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基于共识均衡的相位恢复
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Abstract:
相位恢复是从幅值信息中恢复相位信息，在图像处理等领域发挥重要作用，在实际应用中，往往存在噪声，本文提出一种结合深度学习和即插即用的相位恢复算法，共识均衡相位恢复，运用多个去噪器插入迭代算法，使去噪更加鲁棒。使在迭代求解算法中相位恢复算法与去噪算法达到平衡点，提高了重构质量。本文在仿真和真实数据中对所提算法进行了测试，实验结果表明，该算法在去噪方面表现出更高的鲁棒性，并且具备较强的重构能力。
Phase retrieval is the retrieval of phase information from amplitude information, which plays an important role in image processing and other fields. In practical applications, there is often noise. This paper proposes a phase retrieval algorithm that combines deep learning and plug and play, consensus equalization phase retrieval uses multiple denoising devices to insert iterative algorithms to make denoising more robust. The phase retrieval algorithm and the denoising algorithm reach the balance point in the iterative solution algorithm, and the reconstruction quality is improved. The proposed algorithm is tested in simulation and real data, and the experimental results show that it is more robust for denoising, and has stronger reconstruction ability.
| [1] | Gerchberg, R.W. (1972) A Practical Algorithm for the Determination of Plane from Image and Diffraction Pictures. Optik, 35, 237-246. |
| [2] | Peer, T., Welker, S. and Gerkmann, T. (2022) Beyond Griffin-Lim: Improved Iterative Phase Retrieval for Speech. 2022 International Workshop on Acoustic Signal Enhancement (IWAENC), 5-8 September 2022, Bamberg, 1-5. https://doi.org/10.1109/IWAENC53105.2022.9914686 |
| [3] | Dainty, J.C. and Fienup, J.R. (1987) Phase Retrieval and Image Reconstruction for Astronomy. In: J？rgensen, C., Ed., Image Retrieval: Theory & Application, Academic Press, Cambridge, MA, 231-275. |
| [4] | Fienup, J.R. (1993) Phase-Retrieval Algorithms for a Complicated Optical System. Applied Optics, 32, 1737-1746. https://doi.org/10.1364/AO.32.001737 |
| [5] | Fienup, J.R. (1982) Phase Retrieval Algorithms: A Comparison. Applied Optics, 21, 2758-2769. https://doi.org/10.1364/AO.21.002758 |
| [6] | Elser, V., Rankenburg, I. and Thibault, P. (2007) From the Cover: Searching with Iterated Maps. Proceedings of the National Academy of Sciences, 104, 418-423. https://doi.org/10.1073/pnas.0606359104 |
| [7] | Cahill, J., Casazza, P.G., Peterson, J., et al. (2013) Phase Retrieval by Projections. arXiv:1305.6226 |
| [8] | Bauschke, H.H., Combettes, P.L. and Luke, D.R. (2002) Phase Retrieval, Error Reduction Algorithm, and Fienup Variants: A View from Convex Optimization. Journal of the Optical Society of America A, 19, 1334-1345. https://doi.org/10.1364/JOSAA.19.001334 |
| [9] | Luke, D.R. (2004) Relaxed Averaged Alternating Reflections for Diffraction Imaging. Inverse Problems, 21, 37-50. https://doi.org/10.1088/0266-5611/21/1/004 |
| [10] | Marchesini, S. (2007) Invited Article: A Unified Evaluation of Iterative Projection Algorithms for Phase Retrieval. Review of Scientific Instruments, 78, 229-261. https://doi.org/10.1063/1.2403783 |
| [11] | Wen, Z., Yang, C., Liu, X. and Marchesini, S. (2012) Alternating Direction Methods for Classical and Ptychographic Phase Retrieval. Inverse Problems, 28, Article 115010. https://doi.org/10.1088/0266-5611/28/11/115010 |
| [12] | Netrapalli, P., Jain, P. and Sanghavi, S. (2015) Phase Retrieval Using Alternating Minimization. IEEE Transactions on Signal Processing, 63, 4814-4826. https://doi.org/10.1109/TSP.2015.2448516 |
| [13] | Wang, Y. and Xu, Z. (2014) Phase Retrieval for Sparse Signals. Applied and Computational Harmonic Analysis, 37, 531-544. https://doi.org/10.1016/j.acha.2014.04.001 |
| [14] | Manekar, R., Zhuang, Z., Tayal, K., et al. (2020) Deep Learning Initialized Phase Retrieval. Proceedings of the 34th Conference on Neural Information Processing Systems, Vancouver, 6-12 December 2020, 1-7. |
| [15] | Venkatakrishnan, S.V., Bouman, C.A. and Wohlberg, B. (2013) Plug-and-Play Priors for Model Based Reconstruction. 2013 IEEE Global Conference on Signal and Information Processing, Austin, 3-5 December 2013, 945-948. https://doi.org/10.1109/GlobalSIP.2013.6737048 |
| [16] | Zhang, K., Zuo, W. and Zhang, L. (2019) Deep Plug-and-Play Super-Resolution for Arbitrary Blur Kernels. 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), Long Beach, 15-20 June 2019, 1671-1681. https://doi.org/10.1109/CVPR.2019.00177 |
| [17] | Romano, Y., Elad, M. and Milanfar, P. (2017) The Little Engine That Could: Regularization by Denoising (RED). SIAM Journal on Imaging Sciences, 10, 1804-1844. https://doi.org/10.1137/16M1102884 |
| [18] | Chan, S.H., Wang, X. and Elgendy, O.A. (2016) Plug-and-Play ADMM for Image Restoration: Fixed-Point Convergence and Applications. IEEE Transactions on Computational Imaging, 3, 84-98. https://doi.org/10.1109/TCI.2016.2629286 |
| [19] | Cai, X.J., Gu, G.Y., He, B.S., et al. (2013) A Proximal Point Algorithm Revisit on the Alternating Direction Method of Multipliers. Science China Mathematics, 56, 2179-2186. https://doi.org/10.1007/s11425-013-4683-0 |
| [20] | Tang, J. and Davies, M. (2020) A Fast Stochastic Plug-and-Play ADMM for Imaging Inverse Problems. arXiv: 2006.11630. |
| [21] | Ryu, E., Liu, J., Wang, S., et al. (2019) Plug-and-Play Methods Provably Converge with Properly Trained Denoisers. Proceedings of the 36th International Conference on Machine Learning, Long Beach, 9-15 June 2019, 5546-5557. |
| [22] | Pendu, M.L. and Guillemot, C. (2023) Preconditioned Plug-and-Play ADMM with Locally Adjustable Denoiser for Image Restoration. SIAM Journal on Imaging Sciences, 16, 393-422. https://doi.org/10.1137/22M1504809 |
| [23] | Laroche, C., Almansa, A., Coupeté, E., et al. (2023) Provably Convergent Plug & Play Linearized ADMM, Applied to Deblurring Spatially Varying Kernels. ICASSP 2023-2023 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Rhodes Island, 4-10 June 2023, 1-5. https://doi.org/10.1109/ICASSP49357.2023.10096037 |
| [24] | He, B., Ma, F. and Yuan, X. (2020) Optimally Linearizing the Alternating Direction Method of Multipliers for Convex Programming. Computational Optimization and Applications, 75, 361-388. https://doi.org/10.1007/s10589-019-00152-3 |
| [25] | Wang, X., Juang, J. and Chan, S.H. (2020) Automatic Foreground Extraction from Imperfect Backgrounds Using Multi-Agent Consensus Equilibrium. Journal of Visual Communication and Image Representation, 72, Article 102907. https://doi.org/10.1016/j.jvcir.2020.102907 |
| [26] | Buzzard, G.T., Chan, S.H., Sreehari, S., et al. (2018) Plug-and-Play Unplugged: Optimization-Free Reconstruction Using Consensus Equilibrium. SIAM Journal on Imaging Sciences, 11, 2001-2020. https://doi.org/10.1137/17M1122451 |
| [27] | 柴鸿翔. 基于非凸优化与深度学习的相位恢复算法研究[D]: [硕士学位论文]. 秦皇岛: 燕山大学, 2021. |
