Phase unwrapping via an attention U-shaped convolutional neural network with residual adaptively spatial feature fusion

Xia X., Jing Wenbo, Feng Xuan, Wu Xueni, Zhang Junhao, Liu Tongbo

For Russian citation (Opticheskii Zhurnal):

Xia X., Jing W., Feng X., Wu X., Zhang J., Liu T. Phase unwrapping via an attention U-shaped convolutional neural network with residual adaptively spatial feature fusion (Восстановление фазы сигнала с помощью сверточной нейронной сети архитектуры U-Net с адаптивным слиянием пространственных признаков) [на англ. яз.] // Оптический журнал. 2026. Т. 93. № 7. С. 58–68. http://doi.org/10.17586/1023-5086-2026-93-07-58-68

Xia X., Jing W., Feng X., Wu X., Zhang J., Liu T. Phase unwrapping via an attention U-shaped convolutional neural network with residual adaptively spatial feature fusion [in English] // Opticheskii Zhurnal. 2026. V. 93. № 7. P. 58–68. http://doi.org/10.17586/1023-5086-2026-93-07-58-68

For citation (Journal of Optical Technology):

Abstract:

The subject of the study. In phase measurement, phase unwrapping is a crucial and challenging process. The purpose of the work. Development of a deep convolutional neural network named Phase Unwrapping via an Attention U-shaped Convolutional Neural Network with Residual Adaptively Spatial Feature Fusion. The method aims to produce unwrapped phase maps in a single step. Method. The proposed network uses an attention-guided U-shaped convolutional neural network as backbone. Residual adaptively spatial feature fusion is applied at each layer to enhance feature propagation and suppress noise. Training minimizes a combined loss composed of mean absolute error loss, image gradient loss, and frequency loss. This loss design encourages recovery of fine phase details. The main results. The proposed method outperforms traditional phase unwrapping algorithms and prior learning-based methods on tests with noisy and discontinuous wrapped phases. The method achieves lower root-mean-square error values and shows improved robustness in the examined cases. Practical significance. The results of the fringe projection experiment demonstrate the robustness and generality of the network.

Keywords:

phase unwrapping, deep convolutional neural network, Adaptively Spatial Feature Fusion, fringe projection

Acknowledgements:

Ministry of Science and Technology of the People’s Republic of China (2018YFB1107600), Jilin Scientific and Technological Development Program (20160204009GX), The 111 Project of China (D21009), 2024 Jilin Provincial Department of Education project (JJKH20240922KJ).

OCIS codes: 100.0100, 120.5050

References:

1. Zuo C., Feng S., Huang L., et al. Phase shifting algorithms for fringe projection profilometry: A review // Opt. Lasers Eng. 2018. V. 109. P. 23–59. DOI: 10.1016/j.optlaseng.2018.04.019

2. Dong J., Liu T., Chen F., et al. Simultaneous phase unwrapping and removal of chemical shift (SPURS) using graph cuts: Application in quantitative susceptibility mapping // IEEE Trans. Med. Imaging. 2015. V. 34. № 2. P. 531–540. DOI: 10.1109/TMI.2014.2361764

3. Waghmare R.G., Sukumar P.R., Subrahmanyam G.R.K.S., et al. Particle-filter-based phase estimation in digital holographic interferometry // JOSA. A. 2016. V. 33. № 3. P. 326–332. DOI: 10.1364/JOSAA.33.000326

4. Yu H., Lan Y., Yuan Z., et al. Phase unwrapping in InSAR : A review // IEEE Geosci. Remote Sens. Mag. 2019. V. 7. № 1. P. 40‒58. DOI: 10.1109/MGRS.2018.2873644

5. Dennis M.D.P., Ghiglia C. Two-dimensional phase unwrapping: Theory, algorithms, and software. N.Y.: Wiley & Sons, 1998. P. 5.

6. Goldstein R.M., Zebker H.A., Werner C.L. Satellite radar interferometry: Two-dimensional phase unwrapping // Radio Sci. 1988. V. 23. № 4. P. 713–720. DOI: 10.1029/RS023i004p00713

7. Prati C., Giani M., Leuratti N. SAR interferometry: A 2-D phase unwrapping technique based on phase and absolute values informations // 10th Annu. Int. Symp. Geosci. Remote Sens. 1990. P. 2043–2046. DOI: 10.1109/IGARSS.1990.688929

8. Flynn T.J. Consistent 2-D phase unwrapping guided by a quality map // IGARSS ’96. 1996 Int. Geosci. Remote Sens. Symp. 1996. V. 4. P. 2057–2059. DOI: 10.1109/IGARSS.1996.516887

9. Itoh K. Analysis of the phase unwrapping algorithm // Appl. Opt. 1982. V. 21. № 14. P. 2470. DOI: 10.1364/AO.21.002470

10. Takajo H., Takahashi T. Least-squares phase estimation from the phase difference // JOSA. A. 1988. V. 5. № 3. P. 416–425. DOI: 10.1364/JOSAA.5.000416

11. Wang K., Song L., Wang C., et al. On the use of deep learning for phase recovery // Light Sci. Appl. 2024. V. 13. № 1. P. 1–82. DOI: 10.1038/s41377-023-01340-x

12. Wang K., Li Y., Kemao Q., et al. One-step robust deep learning phase unwrapping // Opt. Exp. 2019. V. 27. № 10. P. 15100–15115. DOI: 10.1364/oe.27.015100

13. Zhou L., Yu H., Pascazio V., et al. PU-GAN: A one-step 2-D InSAR phase unwrapping based on conditional generative adversarial network // IEEE Trans. Geosci. Remote Sens. 2022. V. 60. P. 1–10. DOI: 10.1109/TGRS.2022.3145342

14. Spoorthi G.E., Gorthi S., Gorthi R.K.S.S., et al. PhaseNet: A deep convolutional neural network for two-dimensional phase unwrapping // IEEE Signal Process. Lett. 2019. V. 26. № 1. P. 54–58. DOI: 10.1109/LSP.2018.2879184

15. Spoorthi G., Gorthi R.K.S.S., Gorthi S. PhaseNet 2.0: Phase unwrapping of noisy data based on deep learning approach // IEEE Trans. Image Process. 2020. V. 29. P. 4862–4872. DOI: 10.1109/TIP.2020.2977213

16. Yan K., Yu Y., Sun T., et al. Wrapped phase denoising using convolutional neural networks // Opt. Lasers Eng. 2020. V. 128. P. 105999. DOI: 10.1016/j.optlaseng.2019.105999

17. Tai M., Li W., Liu T., et al. Branch-cut phase unwrapping method based on deep learning // Optik (Stuttg). 2023. V. 295. P. 171510. DOI: 10.1016/j.ijleo.2023.171510

18. Oktay O., Schlemper J., Le Folgoc L., et al. Attention U-Net: Learning where to look for the pancreas // arXiv preprint arXiv: 1804.03999. 2018. http://arxiv.org/abs/1804.03999

19. Liu S., Huang D., Wang Y. Learning spatial fusion for single-shot object detection // arXiv preprint arXiv:1911.09516. 2019. http://arxiv.org/abs/1911.09516