Phase retrieval with one or two diffraction patterns by alternating projections with the null initialization

DOI10.1007/s00041-017-9536-8zbMath1478.65145arXiv1510.07379OpenAlexW2963100598MaRDI QIDQ1645274

Pengwen Chen, Gi-Ren Liu, Albert C. Fannjiang

Publication date: 28 June 2018

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

Full work available at URL: https://arxiv.org/abs/1510.07379

zbMATH Keywords

convergence ratenonconvex minimizationlocal convergencespectral gap conditionfixed point iterationalternating projectionsphase retrievalmultidimensional discrete Fourier transformnull initializationphase retrieval with one or two diffraction patterns

Mathematics Subject Classification ID

Signal theory (characterization, reconstruction, filtering, etc.) (94A12) Numerical methods for discrete and fast Fourier transforms (65T50) Inverse problems (including inverse scattering) in optics and electromagnetic theory (78A46) Numerical solution to inverse problems in abstract spaces (65J22)

Related Items (15)

The numerics of phase retrieval ⋮ Sharp Restricted Isometry Bounds for the Inexistence of Spurious Local Minima in Nonconvex Matrix Recovery ⋮ On global convergence of gradient descent algorithms for generalized phase retrieval problem ⋮ Implicit regularization in nonconvex statistical estimation: gradient descent converges linearly for phase retrieval, matrix completion, and blind deconvolution ⋮ Finding robust minimizer for non-convex phase retrieval ⋮ Gradient descent with random initialization: fast global convergence for nonconvex phase retrieval ⋮ 3D tomographic phase retrieval and unwrapping ⋮ Phase Retrieval by Linear Algebra ⋮ Fixed Point Analysis of Douglas--Rachford Splitting for Ptychography and Phase Retrieval ⋮ Fourier phase retrieval with a single mask by Douglas-Rachford algorithms ⋮ Scalable incremental nonconvex optimization approach for phase retrieval ⋮ Total Variation--Based Phase Retrieval for Poisson Noise Removal ⋮ Variational Phase Retrieval with Globally Convergent Preconditioned Proximal Algorithm ⋮ Local saddles of relaxed averaged alternating reflections algorithms on phase retrieval ⋮ A Spectral Estimation Framework for Phase Retrieval via Bregman Divergence Minimization

Uses Software

• PhaseLift
• Wirtinger Flow

Cites Work

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• On local convergence of the method of alternating projections
• Stable optimizationless recovery from phaseless linear measurements
• Finding best approximation pairs relative to two closed convex sets in Hilbert spaces
• Local linear convergence for alternating and averaged nonconvex projections
• On the recovery of a 2-D function from the modulus of its Fourier transform
• Painless reconstruction from magnitudes of frame coefficients
• Fourier phase retrieval with a single mask by Douglas-Rachford algorithms
• Saving phase: injectivity and stability for phase retrieval
• A partial derandomization of phaselift using spherical designs
• PhaseLiftOff: an accurate and stable phase retrieval method based on difference of trace and Frobenius norms
• Phase retrieval: stability and recovery guarantees
• On signal reconstruction without phase
• An algebraic characterization of injectivity in phase retrieval
• Phase recovery, MaxCut and complex semidefinite programming
• Phase retrieval from coded diffraction patterns
• PhaseLift: Exact and Stable Signal Recovery from Magnitude Measurements via Convex Programming
• Sparse Signal Recovery from Quadratic Measurements via Convex Programming
• Absolute uniqueness of phase retrieval with random illumination
• Phase Retrieval via Wirtinger Flow: Theory and Algorithms
• Solving Random Quadratic Systems of Equations Is Nearly as Easy as Solving Linear Systems
• Array imaging using intensity-only measurements
• Proximity Maps for Convex Sets
• Solving systems of phaseless equations via Kaczmarz methods: a proof of concept study
• The reconstruction of a multidimensional sequence from the phase or magnitude of its Fourier transform
• Phase reconstruction via nonlinear least-squares
• Phase Retrieval Using Alternating Minimization
• On Projection Algorithms for Solving Convex Feasibility Problems
• Phase retrieval from power spectra of masked signals
• Phase Retrieval by Linear Algebra
• Phase Retrieval With Random Gaussian Sensing Vectors by Alternating Projections
• Fourier phasing with phase-uncertain mask
• Uniqueness of two phaseless non-overdetermined inverse acoustics problems in 3-d
• Convex programming in Hilbert space
• Best approximation in inner product spaces

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