Geometry of the phase retrieval problem

DOI10.1088/1361-6420/aba5edzbMath1451.49037arXiv1808.10747OpenAlexW3043683231MaRDI QIDQ5123691

Alexander H. Barnett, Jeremy F. Magland, Charles L. Epstein, Leslie F. Greengard

Publication date: 29 September 2020

Published in: Inverse Problems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1808.10747

zbMATH Keywords

well-posednesstransversalitytangent bundleill-conditioningphase retrievalnon-negativityx-ray crystallographyHIO

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Inverse problems in optimal control (49N45)

Related Items (8)

Total Variation-Based Reconstruction and Phase Retrieval for Diffraction Tomography ⋮ Nearly optimal bounds for the global geometric landscape of phase retrieval ⋮ Phaseless inverse scattering with background information ⋮ Recovering Missing Data in Coherent Diffraction Imaging ⋮ Fixed-distance multipoint formulas for the scattering amplitude from phaseless measurements ⋮ Near-optimal bounds for signal recovery from blind phaseless periodic short-time Fourier transform ⋮ Toward a Mathematical Theory of the Crystallographic Phase Retrieval Problem ⋮ Foreword to special issue of Inverse Problems on modern challenges in imaging

Uses Software

• PhaseLift

Cites Work

• Unnamed Item
• Alternating projections on nontangential manifolds
• Fixed-point algorithms for inverse problems in science and engineering. Based on the presentations at the interdisciplinary workshop, BIRS, Banff, Canada, November 1--6, 2009.
• Stable phase retrieval in infinite dimensions
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• Beyond crystallography: Diffractive imaging using coherent x-ray light sources
• Stability Estimates for Linearized Near-Field Phase Retrieval in X-ray Phase Contrast Imaging
• Phase Retrieval via Wirtinger Flow: Theory and Algorithms
• The reconstruction of a multidimensional sequence from the phase or magnitude of its Fourier transform
• On Projection Algorithms for Solving Convex Feasibility Problems
• Holographic phase retrieval and reference design
• Searching with iterated maps
• Augmented projections for ptychographic imaging
• Phase Retrieval via Matrix Completion

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