Metadata only
Date
2021-01Type
- Journal Article
Abstract
The problem of reconstructing a function from the magnitudes of its frame coefficients has recently been shown to be never uniformly stable in infinite-dimensional spaces [5]. This result also holds for frames that are possibly continuous [2]. On the other hand, in finite-dimensional settings, unique solvability of the problem implies uniform stability.
A prominent example of such a phase retrieval problem is the recovery of a signal from the modulus of its Gabor transform. In this paper, we study Gabor phase retrieval and ask how the stability degrades on a natural family of finite-dimensional subspaces of the signal domain L2 (R). We prove that the stability constant scales at least quadratically exponentially in the dimension of the subspaces. Our construction also shows that typical priors such as sparsity or smoothness promoting penalties do not constitute regularization terms for phase retrieval. Show more
Publication status
publishedExternal links
Journal / series
Applied and Computational Harmonic AnalysisVolume
Pages / Article No.
Publisher
ElsevierSubject
Phase retrieval; Gabor transform; StabilityOrganisational unit
09603 - Alaifari, Rima / Alaifari, Rima
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Is new version of: http://hdl.handle.net/20.500.11850/297919
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