TY - JOUR
T1 - Overlapping domain decomposition methods for ptychographic imaging
AU - Chang, Huibin
AU - Glowinski, Roland
AU - Marchesini, Stefano
AU - Tai, Xue Cheng
AU - Wang, Yang
AU - Zeng, Tieyong
N1 - Funding Information:
Acknowledgments. We would like to thank the two reviewers and the associate editor for their valuable comments, which helped to improve the paper greatly. HC acknowledges support from his hosts Professors Yang Wang and James Sethian during the visits to the Dept. of Math. in Hong Kong University of Science and Technology and CAMERA in Lawrence Berkeley National Lab.
Funding Information:
\ast Submitted to the journal's Computational Methods in Science and Engineering section October 23, 2020; accepted for publication (in revised form) February 28, 2021; published electronically May 10, 2021. https://doi.org/10.1137/20M1375334 \bfF \bfu \bfn \bfd \bfi \bfn \bfg : The work of the first author was partially supported by the NSFC (11871372, 11501413), and by the Natural Science Foundation of Tianjin (18JCYBJC16600). The work of the second author was partly supported by the Hong Kong based Kennedy Wong Foundation. The work of the third author was partially supported by the Department of Energy under Grant DEAC02-05CH11231. The work of the fourth author was partially supported by RG(R)-RC/17-18/02-MATH, HKBU 12300819, NSF/RGC grant N-HKBU214-19, and RC-FNRA-IG/19-20/SCI/01. The work of the fifth author was partially supported by the Hong Kong Research Grant Council grants 16306415 and 16308518, and HK Innovation Technology Fund Grant ITS/044/18FX; The work of the sixth author was partially supported by the CUHK startup, and the CUHK DAG under grant 4053342, 4053405, RGC 14300219, RGC 14302920, and grant NSFC/RGC N CUHK 415/19.
Publisher Copyright:
© 2021 Society for Industrial and Applied Mathematics
PY - 2021/5
Y1 - 2021/5
N2 - In ptychography experiments, redundant scanning is usually required to guarantee the stable recovery, such that a huge number of frames are generated, and thus it poses a great demand on parallel computing to solve this large-scale inverse problem. In this paper, we propose the overlapping domain decomposition methods to solve the nonconvex optimization problem in ptychographic imaging. They decouple the problem defined on the whole domain into subproblems only defined on the subdomains with synchronizing information in the overlapping regions of these subdomains, thus leading to highly parallel algorithms with good load balance. More specifically, for the nonblind recovery (with known probe in advance), by enforcing the continuity of the overlapping regions for the image (sample), the nonlinear optimization model is established based on a novel smooth-truncated amplitude-Gaussian metric (ST-AGM). Such a metric allows for fast calculation of the proximal mapping with closed form, and meanwhile provides the possibility for the convergence guarantee of the first-order nonconvex optimization algorithm due to its Lipschitz smoothness. Then the alternating direction method of multipliers is utilized to generate an efficient overlapping domain decomposition based ptychography algorithm (OD2P) for the two-subdomain domain decomposition (DD), where all subproblems can be computed with closed-form solutions. Due to the Lipschitz continuity for the gradient of the objective function with ST-AGM, the convergence of the proposed OD2P is derived under mild conditions. Moreover, it is extended to more general cases including multiple-subdomain DD and blind recovery. Numerical experiments are further conducted to show the performance of proposed algorithms, demonstrating good convergence speed and robustness to the noise. Especially, we report the virtual wall-clock time of proposed algorithm up to 10 processors, which shows potential for upcoming massively parallel computations.
AB - In ptychography experiments, redundant scanning is usually required to guarantee the stable recovery, such that a huge number of frames are generated, and thus it poses a great demand on parallel computing to solve this large-scale inverse problem. In this paper, we propose the overlapping domain decomposition methods to solve the nonconvex optimization problem in ptychographic imaging. They decouple the problem defined on the whole domain into subproblems only defined on the subdomains with synchronizing information in the overlapping regions of these subdomains, thus leading to highly parallel algorithms with good load balance. More specifically, for the nonblind recovery (with known probe in advance), by enforcing the continuity of the overlapping regions for the image (sample), the nonlinear optimization model is established based on a novel smooth-truncated amplitude-Gaussian metric (ST-AGM). Such a metric allows for fast calculation of the proximal mapping with closed form, and meanwhile provides the possibility for the convergence guarantee of the first-order nonconvex optimization algorithm due to its Lipschitz smoothness. Then the alternating direction method of multipliers is utilized to generate an efficient overlapping domain decomposition based ptychography algorithm (OD2P) for the two-subdomain domain decomposition (DD), where all subproblems can be computed with closed-form solutions. Due to the Lipschitz continuity for the gradient of the objective function with ST-AGM, the convergence of the proposed OD2P is derived under mild conditions. Moreover, it is extended to more general cases including multiple-subdomain DD and blind recovery. Numerical experiments are further conducted to show the performance of proposed algorithms, demonstrating good convergence speed and robustness to the noise. Especially, we report the virtual wall-clock time of proposed algorithm up to 10 processors, which shows potential for upcoming massively parallel computations.
KW - Blind recovery
KW - Overlapping domain decomposition method
KW - Parallel computing
KW - Phase retrieval
KW - Ptychography
KW - Smooth truncated amplitude-Gaussian metric
UR - http://www.scopus.com/inward/record.url?scp=85106549228&partnerID=8YFLogxK
U2 - 10.1137/20M1375334
DO - 10.1137/20M1375334
M3 - Journal article
AN - SCOPUS:85106549228
SN - 1064-8275
VL - 43
SP - B570-B597
JO - SIAM Journal on Scientific Computing
JF - SIAM Journal on Scientific Computing
IS - 3
ER -