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• Vol. 1, Issue 1, 014001 (2022)
Kaiqiang Wang1、2, Qian Kemao3、*, Jianglei Di1、2、4、*, and Jianlin Zhao1、2、*
Author Affiliations
• 1Northwestern Polytechnical University, School of Physical Science and Technology, Shaanxi Key Laboratory of Optical Information Technology, Xi’an, China
• 2Ministry of Industry and Information Technology, Key Laboratory of Light Field Manipulation and Information Acquisition, Xi’an, China
• 3Nanyang Technological University, School of Computer Science and Engineering, Singapore
• 4Guangdong University of Technology, Guangdong Provincial Key Laboratory of Photonics Information Technology, Guangzhou, China
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Kaiqiang Wang, Qian Kemao, Jianglei Di, Jianlin Zhao. Deep learning spatial phase unwrapping: a comparative review[J]. Advanced Photonics Nexus, 2022, 1(1): 014001 Copy Citation Text show less
Fig. 1. Phase unwrapping in OI,1 MRI,2 FPP,4 and InSAR.6
Fig. 2. Datasets of the deep-learning-involved phase unwrapping methods, for (a) dRG, (b) dWC, and (c) dDN. “$R$” and “$I$” represent the real and imaginary parts of CAF, respectively.
Fig. 3. Overall process of deep-learning-involved phase unwrapping methods.
Fig. 4. Illustration of the dRG method.
Fig. 5. Illustration of the dWC method.
Fig. 6. Illustration of the dDN method.
Fig. 7. An example of the RME method.
Fig. 8. An example of the GFS method.
Fig. 9. Entropy histogram of absolute phases from the D_RME, D_GFS, and D_ZPS.
Fig. 10. SAGD maps of different datasets. Red arrows and circles indicate low and high SAGD values, respectively.
Fig. 11. Mean error maps for each network. Red circles indicate high mean error value.
Fig. 12. (a) SAGD maps for D_RME and D_RME1, (b) mean error maps for RME-Net and RME1-Net. Red arrows indicate low SAGD value. Red circles indicate high mean error value and orange circles indicate the comparison part.
Fig. 13. Partial display of results from RME1-Net. “Max”, “Med,” and “Min” represent specific results with maximal, median, and minimal $RMSEm$, respectively. “-C” represents the congruence results.
Fig. 14. Results for the (a) dRG-I and (b) dWC-I in the ideal case. “Max,” “Med,” and “Min” represent specific results with maximal, median, and minimal $RMSEm$, respectively. “-C” represents the congruence results.
Fig. 15. $RMSEm$ of the deep-learning-involved methods for absolute phase in different heights.
Fig. 16. Results for (a) dRG-N, (b) dWC-N, and (c) dDN-N in the noisy case. “GT” represents the pure GT (pure absolute phase), while “GT1” represents the noisy GT (noisy absolute phase). “Max,” “Med,” and “Min” represent specific results with maximal, median, and minimal $RMSEm$, respectively. “-C” represents the congruence results.
Fig. 17. Results in different noise levels. Solid and dashed lines represent the deep-learning-involved and traditional methods, respectively.
Fig. 18. Results for (a) dRG-I, (b) dWC-I, (c) dRG-D, (d) dWC-D, (e) line-scanning, (f) LS, and (g) QG methods in the discontinuous case. “Max,” “Med,” and “Min” represent specific results with maximal, median, and minimal $RMSEm$, respectively. “-C” represents the congruence results. The last columns of each result are discontinuous maps, where 1 (white) represents the position of the discontinuous pixels.
Fig. 19. Results for (a) dRG-A, (b) dWC-A, (c) line-scanning, (d) LS, and (e) QG methods in the aliasing case. “Max,” “Med,” and “Min” represent specific results with maximal, median, and minimal $RMSEm$, respectively. “-C” represents the congruence results. The last columns of each result are aliasing maps, where 1 (white) represents the position of the aliasing pixels.
Fig. 20. Results for (a) dRG-M, (b) dWC-M, (c) line-scanning, (d) LS, and (e) QG methods in the mixed case. “Max,” “Med,” and “Min” represent specific results with maximal, median, and minimal $RMSEm$, respectively. “$−C$” represents the congruence results. The last columns of each result are aliasing or discontinuous maps (called “$A$ and $D$”), where 1 (white) represents the position of the aliasing or discontinuous pixels.
Fig. 21. Schematic diagram of pretraining and retraining.
Fig. 22. Loss plot of pretrained and initialized networks.
 Method Date Author Ref. Network Dataset Loss function dRG 2018 Dardikman and Shaked 22 — — — Dardikman et al. 23 ResNet RDR MSE 2019 Wang et al. 24 Res-UNet RME MSE He et al. 25 3D-ResNet — — Ryu et al. 26 RNN — Total variation + error variation 2020 Dardikman-Yoffe et al. 27 Res-UNet RDR MSE Qin et al. 28 Res-UNet RME MAE 2021 Perera and De Silva 29 LSTM GFS Total variation + error variation Park et al. 30 GAN RDR MAE + adversarial loss Zhou et al. 31 UNet RDR MAE + residues 2022 Xu et al. 32 MNet RME MAE and MS-SSIM Zhou et al. 33 GAN RDR MAE + adversarial loss dWC 2018 Liang et al. 34 — — — Spoorthi et al. 35 SegNet GFS CE 2019 Zhang et al. 36 UNet ZPS CE Zhang et al. 37 DeepLab-V3+ ZPS CE 2020 Wu et al. 38 FRRes-UNet GFS CE Spoorthi et al. 39 Dense-UNet GFS MAE + residues + CE Zhao et al. 40 RAENet ZPS CE 2021 Zhu et al. 41 DeepLab-V3+ ZPS CE 2022 Vengala et al. 42,43 TriNet GSF MSE + CE Zhang and Li 44 EESANet GSF Weighted CE dDN 2020 Yan et al. 45 ResNet ZPS MSE
Table 1. Summary of deep-learning-involved phase unwrapping methods. “—” indicates “not available.”
 Datasets Size Proportion of $h$ from 10 to 30 Proportion of $h$ from 30 to 35 Proportion of $h$ from 35 to 40 Training part of D_RME 20,000 50% 20% 30% Testing part of D_RME 2000 2/3 1/6 1/6 Training part of D_GSF 20,000 50% 20% 30% Testing part of D_GSF 2000 2/3 1/6 1/6 Training part of D_ZPS 20,000 50% 20% 30% Testing part of D_ZPS 2,000 2/3 1/6 1/6 D_RDR for testing 421 — — —
Table 2. Summary of datasets. “—” indicates “not available.”
 D_RME D_GFS D_ZPS D_RDR $RMSEm$ RME-Net 0.0910 0.0982 0.1336 0.1103 GSF-Net 0.2263 0.0985 0.1133 0.1184 ZPS-Net 2.5148 0.4221 0.0821 0.8245 $RMSEsd$ RME-Net 0.0507 0.1037 0.2320 0.1003 GSF-Net 0.4571 0.0234 0.1077 0.1557 ZPS-Net 2.8249 0.6252 0.0220 1.1405 PFS RME-Net 0.0010 0.0085 0.1270 0.0594 GSF-Net 0.1485 0.0020 0.0560 0.0333 ZPS-Net 0.6525 0.4075 0.0010 0.4679
Table 3. RMSEm, RMSEsd, and PFS of phase unwrapping results of RME-Net, GFS-Net, and ZPS-Net.
 Cases Datasets Networks Loss functions Ideal case (Sec. 4.2) ${φ,ψ}$ dRG-I MAE ${φ,k}$ dWC-I CE + MAE Noisy case (Sec. 4.3) ${φn,ψ}$ dRG-N MAE ${φn,k}$ dWC-N CE+MAE {$Rn$ and $In,R$ and $I$} dDN-N MAE Discontinuous case (Sec. 4.4) ${φd,ψd}$ dRG-D MAE ${φd,kd}$ dWC-D CE + MAE Aliasing case (Sec. 4.5) ${φa,ψa}$ dRG-A MAE ${φa,ka}$ dWC-A CE + MAE Mixed case (Sec. 4.6) ${φm,ψm}$ dRG-M MAE ${φm,km}$ dWC-M CE + MAE
Table 4. Summary of networks and corresponding datasets. The form of the dataset is {Input, GT}. The last letter of the network name is the case (“I” for ideal, “N” for noisy, “D” for discontinuous, “A” for aliasing, and “M” for mixed).
 dRG-I dRG-I-C dWC-I $RMSEm$ 0.0989 0.0005 0.0008 $RMSEsd$ 0.0515 0.0157 0.0251 PFS 0.0015 0.0015 0.0025 PIP 0.0044 0.0044 0.0054
Table 5. RMSEm, RMSEsd, PFS, and PIP of the deep-learning-involved methods in the ideal case. “-C” represents the congruence results.
 dRG-N (GT) dRG-N-C (GT1) dWC-N (GT1) dDN-N (GT) dDN-N-C (GT1) $RMSEm$ 0.1367 0.0285 0.0435 0.0883 0.0229 $RMSEsd$ 0.1154 0.1148 0.1197 0.2915 0.3056 PFS 0.2525 0.2525 0.2840 0.1976 0.1976 PIP 0.0013 0.0013 0.0014 0.0108 0.0088
Table 6. RMSEm, RMSEsd, PFS, and PIP of the deep-learning-involved methods in the noisy case. “GT” represents the pure GT (pure absolute phase), while “GT1” represents the noisy GT (noisy absolute phase). “-C” represents the congruence results.
 dRG-I dRG-D dRG-D-C dWC-I dWC-D Line-scanning LS QG $RMSEm$ 2.0230 0.1230 0.0261 1.2209 0.0219 3.8054 1.3655 2.4204 $RMSEsd$ 1.7817 0.1636 0.1827 1.3777 0.1543 3.7172 1.0408 2.5014 PFS 0.8120 0.0770 0.0770 0.7385 0.0785 0.9405 0.7120 0.8565 PIP 0.2407 0.0112 0.0112 0.1128 0.0077 0.4400 0.1073 0.2789
Table 7. RMSEm, RMSEsd, PFS, and PIP of the deep-learning-involved and traditional methods in the discontinuous case. “-C” represents the congruence results.
 dRG-A dRG-A-C dWC-A Line-scanning LS QG $RMSEm$ 0.1958 0.0078 0.0107 40.5128 6.7199 39.8846 $RMSEsd$ 0.1390 0.1503 0.1612 21.0695 3.1294 23.0389 PFS 0.0075 0.0075 0.0120 0.9820 0.9895 0.9895 PIP 0.0765 0.0765 0.0467 0.9102 0.5705 0.8369
Table 8. RMSEm, RMSEsd, PFS, and PIP of the deep-learning-involved and traditional methods in the aliasing case. “-C” represents the congruence results.
 dRG-M dRG-M-C dWC-M Line-scanning LS QG $RMSEm$ 0.2362 0.1266 0.2206 38.4389 10.8350 39.4653 $RMSEsd$ 0.3101 0.3790 0.4618 21.0695 3.6269 18.1084 PFS 0.3740 0.3740 0.4810 1.0000 1.0000 1.0000 PIP 0.0106 0.0106 0.0107 0.9569 0.7600 0.9107
Table 9. RMSEm, RMSEsd, PFS, and PIP of the deep-learning-involved and traditional methods in the mixed case. “-C” represents the congruence results.
 Cases dRG dWC dDN Line-scanning LS QG WFT-QG Ideal ✓ ✓ ✓ ✓✓ ✓ ✓ — Slight noise ✓ ✓ ✓ ✓ ✓ ✓ ✓ Moderate noise ✓✓ ✓✓ ✓ ✗ ✗ ✗ ✓✓ Severe noise ✓✓ ✓✓ ✓ ✗ ✗ ✗ ✓✓ Discontinuity ✓✓ ✓✓ — ✗ ✗ ✗ — Aliasing ✓✓ ✓✓ — ✗ ✗ ✗ — Mixed ✓✓ ✓✓ — ✗ ✗ ✗ —
Table 10. Performance statistics in the ideal, noisy, discontinuous, and aliasing cases. “✓” represents “capable.” “✓✓” represents “best and recommended.” “✗” represents “incapable.” “—” indicates “not applicable.”
Kaiqiang Wang, Qian Kemao, Jianglei Di, Jianlin Zhao. Deep learning spatial phase unwrapping: a comparative review[J]. Advanced Photonics Nexus, 2022, 1(1): 014001