Alternating Projection, Ptychographic Imaging and Phase Synchronization

Abstract

We demonstrate necessary and sufficient conditions of the local convergence of the alternating projection algorithm to a unique solution up to a global phase factor. Additionally, for the ptychography imaging problem, we discuss phase synchronization and graph connection Laplacian, and show how to construct an accurate initial guess to accelerate convergence speed to handle the big imaging data in the coming new light source era.

References in corpus (13)

• X-ray image reconstruction from a diffraction pattern alone
• High-resolution ab initio three-dimensional X-ray diffraction microscopy
• Relaxed Averaged Alternating Reflections for Diffraction Imaging
• Coherent methods in the X-ray sciences
• The Complex Gradient Operator and the CR-Calculus
• An algebraic characterization of injectivity in phase retrieval
• Ultrafast, ultrabright, X-ray holography using a uniformly-redundant array
• Augmented projections for ptychographic imaging
• Phase Retrieval with Random Phase Illumination
• Spectral Convergence of the connection Laplacian from random samples
• Fourier phasing with phase-uncertain mask
• Iterative Algorithms for Ptychographic Phase Retrieval
• Phase Retrieval for Sparse Signals

Cited by in corpus (33)

• PyNX: high performance computing toolkit for coherent X-ray imaging based on operators
• Blind Ptychographic Phase Retrieval via Convergent Alternating Direction Method of Multipliers
• Solving Systems of Random Quadratic Equations via Truncated Amplitude Flow
• Single-frame far-field diffractive imaging with randomized illumination
• Shaping Coherent X-rays with Binary Optics
• Connection graph Laplacian methods can be made robust to noise
• Stability estimates for phase retrieval from discrete Gabor measurements
• Accelerating ptychographic reconstructions using spectral initializations
• On recovery guarantees for angular synchronization
• Denoising Poisson Phaseless Measurements via Orthogonal Dictionary Learning
• A modular software framework for the design and implementation of ptychography algorithms
• Optimal Rates of Convergence for Noisy Sparse Phase Retrieval via Thresholded Wirtinger Flow
• Well conditioned ptychograpic imaging via lost subspace completion
• A general framework for denoising phaseless diffraction measurements
• Latent common manifold learning with alternating diffusion: analysis and applications
• Embedding Riemannian Manifolds by the Heat Kernel of the Connection Laplacian
• Ptychographic reconstruction with wavefront initialization
• Nonconvex set intersection problems: From projection methods to the Newton method for super-regular sets
• Embeddings of Riemannian Manifolds with Finite Eigenvector Fields of Connection Laplacian
• Sparsified Cholesky and Multigrid Solvers for Connection Laplacians
• An iterative warping and clustering algorithm to estimate multiple wave-shape functions from a nonstationary oscillatory signal
• Analytic Formulas for Alternating Projection Sequences for the Positive Semidefinite Cone and an Application to Convergence Analysis
• A direct solver for the phase retrieval problem in ptychographic imaging
• Phase Retrieval by Alternating Minimization with Random Initialization
• Hardness Results for Structured Linear Systems
• $L^0$-regularized Variational Methods for Sparse Phase Retrieval
• Low-dose cryo electron ptychography via non-convex Bayesian optimization
• Graph connection Laplacian and random matrices with random blocks
• Toward a mathematical theory of the crystallographic phase retrieval problem
• Gaze-Contingent Retinal Speckle Suppression for Perceptually-Matched Foveated Holographic Displays
• Evaluation of modified uniformly redundant arrays as structured illuminations for ptychography
• Phase Retrieval for $L^2([-\pi ,\pi ])$ via the Provably Accurate and Noise Robust Numerical Inversion of Spectrogram Measurements
• Extending time-domain ptychography to generalized phase-only transfer functions