Phase Retrieval In The General Setting Of Continuous Frames For Banach Spaces

DOI10.1137/16M1071481zbMath1368.42028arXiv1604.03163MaRDI QIDQ5738247

Rima Alaifari, Philipp Grohs

Publication date: 9 June 2017

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1604.03163

zbMATH Keywords

stabilityphase retrievalcontinuous Banach frames

Mathematics Subject Classification ID

Sequence spaces (including Köthe sequence spaces) (46A45) Signal theory (characterization, reconstruction, filtering, etc.) (94A12) General harmonic expansions, frames (42C15) Inverse problems in optimal control (49N45)

Related Items (26)

Stable Gabor phase retrieval for multivariate functions ⋮ Phase retrieval of complex and vector-valued functions ⋮ On the effect of zero-flipping on the stability of the phase retrieval problem in the Paley-Wiener class ⋮ Stability estimates for phase retrieval from discrete Gabor measurements ⋮ Gabor phase retrieval is severely ill-posed ⋮ Sign retrieval in shift-invariant spaces with totally positive generator ⋮ Phase retrieval of real-valued signals in a shift-invariant space ⋮ Non-Uniqueness Theory in Sampled STFT Phase Retrieval ⋮ Stable phase retrieval and perturbations of frames ⋮ Reconstructing real-valued functions from unsigned coefficients with respect to wavelet and other frames ⋮ Continuous Schauder frames for Banach spaces ⋮ Stable Gabor phase retrieval in Gaussian shift-invariant spaces via biorthogonality ⋮ Phase Retrieval: Uniqueness and Stability ⋮ Phase retrieval of bandlimited functions for the wavelet transform ⋮ Uniqueness and stability for the solution of a nonlinear least squares problem ⋮ Injective continuous frames and quantum detections ⋮ Applied harmonic analysis and data processing. Abstracts from the workshop held March 25--31, 2018 ⋮ Stable phase retrieval from locally stable and conditionally connected measurements ⋮ Phaseless sampling and reconstruction of real-valued signals in shift-invariant spaces ⋮ Stable phaseless sampling and reconstruction of real-valued signals with finite rate of innovation ⋮ Phaseless reconstruction from space-time samples ⋮ Phase retrieval in infinite-dimensional Hilbert spaces ⋮ Stable phase retrieval in infinite dimensions ⋮ Phase-retrieval in shift-invariant spaces with Gaussian generator ⋮ Discretizing \(L_p\) norms and frame theory ⋮ Ill-Posed Problems: From Linear to Nonlinear and Beyond

Uses Software

• PhaseLift

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Reconstruction of signals from magnitudes of redundant representations: the complex case
• Reconstruction of bandlimited functions from unsigned samples
• Phase retrieval for the Cauchy wavelet transform
• The collected works of Arne Beurling. Volume 1: Complex analysis. Volume 2: Harmonic analysis. Ed. by Lennart Carleson, Paul Malliavin, John Neuberger, John Wermer
• Reconstructing real-valued functions from unsigned coefficients with respect to wavelet and other frames
• Saving phase: injectivity and stability for phase retrieval
• Stable phase retrieval in infinite dimensions
• On signal reconstruction without phase
• Phase retrieval in infinite-dimensional Hilbert spaces
• Phase Retrieval via Matrix Completion
• On Lipschitz analysis and Lipschitz synthesis for the phase retrieval problem

This page was built for publication: Phase Retrieval In The General Setting Of Continuous Frames For Banach Spaces