Fourier Phase Retrieval with a Single Mask by Douglas-Rachford Algorithm

2015/09/02 by Pengwen Chen, Chen, Pengwen, Albert Fannjiang +1
Biochemistry, Genetics and Molecular Biology · Materials Science · Physics and Astronomy · #Advanced Electron Microscopy Techniques and Applications #Advanced X-ray Imaging Techniques #Data Analysis #Electron and X-Ray Spectroscopy Techniques #FOS: Mathematics #FOS: Physical sciences #Numerical Analysis (math.NA) #Optics (physics.optics) #Statistics and Probability (physics.data-an)

paper · pdf · doi:10.48550/arxiv.1509.00888

openalex publication_date 2015/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

Douglas-Rachford (DR) algorithm is analyzed for Fourier phase retrieval with a single random phase mask. Local, geometric convergence to a unique fixed point is proved with numerical demonstration of global convergence.

Citations

• Splitting Algorithms for the Sum of Two Nonlinear Operators
• Saving phase: Injectivity and stability for phase retrieval
• Invertibility and Robustness of Phaseless Reconstruction
• PhaseLift: Exact and Stable Signal Recovery from Magnitude Measurements via Convex Programming
• Phase Recovery, MaxCut and Complex Semidefinite Programming

Related

• Convex combination of alternating projection and Douglas-Rachford\n operators for phase retrieval
• An elementary approach for the phase retrieval problem
• Fourier Phase Retrieval: Uniqueness and Algorithms
• Fourier-Domain Fixed Point Algorithms with Coded Diffraction Patterns
• No existence of linear algorithm for Fourier phase retrieval