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.
@article{JEDP_2017____A10_0,
author = {Waldspurger, Ir\`ene},
title = {Wavelet transform modulus: phase retrieval and scattering},
journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
note = {talk:10},
pages = {1--10},
publisher = {Groupement de recherche 2434 du CNRS},
year = {2017},
doi = {10.5802/jedp.660},
language = {en},
url = {http://www.numdam.org/articles/10.5802/jedp.660/}
}
TY - JOUR AU - Waldspurger, Irène TI - Wavelet transform modulus: phase retrieval and scattering JO - Journées équations aux dérivées partielles N1 - talk:10 PY - 2017 SP - 1 EP - 10 PB - Groupement de recherche 2434 du CNRS UR - http://www.numdam.org/articles/10.5802/jedp.660/ DO - 10.5802/jedp.660 LA - en ID - JEDP_2017____A10_0 ER -
%0 Journal Article %A Waldspurger, Irène %T Wavelet transform modulus: phase retrieval and scattering %J Journées équations aux dérivées partielles %Z talk:10 %D 2017 %P 1-10 %I Groupement de recherche 2434 du CNRS %U http://www.numdam.org/articles/10.5802/jedp.660/ %R 10.5802/jedp.660 %G en %F JEDP_2017____A10_0
Waldspurger, Irène. Wavelet transform modulus: phase retrieval and scattering. Journées équations aux dérivées partielles (2017), Talk no. 10, 10 p. doi : 10.5802/jedp.660. http://www.numdam.org/articles/10.5802/jedp.660/
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