Uniqueness results in an extension of Pauli's phase retrieval problem

DOI10.1016/j.acha.2014.01.003zbMath1296.81020arXiv1009.3418OpenAlexW3098649584MaRDI QIDQ741261

Philippe Jaming

Publication date: 11 September 2014

Published in: Applied and Computational Harmonic Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1009.3418

zbMATH Keywords

fractional Fourier transformphase retrievalPauli problementire function of finite order

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Spaces of measures, convergence of measures (28A33) Quantum state estimation, approximate cloning (81P50)

Related Items (36)

On foundational discretization barriers in STFT phase retrieval ⋮ Phase retrieval via polarization in dynamical sampling ⋮ Total Variation-Based Reconstruction and Phase Retrieval for Diffraction Tomography ⋮ On the stability of Fourier phase retrieval ⋮ Phase Retrieval from Linear Canonical Transforms ⋮ A simple observation on the uncertainty principle for the fractional Fourier transform ⋮ Minimal determination of a pure qutrit state and four-measurement protocol for pure qudit state ⋮ On the effect of zero-flipping on the stability of the phase retrieval problem in the Paley-Wiener class ⋮ Phase retrieval by binary questions: which complementary subspace is closer? ⋮ Algorithms and error bounds for noisy phase retrieval with low-redundancy frames ⋮ Zak transform and non-uniqueness in an extension of Pauli's phase retrieval problem ⋮ Fractional Fourier transform, signal processing and uncertainty principles ⋮ Dynamical quantum tomography ⋮ Non-Uniqueness Theory in Sampled STFT Phase Retrieval ⋮ Phase retrieval from intensity difference of linear canonical transform ⋮ The phase retrieval problem for solutions of the Helmholtz equation ⋮ Stable recovery of weighted sparse signals from phaseless measurements via weighted l₁ minimization ⋮ Phase retrieval for \(L^2([-\pi, \pi)\) via the provably accurate and noise robust numerical inversion of spectrogram measurements] ⋮ Uniqueness of phase retrieval from three measurements ⋮ Phase Retrieval: Uniqueness and Stability ⋮ Phase retrieval of bandlimited functions for the wavelet transform ⋮ Ambiguities in one-dimensional discrete phase retrieval from Fourier magnitudes ⋮ Constrained quantum tomography of semi-algebraic sets with applications to low-rank matrix recovery ⋮ Time-frequency localization for the fractional Fourier transform in signal processing and uncertainty principles ⋮ Unnamed Item ⋮ Pure state `really' informationally complete with rank-1 POVM ⋮ Phaseless reconstruction from space-time samples ⋮ The matrix completion method for phase retrieval from fractional Fourier transform magnitudes ⋮ Nonuniqueness of phase retrieval for three fractional Fourier transforms ⋮ Translation uniqueness of phase retrieval and magnitude retrieval of band-limited signals ⋮ Phase retrieval from sampled Gabor transform magnitudes: counterexamples ⋮ Stable phase retrieval in infinite dimensions ⋮ Phase retrieval for wide band signals ⋮ Injectivity of Gabor phase retrieval from lattice measurements ⋮ A note on the phase retrieval of holomorphic functions ⋮ Stable phase retrieval with low-redundancy frames

Uses Software

• PhaseLift

Cites Work

• On the Pauli problem
• The Pauli problem, state reconstruction and quantum-real numbers
• Phase retrieval
• Hermite functions and uncertainty principles for the Fourier and the windowed Fourier trans\-forms.
• Phase retrieval and magnitude retrieval of entire functions
• Time-frequency and time-scale methods. Adaptive decompositions, uncertainty principles, and sampling
• Quantum tomography under prior information
• Saving phase: injectivity and stability for phase retrieval
• Stable phase retrieval with low-redundancy frames
• Discrete radar ambiguity problems
• On signal reconstruction without phase
• Phase recovery, MaxCut and complex semidefinite programming
• The Mathematics of Computerized Tomography
• PhaseLift: Exact and Stable Signal Recovery from Magnitude Measurements via Convex Programming
• Uncertainty principles associated to non-degenerate quadratic forms
• On the Determination of the Phase of a Fourier Integral, I
• Hardy’s theorem and rotations
• Radar Ambiguity Functions and Group Theory
• The Fractional Order Fourier Transform and its Application to Quantum Mechanics
• Are wave functions uniquely determined by their position and momentum distributions?
• Optical Wavefront Reconstruction: Theory and Numerical Methods
• The phase retrieval problem
• Phase Retrieval via Matrix Completion
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Uniqueness results in an extension of Pauli's phase retrieval problem