Phase retrievable projective representation frames for finite abelian groups

DOI10.1007/s00041-017-9570-6zbMath1440.42156OpenAlexW2766752906MaRDI QIDQ1710652

Ted Juste, Lan Li, Chuangxun Cheng, De Guang Han, Joseph P. Brennan

Publication date: 23 January 2019

Published in: The Journal of Fourier Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00041-017-9570-6

zbMATH Keywords

group representationsframesphase retrieval

Mathematics Subject Classification ID

Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) (46C05) Finite abelian groups (20K01) General harmonic expansions, frames (42C15) Projective representations and multipliers (20C25)

Related Items (17)

Phase Retrieval from Linear Canonical Transforms ⋮ Phase retrieval of complex and vector-valued functions ⋮ Quantum injectivity of multi-window Gabor frames in finite dimensions ⋮ On twisted group frames ⋮ Phase retrieval for affine groups over prime fields ⋮ Phase retrieval from short-time fractional Fourier measurements using alternating direction method of multipliers ⋮ Phase retrieval from intensity difference of linear canonical transform ⋮ Some properties of exact phase retrievable subspaces ⋮ Phase retrieval in quaternion Euclidean spaces ⋮ Phase retrieval for nilpotent groups ⋮ Phase retrieval for continuous Gabor frames on locally compact abelian groups ⋮ FROG-measurement based phase retrieval for analytic signals ⋮ Phase-retrievable operator-valued frames and representations of quantum channels ⋮ Using tensor product dual frames for phase retrieval problems ⋮ Near-optimal bounds for signal recovery from blind phaseless periodic short-time Fourier transform ⋮ On the existence of maximal spanning vectors in \(L^2( \mathbb{Q}_2)\) and \(L^2( \mathbb{F}_2((T)))\) ⋮ Ill-Posed Problems: From Linear to Nonlinear and Beyond

Uses Software

• PhaseLift

Cites Work

• Unnamed Item
• Phase retrieval from Gabor measurements
• A character theory for projective representations of finite groups.
• Solving quadratic equations via phaselift when there are about as many equations as unknowns
• Painless reconstruction from magnitudes of frame coefficients
• Saving phase: injectivity and stability for phase retrieval
• Invertibility and robustness of phaseless reconstruction
• Stable phase retrieval with low-redundancy frames
• Phase retrieval from very few measurements
• On signal reconstruction without phase
• An algebraic characterization of injectivity in phase retrieval
• PhaseLift: Exact and Stable Signal Recovery from Magnitude Measurements via Convex Programming
• Phase Retrieval with Polarization
• Phase retrieval from power spectra of masked signals
• Reconstruction of Signals From Their Autocorrelation and Cross-Correlation Vectors, With Applications to Phase Retrieval and Blind Channel Estimation
• Projective Representations of Abelian Groups
• Phase Retrieval via Matrix Completion
• On Lipschitz analysis and Lipschitz synthesis for the phase retrieval problem

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