Skip to Main content Skip to Navigation
Journal articles

Phase retrieval for the Cauchy wavelet transform

Abstract : We consider the phase retrieval problem in which one tries to reconstruct a function from the modulus of its wavelet transform. We study the unicity and stability of the reconstruction. In the case where the wavelets are Cauchy wavelets, we prove that the modulus of the wavelet transform uniquely determines the function up to a global phase. We show that the reconstruction operator is continuous but not uniformly continuous. We describe how to construct pairs of functions which are far away in L 2-norm but whose wavelet transforms are very close, in modulus. The principle is to modulate the wavelet transform of a fixed initial function by a phase which varies slowly in both time and frequency. This construction seems to cover all the instabilities that we observe in practice; we give a partial formal justification to this fact. Finally, we describe an exact reconstruction algorithm and use it to numerically confirm our analysis of the stability question.
Document type :
Journal articles
Complete list of metadatas

Cited literature [19 references]  Display  Hide  Download
Contributor : Irène Waldspurger <>
Submitted on : Wednesday, November 22, 2017 - 7:17:33 PM
Last modification on : Thursday, March 5, 2020 - 6:35:42 PM


Files produced by the author(s)


  • HAL Id : hal-01645090, version 1


Irène Waldspurger, Stéphane Mallat. Phase retrieval for the Cauchy wavelet transform. Journal of Fourier Analysis and Applications, Springer Verlag, 2015. ⟨hal-01645090⟩



Record views


Files downloads