Stable Gabor phase retrieval for multivariate functions

Philipp Grohs; Martin Rathmair

doi:10.4171/jems/1114

Titel

Stable Gabor phase retrieval for multivariate functions

Autor*in

Philipp Grohs

Universität Wien

Martin Rathmair

Universität Wien

Abstract

In recent work [P. Grohs and M. Rathmair, Stable Gabor phase retrieval and spectral clustering, Comm. Pure Appl. Math. (2018)] the instabilities of the Gabor phase retrieval problem, i.e., the problem of reconstructing a function f from its spectrogram ∣Gf∣, where Gf(x,y)=∫Rdf(t)e−π∣t−x∣2e−2πit⋅ydt,x,y∈Rd, have been completely classified in terms of the disconnectedness of the spectrogram. These findings, however, were crucially restricted to the one-dimensional case (d=1) and therefore not relevant for many practical applications. In the present paper we not only generalize the aforementioned results to the multivariate case but also significantly improve on them. Our new results have comprehensive implications in various applications such as ptychography, a highly popular method in coherent diffraction imaging.

Stichwort

Phase retrievalstabilityGabor transformCheeger constantlogarithmic derivative

Objekt-Typ

journal article

Sprache

Englisch [eng]

Persistent identifier

phaidra.univie.ac.at/o:1653670

DOI

10.4171/jems/1114

Erschienen in

Titel