Wavelet transform modulus: phase retrieval and scattering
Irène Waldspurger1
1 CNRS & Université Paris-Dauphine INRIA Team Mokaplan CEREMADE, UMR CNRS 7534 Place du Maréchal de Lattre de Tassigny 75775 Paris Cedex 16, France
Journées équations aux dérivées partielles (2017), Exposé no. 10, 10 p.

We discuss the problem that consists in reconstructing a function from the modulus of its wavelet transform. In the case where the wavelets are Cauchy wavelets, all analytic functions are uniquely determined by this modulus. Additionally, although it is not uniformly continuous, the reconstruction operator enjoys a form of local stability. We describe these two results, and give an idea of the proof of the first one. To conclude, we present a related result on a more sophisticated operator, based on the wavelet transform modulus: the scattering transform.

Publié le :
DOI : 10.5802/jedp.660
Irène Waldspurger 1

1 CNRS & Université Paris-Dauphine INRIA Team Mokaplan CEREMADE, UMR CNRS 7534 Place du Maréchal de Lattre de Tassigny 75775 Paris Cedex 16, France 
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Irène Waldspurger. Wavelet transform modulus: phase retrieval and scattering. Journées équations aux dérivées partielles (2017), Exposé no. 10, 10 p. doi : 10.5802/jedp.660. https://proceedings.centre-mersenne.org/articles/10.5802/jedp.660/

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