Reconstructing real-valued functions from unsigned coefficients with respect to wavelet and other frames

DOI10.1007/s00041-016-9513-7zbMath1380.42024arXiv1601.07579OpenAlexW2962901532MaRDI QIDQ1691992

Gaurav Thakur, Philipp Grohs, Rima Alaifari, Ingrid Daubechies

Publication date: 25 January 2018

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

Full work available at URL: https://arxiv.org/abs/1601.07579

zbMATH Keywords

samplingstabilityinjectivityphase retrievalsemi-discrete frames

Mathematics Subject Classification ID

Signal theory (characterization, reconstruction, filtering, etc.) (94A12) General harmonic expansions, frames (42C15) Sampling theory in information and communication theory (94A20) Inverse problems in optimal control (49N45)

Related Items (14)

On the stability of Fourier phase retrieval ⋮ Phase retrieval of real-valued functions in Sobolev space ⋮ Phase retrieval of real-valued signals in a shift-invariant space ⋮ Non-Uniqueness Theory in Sampled STFT Phase Retrieval ⋮ Injectivity conditions for STFT phase retrieval on \(\mathbb{Z}\), \(\mathbb{Z}_d\) and \(\mathbb{R}^d\) ⋮ Phase retrieval of bandlimited functions for the wavelet transform ⋮ Applied harmonic analysis and data processing. Abstracts from the workshop held March 25--31, 2018 ⋮ Phaseless sampling and reconstruction of real-valued signals in shift-invariant spaces ⋮ Phase Retrieval In The General Setting Of Continuous Frames For Banach Spaces ⋮ Conjugate phase retrieval in Paley-Wiener space ⋮ Stable phase retrieval in infinite dimensions ⋮ Local and global phaseless sampling in real spline spaces ⋮ Phase-retrieval in shift-invariant spaces with Gaussian generator ⋮ Ill-Posed Problems: From Linear to Nonlinear and Beyond

Uses Software

• PhaseLift

Cites Work

• Reconstruction of bandlimited functions from unsigned samples
• Phase retrieval for the Cauchy wavelet transform
• Foundations of time-frequency analysis
• Phase retrieval of real-valued signals in a shift-invariant space
• Saving phase: injectivity and stability for phase retrieval
• Algorithms and error bounds for noisy phase retrieval with low-redundancy frames
• Wave atoms and sparsity of oscillatory patterns
• On signal reconstruction without phase
• Phase retrieval in infinite-dimensional Hilbert spaces
• Phase Retrieval with Polarization
• On the Determination of the Phase of a Fourier Integral, I
• New tight frames of curvelets and optimal representations of objects with piecewise C² singularities
• The phase retrieval problem
• Phase Retrieval In The General Setting Of Continuous Frames For Banach Spaces
• Phase Retrieval via Matrix Completion
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Reconstructing real-valued functions from unsigned coefficients with respect to wavelet and other frames