Abstract
Ground-based astronomy utilizes modern telescopes to obtain information on the universe by analyzing recorded signals. Due to atmospheric turbulence, the reconstruction process requires solving a deconvolution problem with an unknown point spread function (PSF). The crucial step in PSF estimation is to obtain a high-resolution phase from low-resolution phase gradients, which is a challenging problem. In this paper, when multiple frames of low-resolution phase gradients are available, we introduce PhaseNet, a deep learning approach based on the Taylor frozen flow hypothesis. Our approach incorporates a data-driven residual regularization term, of which the gradient is parameterized by a network, into the Laplacian regularization based model. To solve the model, we unroll the Nesterov accelerated gradient algorithm so that the network can be efficiently and effectively trained. Finally, we evaluate the performance of PhaseNet under various atmospheric conditions and demonstrate its superiority over TV and Laplacian regularization based methods.
| Original language | English |
|---|---|
| Pages (from-to) | 1511-1538 |
| Number of pages | 28 |
| Journal | SIAM Journal on Imaging Sciences |
| Volume | 17 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 2024 |
| Externally published | Yes |
Bibliographical note
Publisher Copyright:© 2024 Society for Industrial and Applied Mathematics.
Funding
\\ast Received by the editors August 7, 2023; accepted for publication (in revised form) April 9, 2024; published electronically July 15, 2024. Dihan Zheng and Shiqi Tang contributed equally to this work. https://doi.org/10.1137/23M1592377 Funding: The work of the first and fifth authors was funded by the National Key R\\&D Program of China under grant 2021YFA1001300 and the National Natural Science Foundation of China under grant 12271291. The work of the third and fourth authors was funded by the Austrian Science Fund (FWF), project F6805-N36, SFB Tomography Across the Scales. The work of the second and sixth authors was funded by HKRGC GRF grants CityU1101120, CityU11309922, and CRF grant C1013-21GF. \\dagger Yau Mathematical Sciences Center, Tsinghua University, Beijing, China ([email protected]). \\ddagger Department of Mathematics, City University of Hong Kong, Kowloon Tong, Hong Kong (sqtang2-c@my. cityu.edu.hk). \\S Industrial Mathematics Institute, Johannes Kepler University, 4040 Linz, Austria ([email protected]. ac.at). \\P Industrial Mathematics Institute, Johannes Kepler University, 4040 Linz, Austria, and Johann Radon Institute for Computational and Applied Mathematics, 4040 Linz, Austria ([email protected]). \\| Yau Mathematical Sciences Center, Tsinghua University, Beijing, China, and Yanqi Lake Beijing Institute of Mathematical Sciences and Applications, Beijing, China ([email protected]). \\#Department of Mathematics, City University of Hong Kong, Kowloon Tong, Hong Kong, and Hong Kong Center for Cerebro-Cardiovascular Health Engineering, Hong Kong Science Park, Hong Kong ([email protected]).
Keywords
- astronomical imaging
- deep unrolling method
- image deconvolution
- machine learning