Time: Tuesday, February 2, 2016

Speaker: Dr. Irène Waldspurger (Massachusetts Institute of Technology)

Title: Wavelet transform modulus: phase retrieval and scattering

Abstract: We consider the problem of reconstructing a function from the modulus of its wavelet transform. This inverse problem belongs to the class of so-called "phase retrieval problems". From a theoretical point of view, we can show that any function is uniquely determined by its wavelet transform modulus, at least for a specific choice of wavelets. The reconstruction may not be stable to noise in a strong sense; nevertheless, it is locally stable. We also have a reconstruction algorithm that enjoys good empirical performances. After describing these results, we will see which consequences they have for the study of a more sophisticated representation: the scattering transform, introduced by Mallat.

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