clausel, Marianne and Oberlin, Thomas and Perrier, Valérie The monogenic synchrosqueezed wavelet transform: a tool for the decomposition/demodulation of AM–FM images. (2015) Applied and Computational Harmonic Analysis, vol. 39 (n° 3). pp. 450-486. ISSN 1063-5203

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Official URL: http://dx.doi.org/10.1016/j.acha.2014.10.003

Abstract

The synchrosqueezing method aims at decomposing 1D functions into superpositions of a small number of “Intrinsic Modes”, supposed to be well separated both in time and frequency. Based on the unidimensional wavelet transform and its reconstruction properties, the synchrosqueezing transform provides a powerful representation of multicomponent signals in the time–frequency plane, together with a reconstruction of each mode. In this paper, a bidimensional version of the synchrosqueezing transform is defined, by considering a well-adapted extension of the concept of analytic signal to images: the monogenic signal. We introduce the concept of “Intrinsic Monogenic Mode”, that is the bidimensional counterpart of the notion of Intrinsic Mode. We also investigate the properties of its associated Monogenic Wavelet Decomposition. This leads to a natural bivariate extension of the Synchrosqueezed Wavelet Transform, for decomposing and processing multicomponent images. Numerical tests validate the effectiveness of the method on synthetic and real images.

Item Type:Article
Additional Information:Thanks to Elsevier editor. The definitive version is available at http://www.sciencedirect.com The original PDF of the article can be found at Applied and Computational Harmonic Analysis website : http://dx.doi.org/10.1016/j.acha.2014.10.003
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - INPT (FRANCE)
Other partners > Institut National Polytechnique de Grenoble (FRANCE)
French research institutions > Institut National de la Recherche en Informatique et en Automatique - INRIA (FRANCE)
Other partners > Université Grenoble Alpes - UGA (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UPS (FRANCE)
Université de Toulouse > Université Toulouse - Jean Jaurès - UT2J (FRANCE)
Université de Toulouse > Université Toulouse 1 Capitole - UT1 (FRANCE)
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Deposited By: IRIT IRIT
Deposited On:28 Feb 2017 16:17

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