Section: New Results

Phase retrieval for wavelet transforms

I. Waldspurger

[15]

This article describes an algorithm for solving a particular phase retrieval problem, with important applications in audio processing: the reconstruction of a function from the modulus of its wavelet transform. Previous algorithms for this problem were either unreliable in certain regimes, or too slow to be applied to large-dimensional audio signals. Ours relies on a new reformulation of the phase retrieval problem, that involves the holomorphic extension of the wavelet transform. Numerical results, on audio and non-audio signals, show it allows precise reconstruction, and is stable to noise. Its complexity is linear in the size of the unknown signal, up to logarithmic factors. It can thus be applied to large signals.