Phase Retrieval of Bandlimited Functions for the Wavelet Transform
Francesca Bartolucci - ETH Zürich
We study the problem of phase retrieval in which one aims to recover a function from the magnitude of its wavelet transform. It is already known that if the wavelet is a Cauchy wavelet, then the modulus of the wavelet transform uniquely determines the analytic part of any square-integrable function. We consider bandlimited functions and derive new uniqueness results for phase retrieval, where the wavelet itself can be complex-valued. In particular, we prove the first uniqueness result for the case that the wavelet has a finite number of vanishing moments. In addition, we establish the first result on unique reconstruction from samples of the wavelet transform magnitude when the wavelet coefficients are complex-valued.
Francesca Bartolucci is a Postdoc at the Department of Mathematics at ETH Zürich. She received her PhD at the University of Genova under the supervision of Filippo De Mari and Ernesto De Vito with the thesis entitled "Radon transforms: Unitarization, Inversion and Wavefront sets". Her research interests include phase retrieval problems, group representations theory, wavelet analysis, shearlet analysis, microlocal analysis and Radon transforms.
2020-11-10 at 3:00 pm