• Advanced Photonics Nexus
  • 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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    DOI: 10.1117/1.APN.1.1.014001 Cite this Article
    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
    Phase unwrapping in OI,1 MRI,2 FPP,4 and InSAR.6
    Fig. 1. Phase unwrapping in OI,1 MRI,2 FPP,4 and InSAR.6
    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. 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.
    Overall process of deep-learning-involved phase unwrapping methods.
    Fig. 3. Overall process of deep-learning-involved phase unwrapping methods.
    Illustration of the dRG method.
    Fig. 4. Illustration of the dRG method.
    Illustration of the dWC method.
    Fig. 5. Illustration of the dWC method.
    Illustration of the dDN method.
    Fig. 6. Illustration of the dDN method.
    An example of the RME method.
    Fig. 7. An example of the RME method.
    An example of the GFS method.
    Fig. 8. An example of the GFS method.
    Entropy histogram of absolute phases from the D_RME, D_GFS, and D_ZPS.
    Fig. 9. Entropy histogram of absolute phases from the D_RME, D_GFS, and D_ZPS.
    SAGD maps of different datasets. Red arrows and circles indicate low and high SAGD values, respectively.
    Fig. 10. SAGD maps of different datasets. Red arrows and circles indicate low and high SAGD values, respectively.
    Mean error maps for each network. Red circles indicate high mean error value.
    Fig. 11. Mean error maps for each network. Red circles indicate high mean error value.
    (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. 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.
    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. 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.
    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. 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.
    RMSEm of the deep-learning-involved methods for absolute phase in different heights.
    Fig. 15. RMSEm of the deep-learning-involved methods for absolute phase in different heights.
    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. 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.
    Results in different noise levels. Solid and dashed lines represent the deep-learning-involved and traditional methods, respectively.
    Fig. 17. Results in different noise levels. Solid and dashed lines represent the deep-learning-involved and traditional methods, respectively.
    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. 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.
    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. 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.
    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. 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.
    Schematic diagram of pretraining and retraining.
    Fig. 21. Schematic diagram of pretraining and retraining.
    Loss plot of pretrained and initialized networks.
    Fig. 22. Loss plot of pretrained and initialized networks.
    MethodDateAuthorRef.NetworkDatasetLoss function
    dRG2018Dardikman and Shaked22
    Dardikman et al.23ResNetRDRMSE
    2019Wang et al.24Res-UNetRMEMSE
    He et al.253D-ResNet
    Ryu et al.26RNNTotal variation + error variation
    2020Dardikman-Yoffe et al.27Res-UNetRDRMSE
    Qin et al.28Res-UNetRMEMAE
    2021Perera and De Silva29LSTMGFSTotal variation + error variation
    Park et al.30GANRDRMAE + adversarial loss
    Zhou et al.31UNetRDRMAE + residues
    2022Xu et al.32MNetRMEMAE and MS-SSIM
    Zhou et al.33GANRDRMAE + adversarial loss
    dWC2018Liang et al.34
    Spoorthi et al.35SegNetGFSCE
    2019Zhang et al.36UNetZPSCE
    Zhang et al.37DeepLab-V3+ZPSCE
    2020Wu et al.38FRRes-UNetGFSCE
    Spoorthi et al.39Dense-UNetGFSMAE + residues + CE
    Zhao et al.40RAENetZPSCE
    2021Zhu et al.41DeepLab-V3+ZPSCE
    2022Vengala et al.42,43TriNetGSFMSE + CE
    Zhang and Li44EESANetGSFWeighted CE
    dDN2020Yan et al.45ResNetZPSMSE
    Table 1. Summary of deep-learning-involved phase unwrapping methods. “—” indicates “not available.”
    DatasetsSizeProportion of h from 10 to 30Proportion of h from 30 to 35Proportion of h from 35 to 40
    Training part of D_RME20,00050%20%30%
    Testing part of D_RME20002/31/61/6
    Training part of D_GSF20,00050%20%30%
    Testing part of D_GSF20002/31/61/6
    Training part of D_ZPS20,00050%20%30%
    Testing part of D_ZPS2,0002/31/61/6
    D_RDR for testing421
    Table 2. Summary of datasets. “—” indicates “not available.”
    D_RMED_GFSD_ZPSD_RDR
    RMSEmRME-Net0.09100.09820.13360.1103
    GSF-Net0.22630.09850.11330.1184
    ZPS-Net2.51480.42210.08210.8245
    RMSEsdRME-Net0.05070.10370.23200.1003
    GSF-Net0.45710.02340.10770.1557
    ZPS-Net2.82490.62520.02201.1405
    PFSRME-Net0.00100.00850.12700.0594
    GSF-Net0.14850.00200.05600.0333
    ZPS-Net0.65250.40750.00100.4679
    Table 3. RMSEm, RMSEsd, and PFS of phase unwrapping results of RME-Net, GFS-Net, and ZPS-Net.
    CasesDatasetsNetworksLoss functions
    Ideal case (Sec. 4.2){φ,ψ}dRG-IMAE
    {φ,k}dWC-ICE + MAE
    Noisy case (Sec. 4.3){φn,ψ}dRG-NMAE
    {φn,k}dWC-NCE+MAE
    {Rn and In,R and I}dDN-NMAE
    Discontinuous case (Sec. 4.4){φd,ψd}dRG-DMAE
    {φd,kd}dWC-DCE + MAE
    Aliasing case (Sec. 4.5){φa,ψa}dRG-AMAE
    {φa,ka}dWC-ACE + MAE
    Mixed case (Sec. 4.6){φm,ψm}dRG-MMAE
    {φm,km}dWC-MCE + 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-IdRG-I-CdWC-I
    RMSEm0.09890.00050.0008
    RMSEsd0.05150.01570.0251
    PFS0.00150.00150.0025
    PIP0.00440.00440.0054
    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)
    RMSEm0.13670.02850.04350.08830.0229
    RMSEsd0.11540.11480.11970.29150.3056
    PFS0.25250.25250.28400.19760.1976
    PIP0.00130.00130.00140.01080.0088
    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-IdRG-DdRG-D-CdWC-IdWC-DLine-scanningLSQG
    RMSEm2.02300.12300.02611.22090.02193.80541.36552.4204
    RMSEsd1.78170.16360.18271.37770.15433.71721.04082.5014
    PFS0.81200.07700.07700.73850.07850.94050.71200.8565
    PIP0.24070.01120.01120.11280.00770.44000.10730.2789
    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-AdRG-A-CdWC-ALine-scanningLSQG
    RMSEm0.19580.00780.010740.51286.719939.8846
    RMSEsd0.13900.15030.161221.06953.129423.0389
    PFS0.00750.00750.01200.98200.98950.9895
    PIP0.07650.07650.04670.91020.57050.8369
    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-MdRG-M-CdWC-MLine-scanningLSQG
    RMSEm0.23620.12660.220638.438910.835039.4653
    RMSEsd0.31010.37900.461821.06953.626918.1084
    PFS0.37400.37400.48101.00001.00001.0000
    PIP0.01060.01060.01070.95690.76000.9107
    Table 9. RMSEm, RMSEsd, PFS, and PIP of the deep-learning-involved and traditional methods in the mixed case. “-C” represents the congruence results.
    CasesdRGdWCdDNLine-scanningLSQGWFT-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
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