Variational Phase Retrieval with Globally Convergent Preconditioned Proximal Algorithm

Huibin Chang; Stefano Marchesini; Yifei Lou; Tieyong Zeng

doi:10.1137/17M1120439

Variational Phase Retrieval with Globally Convergent Preconditioned Proximal Algorithm

Huibin Chang^*
, Stefano Marchesini
, Yifei Lou
, Tieyong Zeng

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

22 Citations (Scopus)

49 Downloads (Pure)

Abstract

We reformulate the original phase retrieval problem into two variational models (with and without regularization), both containing a globally Lipschitz differentiable term. These two models can be efficiently solved via the proposed Partially Preconditioned Proximal Alternating Linearized Minimization (P³ALM) for masked Fourier measurements. Thanks to the Lipschitz differentiable term, we prove the global convergence of P³ALM for solving the nonconvex phase retrieval problems. Extensive experiments are conducted to show the effectiveness of the proposed methods.

Original language	English
Pages (from-to)	56-93
Number of pages	38
Journal	SIAM Journal on Imaging Sciences
Volume	11
Issue number	1
DOIs	https://doi.org/10.1137/17M1120439
Publication status	Published - 11 Jan 2018

User-Defined Keywords

Global convergence
Partially preconditioned proximal alternating linearized minimization
Phase retrieval
Poisson/Gaussian noise
Regularization
Total variation
Variational model

Access to Document

10.1137/17M1120439

Full TextFinal published version, 1.63 MB

Cite this

@article{29e0e8d169744acc9fe144b8cc8b8bc1,

title = "Variational Phase Retrieval with Globally Convergent Preconditioned Proximal Algorithm",

abstract = "We reformulate the original phase retrieval problem into two variational models (with and without regularization), both containing a globally Lipschitz differentiable term. These two models can be efficiently solved via the proposed Partially Preconditioned Proximal Alternating Linearized Minimization (P3ALM) for masked Fourier measurements. Thanks to the Lipschitz differentiable term, we prove the global convergence of P3ALM for solving the nonconvex phase retrieval problems. Extensive experiments are conducted to show the effectiveness of the proposed methods.",

keywords = "Global convergence, Partially preconditioned proximal alternating linearized minimization, Phase retrieval, Poisson/Gaussian noise, Regularization, Total variation, Variational model",

author = "Huibin Chang and Stefano Marchesini and Yifei Lou and Tieyong Zeng",

note = "Funding information: The work of the first author was partially supported by the National Natural Science Foundation of China (11501413, 11426165, and 51609259), the China Scho l arship Council (CSC), 2017-Outstanding Young Innovation Team Cultivation Program 043-135202TD1703, Young Backbone of Innovative Personnel Training Program 043-135205GC37, and Innovation Project 043-135202XC1605 of Tianjin Normal University. The work of the third author was partially supported by NSF grant DMS-1522786. The work of the fourth author was partially supported by NSFC 11271049 and RGC 12302714. This work was also p artially funded by the Center for Applied Mathematics for Energy Research Applications, a joint ASCR-BES funded project within the Office of Science, US Department of Energy, under contract DOE-DE-AC03-76SF00098. Publisher copyright: {\textcopyright} 2018, Society for Industrial and Applied Mathematics",

year = "2018",

month = jan,

day = "11",

doi = "10.1137/17M1120439",

language = "English",

volume = "11",

pages = "56--93",

journal = "SIAM Journal on Imaging Sciences",

issn = "1936-4954",

publisher = "Society for Industrial and Applied Mathematics (SIAM)",

number = "1",

}

TY - JOUR

T1 - Variational Phase Retrieval with Globally Convergent Preconditioned Proximal Algorithm

AU - Chang, Huibin

AU - Marchesini, Stefano

AU - Lou, Yifei

AU - Zeng, Tieyong

N1 - Funding information: The work of the first author was partially supported by the National Natural Science Foundation of China (11501413, 11426165, and 51609259), the China Scho l arship Council (CSC), 2017-Outstanding Young Innovation Team Cultivation Program 043-135202TD1703, Young Backbone of Innovative Personnel Training Program 043-135205GC37, and Innovation Project 043-135202XC1605 of Tianjin Normal University. The work of the third author was partially supported by NSF grant DMS-1522786. The work of the fourth author was partially supported by NSFC 11271049 and RGC 12302714. This work was also p artially funded by the Center for Applied Mathematics for Energy Research Applications, a joint ASCR-BES funded project within the Office of Science, US Department of Energy, under contract DOE-DE-AC03-76SF00098. Publisher copyright: © 2018, Society for Industrial and Applied Mathematics

PY - 2018/1/11

Y1 - 2018/1/11

N2 - We reformulate the original phase retrieval problem into two variational models (with and without regularization), both containing a globally Lipschitz differentiable term. These two models can be efficiently solved via the proposed Partially Preconditioned Proximal Alternating Linearized Minimization (P3ALM) for masked Fourier measurements. Thanks to the Lipschitz differentiable term, we prove the global convergence of P3ALM for solving the nonconvex phase retrieval problems. Extensive experiments are conducted to show the effectiveness of the proposed methods.

AB - We reformulate the original phase retrieval problem into two variational models (with and without regularization), both containing a globally Lipschitz differentiable term. These two models can be efficiently solved via the proposed Partially Preconditioned Proximal Alternating Linearized Minimization (P3ALM) for masked Fourier measurements. Thanks to the Lipschitz differentiable term, we prove the global convergence of P3ALM for solving the nonconvex phase retrieval problems. Extensive experiments are conducted to show the effectiveness of the proposed methods.

KW - Global convergence

KW - Partially preconditioned proximal alternating linearized minimization

KW - Phase retrieval

KW - Poisson/Gaussian noise

KW - Regularization

KW - Total variation

KW - Variational model

UR - https://www.scopus.com/pages/publications/85045679403

U2 - 10.1137/17M1120439

DO - 10.1137/17M1120439

M3 - Journal article

AN - SCOPUS:85045679403

SN - 1936-4954

VL - 11

SP - 56

EP - 93

JO - SIAM Journal on Imaging Sciences

JF - SIAM Journal on Imaging Sciences

IS - 1

ER -

Variational Phase Retrieval with Globally Convergent Preconditioned Proximal Algorithm

Abstract

User-Defined Keywords

Access to Document

Other files and links

Fingerprint

Cite this