The Monogenic Synchrosqueezed Wavelet Transform: A tool for the Decomposition/Demodulation of AM-FM images

Marianne Clausel (1) , Thomas Oberlin (2) , Valérie Perrier (2)

1 SAM - Statistique Apprentissage Machine
2 MGMI - Modélisation Géométrique & Multirésolution pour l'Image

The synchrosqueezing method aims at decomposing 1D functions as 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. The natural bidimensional counterpart of the notion of Intrinsic Mode is then the concept of ''Intrinsic Monogenic Mode'' that we define. Thereafter, we 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 for different examples.

Mots clés: directional time-frequency image analysis; wavelet transform; monogenic signal; synchrosqueezing; directional time-frequency image analysis

Domaines: Traitement du signal et de l'image [eess.SP]

Marianne Clausel, Thomas Oberlin, Valérie Perrier. The Monogenic Synchrosqueezed Wavelet Transform: A tool for the Decomposition/Demodulation of AM-FM images. SIGMA'2012 - Workshop on Signal, Image, Geometry, Modelling, Approximation, Nov 2012, Marseille, France. ⟨hal-00754704⟩