Alternating projection, ptychographic imaging and phase synchronization

S Marchesini, YC Tu, H Wu - Applied and Computational Harmonic …, 2016 - Elsevier
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 …

Ambiguities in one-dimensional discrete phase retrieval from Fourier magnitudes

R Beinert, G Plonka - Journal of Fourier Analysis and Applications, 2015 - Springer
The present paper is a survey aiming at characterizing all solutions of the discrete phase
retrieval problem. Restricting ourselves to discrete signals with finite support, this problem …

Phase retrieval from incomplete magnitude information via total variation regularization

H Chang, Y Lou, MK Ng, T Zeng - SIAM Journal on Scientific Computing, 2016 - SIAM
The phase retrieval problem has drawn considerable attention, as many optical detection
devices can only measure magnitudes of the Fourier transform of the underlying object …

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

P Chen, A Fannjiang, GR Liu - Journal of Fourier Analysis and …, 2018 - Springer
Alternating projection (AP) of various forms, including the parallel AP (PAP), real-
constrained AP (RAP) and the serial AP (SAP), are proposed to solve phase retrieval with at …

Total variation-based reconstruction and phase retrieval for diffraction tomography

R Beinert, M Quellmalz - SIAM Journal on Imaging Sciences, 2022 - SIAM
In optical diffraction tomography (ODT), the three-dimensional scattering potential of a
microscopic object rotating around its center is recovered by a series of illuminations with …

Fixed Point Analysis of Douglas--Rachford Splitting for Ptychography and Phase Retrieval

A Fannjiang, Z Zhang - SIAM Journal on Imaging Sciences, 2020 - SIAM
Douglas--Rachford splitting (DRS) methods based on the proximal point algorithms for the
Poisson and Gaussian log-likelihood functions are proposed for ptychography and phase …

Complex Noise-Based Phase Retrieval Using Total Variation and Wavelet Transform Regularization

X Qin, X Gao, X Yang, M **e - Photonics, 2024 - mdpi.com
This paper presents a phase retrieval algorithm that incorporates sparsity priors into total
variation and framelet regularization. The proposed algorithm exploits the sparsity priors in …

Blind ptychography: uniqueness and ambiguities

A Fannjiang, P Chen - Inverse Problems, 2020 - iopscience.iop.org
Blind ptychography: uniqueness and ambiguities - IOPscience Skip to content IOP Science
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Fourier phase retrieval with a single mask by Douglas–Rachford algorithms

P Chen, A Fannjiang - Applied and computational harmonic analysis, 2018 - Elsevier
Abstract The Fourier-domain Douglas–Rachford (FDR) algorithm is analyzed for phase
retrieval with a single random mask. Since the uniqueness of phase retrieval solution …

Illumination strategies for intensity-only imaging

A Novikov, M Moscoso, G Papanicolaou - SIAM Journal on Imaging Sciences, 2015 - SIAM
We propose a new strategy for narrow band, active array imaging of weak localized
scatterers when only the intensities are recorded and measured at the array. We consider a …