Phase Retrieval from Incomplete Magnitude Information via Total Variation Regularization

DOI10.1137/15M1029357zbMath1352.49034OpenAlexW2554330058MaRDI QIDQ2833539

Tieyong Zeng, Huibin Chang, Yifei Lou, Michael Kwok-Po Ng

Publication date: 18 November 2016

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/15m1029357

zbMATH Keywords

phase retrievaltotal variation regularizationalternative directional multiplier methodpartial magnitudes

Mathematics Subject Classification ID

Ill-posedness and regularization problems in numerical linear algebra (65F22) Applications of functional analysis in optimization, convex analysis, mathematical programming, economics (46N10) Numerical methods for inverse problems for boundary value problems involving PDEs (65N21) Inverse problems in optimal control (49N45) Problems with incomplete information (optimization) (49N30)

Related Items

Numerical optimization algorithms for wavefront phase retrieval from multiple measurements, On global convergence of gradient descent algorithms for generalized phase retrieval problem, Finding robust minimizer for non-convex phase retrieval, Phase retrieval: a data-driven wavelet frame based approach, Non-negativity constraints in the one-dimensional discrete-time phase retrieval problem, One-dimensional phase retrieval: regularization, box relaxation and uniqueness, Total Variation--Based Phase Retrieval for Poisson Noise Removal, Variational Phase Retrieval with Globally Convergent Preconditioned Proximal Algorithm, Poisson image denoising based on fractional-order total variation, Local and global phaseless sampling in real spline spaces, Unnamed Item, The Cramer–Rao lower bound in a non-AWGN model for the affine phase retrieval, Local saddles of relaxed averaged alternating reflections algorithms on phase retrieval, A Total Variation Based Method for Multivariate Time Series Segmentation

Uses Software

• PhaseLift
• PhaseCut
• Wirtinger Flow

Cites Work

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• Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers
• Nonlinear total variation based noise removal algorithms
• A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
• A multiphase image segmentation based on fuzzy membership functions and L1-norm fidelity
• Phase retrieval for imaging problems
• An alternating direction algorithm for matrix completion with nonnegative factors
• PhaseLiftOff: an accurate and stable phase retrieval method based on difference of trace and Frobenius norms
• On signal reconstruction without phase
• An algebraic characterization of injectivity in phase retrieval
• Phase recovery, MaxCut and complex semidefinite programming
• PhaseLift: Exact and Stable Signal Recovery from Magnitude Measurements via Convex Programming
• Constrained Total Variation Deblurring Models and Fast Algorithms Based on Alternating Direction Method of Multipliers
• On the $O(1/n)$ Convergence Rate of the Douglas–Rachford Alternating Direction Method
• 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
• Alternating direction methods for classical and ptychographic phase retrieval
• The Split Bregman Method for L1-Regularized Problems
• Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?
• Augmented Lagrangian Method, Dual Methods, and Split Bregman Iteration for ROF, Vectorial TV, and High Order Models
• The reconstruction of a multidimensional sequence from the phase or magnitude of its Fourier transform
• Mathematical Considerations for the Problem of Fourier Transform Phase Retrieval from Magnitude
• Optical Wavefront Reconstruction: Theory and Numerical Methods
• Relaxed averaged alternating reflections for diffraction imaging
• Convergence Rate of Overlapping Domain Decomposition Methods for the Rudin--Osher--Fatemi Model Based on a Dual Formulation
• Fourier phasing with phase-uncertain mask
• Phase Retrieval via Matrix Completion