Phase retrieval for wavelet transforms
Waldspurger, Irène (2017), Phase retrieval for wavelet transforms, IEEE Transactions on Information Theory, 63, 5, p. 2993 - 3009. 10.1109/TIT.2017.2672727
TypeArticle accepté pour publication ou publié
Journal nameIEEE Transactions on Information Theory
IEEE - Institute of Electrical and Electronics Engineers
2993 - 3009
MetadataShow full item record
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)This article describes a new algorithm that solves a particular phase retrieval problem, with important applications in audio processing: the reconstruction of a function from its scalogram, that is, from the modulus of its wavelet transform. It is a multiscale iterative algorithm, that reconstructs the signal from low to high frequencies. It relies on a new reformulation of the phase retrieval problem, that involves the holomorphic extension of the wavelet transform. This reformulation allows to propagate phase information from low to high frequencies. Numerical results, on audio and non-audio signals, show that reconstruction is precise and stable to noise. The complexity of the algorithm is linear in the size of the signal, up to logarithmic factors. It can thus be applied to large signals.
Subjects / KeywordsPhase retrieval; scalogram; iterative algorithms; multiscale method
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