Abstract

The presence of speckle noise and dislocations makes phase restoration potentially difficult in quantitative phase imaging and metrology. Unfortunately, there is no appropriate approach to deal with phase data corrupted by high speckle noise and phase dislocations. Usually, processing schemes may deal with low-pass phase filtering, phase unwrapping, or phase inpainting. This paper discusses the efficient processing to deal with noisy phase maps corrupted with phase dislocations. Six processing schemes, combining four operations, are evaluated. The investigation is carried out by realistic numerical simulations in which strong decorrelation phase noise and phase dislocations are generated. As a result, most robust and faster processing is established. The applicability of the optimal scheme is demonstrated through deformation measurement in dental materials.

© 2019 Optical Society of America

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References

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    [Crossref]
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  18. B. N. Li, X. Shan, K. Xiang, N. An, J. Xu, W. Huang, and E. Kobayashi, “Evaluation of robust wave image processing methods for magnetic resonance elastography,” Comput. Biol. Med. 54, 100–108 (2014).
    [Crossref]
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    [Crossref]
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    [Crossref]
  24. M. Zhao, L. Huang, Q. Zhang, X. Su, A. Asundi, and Q. Kemao, “Quality-guided phase unwrapping technique: comparison of quality maps and guiding strategies,” Appl. Opt. 50, 6214–6224 (2011).
    [Crossref]
  25. H. Yu, Y. Lan, J. Xu, D. An, and H. Lee, “Large-scale L0-norm and L1-norm 2-D phase unwrapping,” IEEE Trans. Geosci. Remote Sensing 55, 4712–4728 (2017).
    [Crossref]
  26. J. Xu, D. An, X. Huang, and P. Yi, “An efficient minimum-discontinuity phase-unwrapping method,” IEEE Geosci. Remote Sens. Lett. 13, 666–670 (2016).
    [Crossref]
  27. M. Rivera, F. J. Hernandez-Lopez, and A. Gonzalez, “Phase unwrapping by accumulation of residual maps,” Opt. Laser Eng. 64, 51–58 (2015).
    [Crossref]
  28. Y. Guo, X. Chen, and T. Zhang, “Robust phase unwrapping algorithm based on least squares,” Opt. Laser Eng. 63, 25–29 (2014).
    [Crossref]
  29. H. Xia, S. Montresor, R. Guo, J. C. Li, F. Yan, H. Cheng, and P. Picart, “Phase calibration unwrapping algorithm for phase data corrupted by strong decorrelation speckle noise,” Opt. Express 24, 28713–28730 (2016).
    [Crossref]
  30. D. Zheng, F. Da, Q. Kemao, and H. S. Seah, “Phase-shifting profilometry combined with Gray-code patterns projection: unwrapping error removal by an adaptive median filter,” Opt. Express 25, 4700–4713 (2017).
    [Crossref]
  31. X. Xie, “Iterated unscented Kalman filter for phase unwrapping of interferometric fringes,” Opt. Express 24, 18872–18897 (2016).
    [Crossref]
  32. Q. Kemao, “Applications of windowed Fourier fringe analysis in optical measurement: a review,” Opt. Laser Eng. 66, 67–73 (2015).
    [Crossref]
  33. S. Montresor and P. Picart, “Quantitative appraisal for noise reduction in digital holographic phase imaging,” Opt. Express 24, 14322–14343 (2016).
    [Crossref]
  34. H. Xia, S. Montresor, P. Picart, R. Guo, and J. C. Li, “Comparative analysis for combination of unwrapping and de-noising of phase data with high speckle decorrelation noise,” Opt. Laser Eng. 107, 71–77 (2018).
    [Crossref]
  35. H. Xia, S. Montresor, R. Guo, J. C. Li, F. Olchewsky, J.-M. Desse, and P. Picart, “Robust processing of phase dislocations based on combined unwrapping and inpainting approaches,” Opt. Lett. 42, 322–325 (2017).
    [Crossref]
  36. Q. Kemao, “Windowed Fourier transform for fringe pattern analysis,” Appl. Opt. 43, 2695–2702 (2004).
    [Crossref]
  37. H. Xia, R. Guo, Z. Fan, H. Cheng, and B. Yang, “Non-invasive mechanical measurement for transparent objects by digital holographic interferometry based on iterative least-squares phase unwrapping,” Exp. Mech. 52, 439–445 (2012).
    [Crossref]
  38. S. A. Villar, S. Torcida, and G. G. Acosta, “Median filtering: a new insight,” J. Math. Imaging Vis. 58, 130–146 (2017).
    [Crossref]
  39. A. Criminisi, P. Pérez, and K. Toyama, “Region filling and object removal by exemplar-based image inpainting,” IEEE Trans. Image Process. 13, 1200–1212 (2004).
    [Crossref]
  40. H. Xia, P. Picart, S. Montresor, R. Guo, J. C. Li, O. Yusuf-Solieman, J. C. Durand, and M. Fages, “Mechanical behavior of CAD/CAM occlusal ceramic reconstruction assessed by digital color holography,” Dent. Mater. 34, 1222–1234 (2018).
    [Crossref]

2018 (2)

H. Xia, S. Montresor, P. Picart, R. Guo, and J. C. Li, “Comparative analysis for combination of unwrapping and de-noising of phase data with high speckle decorrelation noise,” Opt. Laser Eng. 107, 71–77 (2018).
[Crossref]

H. Xia, P. Picart, S. Montresor, R. Guo, J. C. Li, O. Yusuf-Solieman, J. C. Durand, and M. Fages, “Mechanical behavior of CAD/CAM occlusal ceramic reconstruction assessed by digital color holography,” Dent. Mater. 34, 1222–1234 (2018).
[Crossref]

2017 (13)

S. A. Villar, S. Torcida, and G. G. Acosta, “Median filtering: a new insight,” J. Math. Imaging Vis. 58, 130–146 (2017).
[Crossref]

H. Xia, S. Montresor, R. Guo, J. C. Li, F. Olchewsky, J.-M. Desse, and P. Picart, “Robust processing of phase dislocations based on combined unwrapping and inpainting approaches,” Opt. Lett. 42, 322–325 (2017).
[Crossref]

H. Yu, Y. Lan, J. Xu, D. An, and H. Lee, “Large-scale L0-norm and L1-norm 2-D phase unwrapping,” IEEE Trans. Geosci. Remote Sensing 55, 4712–4728 (2017).
[Crossref]

J. Dong, F. Chen, D. Zhou, T. Liu, Z. Yu, and Y. Wang, “Phase unwrapping with graph cuts optimization and dual decomposition acceleration for 3D high-resolution MRI data,” Magn. Reson. Med. 77, 1353–1358 (2017).
[Crossref]

D. Zheng, F. Da, Q. Kemao, and H. S. Seah, “Phase-shifting profilometry combined with Gray-code patterns projection: unwrapping error removal by an adaptive median filter,” Opt. Express 25, 4700–4713 (2017).
[Crossref]

T. Nguyen, V. Bui, V. Lam, C. B. Raub, L.-C. Chang, and G. Nehmetallah, “Automatic phase aberration compensation for digital holographic microscopy based on deep learning background detection,” Opt. Express 25, 15043–15057 (2017).
[Crossref]

N. A. Turko and N. T. Shaked, “Simultaneous two-wavelength phase unwrapping using an external module for multiplexing off-axis holography,” Opt. Lett. 42, 73–76 (2017).
[Crossref]

M. Wang, F. Li, M. Zheng, W. Lu, Y. Jia, Q. Yu, S. Zhao, and J. Wu, “Realization of absolute-phase unwrapping and speckle suppression in laser digital holography,” Ann. Phys. (Berlin) 529, 1600378 (2017).
[Crossref]

J. C. Estrada, J. L. Marroquin, and O. M. Medina, “Reconstruction of local frequencies for recovering the unwrapped phase in optical interferometry,” Sci. Rep. 7, 6727 (2017).
[Crossref]

S. Xia, Y. Huang, S. Peng, Y. Wu, and X. Tan, “Robust phase unwrapping for phase images in Fourier domain Doppler optical coherence tomography,” J. Biomed. Opt. 22, 36014 (2017).
[Crossref]

M. Zhang, Q. Chen, T. Tao, S. Feng, Y. Hu, H. Li, and C. Zuo, “Robust and efficient multi-frequency temporal phase unwrapping: optimal fringe frequency and pattern sequence selection,” Opt. Express 25, 20381–20400 (2017).
[Crossref]

M. Padilla, M. Servin, and G. Garnica, “Profilometry with digital fringe-projection at the spatial and temporal Nyquist frequencies,” Opt. Express 25, 22292–22302 (2017).
[Crossref]

Z. Jiang, J. Wang, Q. Song, and Z. Zhou, “A refined cluster-analysis-based multibaseline phase-unwrapping algorithm,” IEEE Geosci. Remote Sens. Lett. 14, 1565–1569 (2017).
[Crossref]

2016 (11)

G. Du, C. Zhang, C. Zhou, S. Si, H. Li, and Y. Li, “Iterative two-step temporal phase-unwrapping applied to high sensitivity three-dimensional profilometry,” Opt. Lasers Eng. 79, 22–28 (2016).
[Crossref]

J. Gao, “Reliability-map-guided phase unwrapping method,” IEEE Geosci. Remote Sens. Lett. 13, 716–720 (2016).
[Crossref]

M. Arevalillo-Herráez, F. R. Villatoro, and M. A. Gdeisat, “A robust and simple measure for quality-guided 2D phase unwrapping algorithms,” IEEE Trans. Image Process. 25, 2601–2609 (2016).
[Crossref]

Y. Wang, D. Huang, Y. Su, and X. S. Yao, “Two-dimensional phase unwrapping in Doppler Fourier domain optical coherence tomography,” Opt. Express 24, 26129–26145 (2016).
[Crossref]

Y. Xu, D. Darga, J. Smid, A. M. Zysk, D. Teh, S. A. Boppart, and P. S. Carney, “Filtering for unwrapping noisy Doppler optical coherence tomography images for extended microscopic fluid velocity measurement range,” Opt. Lett. 41, 4024–4027 (2016).
[Crossref]

H. Yu and Y. Lan, “Robust two-dimensional phase unwrapping for multibaseline SAR interferograms: A two-stage programming approach,” IEEE Trans. Geosci. Remote Sensing 54, 5217–5225 (2016).
[Crossref]

S. Wu, L. Zhu, S. Pan, and L. Yang, “Spatiotemporal three-dimensional phase unwrapping in digital speckle pattern interferometry,” Opt. Lett. 41, 1050–1053 (2016).
[Crossref]

X. Xie, “Iterated unscented Kalman filter for phase unwrapping of interferometric fringes,” Opt. Express 24, 18872–18897 (2016).
[Crossref]

J. Xu, D. An, X. Huang, and P. Yi, “An efficient minimum-discontinuity phase-unwrapping method,” IEEE Geosci. Remote Sens. Lett. 13, 666–670 (2016).
[Crossref]

H. Xia, S. Montresor, R. Guo, J. C. Li, F. Yan, H. Cheng, and P. Picart, “Phase calibration unwrapping algorithm for phase data corrupted by strong decorrelation speckle noise,” Opt. Express 24, 28713–28730 (2016).
[Crossref]

S. Montresor and P. Picart, “Quantitative appraisal for noise reduction in digital holographic phase imaging,” Opt. Express 24, 14322–14343 (2016).
[Crossref]

2015 (5)

M. Rivera, F. J. Hernandez-Lopez, and A. Gonzalez, “Phase unwrapping by accumulation of residual maps,” Opt. Laser Eng. 64, 51–58 (2015).
[Crossref]

Q. Kemao, “Applications of windowed Fourier fringe analysis in optical measurement: a review,” Opt. Laser Eng. 66, 67–73 (2015).
[Crossref]

B. Tayebi, M. Jafarfard, F. Sharif, Y. Song, D. Har, and D. Kim, “Large step-phase measurement by a reduced-phase triple-illumination interferometer,” Opt. Express 23, 11264–11271 (2015).
[Crossref]

J. de Souza, M. Oliveira, and P. dos Santos, “Branch-cut algorithm for optical phase unwrapping,” Opt. Lett. 40, 3456–3459 (2015).
[Crossref]

R. Schlögel, C. Doubre, J. P. Malet, and F. Masson, “Landslide deformation monitoring with ALOS/PALSAR imagery: a D-InSAR geomorphological interpretation method,” Geomorphology 231, 314–330 (2015).
[Crossref]

2014 (3)

P. Daga, T. Pendse, M. Modat, M. White, L. Mancini, G. P. Winston, A. W. McEvoy, J. Thornton, T. Yousry, I. Drobnjakand, and J. S. Duncan, “Susceptibility artifact correction using dynamic graph cuts: Application to neurosurgery,” Med. Image Anal. 18, 1132–1142 (2014).
[Crossref]

B. N. Li, X. Shan, K. Xiang, N. An, J. Xu, W. Huang, and E. Kobayashi, “Evaluation of robust wave image processing methods for magnetic resonance elastography,” Comput. Biol. Med. 54, 100–108 (2014).
[Crossref]

Y. Guo, X. Chen, and T. Zhang, “Robust phase unwrapping algorithm based on least squares,” Opt. Laser Eng. 63, 25–29 (2014).
[Crossref]

2012 (1)

H. Xia, R. Guo, Z. Fan, H. Cheng, and B. Yang, “Non-invasive mechanical measurement for transparent objects by digital holographic interferometry based on iterative least-squares phase unwrapping,” Exp. Mech. 52, 439–445 (2012).
[Crossref]

2011 (1)

2004 (2)

A. Criminisi, P. Pérez, and K. Toyama, “Region filling and object removal by exemplar-based image inpainting,” IEEE Trans. Image Process. 13, 1200–1212 (2004).
[Crossref]

Q. Kemao, “Windowed Fourier transform for fringe pattern analysis,” Appl. Opt. 43, 2695–2702 (2004).
[Crossref]

Acosta, G. G.

S. A. Villar, S. Torcida, and G. G. Acosta, “Median filtering: a new insight,” J. Math. Imaging Vis. 58, 130–146 (2017).
[Crossref]

An, D.

H. Yu, Y. Lan, J. Xu, D. An, and H. Lee, “Large-scale L0-norm and L1-norm 2-D phase unwrapping,” IEEE Trans. Geosci. Remote Sensing 55, 4712–4728 (2017).
[Crossref]

J. Xu, D. An, X. Huang, and P. Yi, “An efficient minimum-discontinuity phase-unwrapping method,” IEEE Geosci. Remote Sens. Lett. 13, 666–670 (2016).
[Crossref]

An, N.

B. N. Li, X. Shan, K. Xiang, N. An, J. Xu, W. Huang, and E. Kobayashi, “Evaluation of robust wave image processing methods for magnetic resonance elastography,” Comput. Biol. Med. 54, 100–108 (2014).
[Crossref]

Arevalillo-Herráez, M.

M. Arevalillo-Herráez, F. R. Villatoro, and M. A. Gdeisat, “A robust and simple measure for quality-guided 2D phase unwrapping algorithms,” IEEE Trans. Image Process. 25, 2601–2609 (2016).
[Crossref]

Asundi, A.

Boppart, S. A.

Bui, V.

Carney, P. S.

Chang, L.-C.

Chen, F.

J. Dong, F. Chen, D. Zhou, T. Liu, Z. Yu, and Y. Wang, “Phase unwrapping with graph cuts optimization and dual decomposition acceleration for 3D high-resolution MRI data,” Magn. Reson. Med. 77, 1353–1358 (2017).
[Crossref]

Chen, Q.

Chen, X.

Y. Guo, X. Chen, and T. Zhang, “Robust phase unwrapping algorithm based on least squares,” Opt. Laser Eng. 63, 25–29 (2014).
[Crossref]

Cheng, H.

H. Xia, S. Montresor, R. Guo, J. C. Li, F. Yan, H. Cheng, and P. Picart, “Phase calibration unwrapping algorithm for phase data corrupted by strong decorrelation speckle noise,” Opt. Express 24, 28713–28730 (2016).
[Crossref]

H. Xia, R. Guo, Z. Fan, H. Cheng, and B. Yang, “Non-invasive mechanical measurement for transparent objects by digital holographic interferometry based on iterative least-squares phase unwrapping,” Exp. Mech. 52, 439–445 (2012).
[Crossref]

Criminisi, A.

A. Criminisi, P. Pérez, and K. Toyama, “Region filling and object removal by exemplar-based image inpainting,” IEEE Trans. Image Process. 13, 1200–1212 (2004).
[Crossref]

Da, F.

Daga, P.

P. Daga, T. Pendse, M. Modat, M. White, L. Mancini, G. P. Winston, A. W. McEvoy, J. Thornton, T. Yousry, I. Drobnjakand, and J. S. Duncan, “Susceptibility artifact correction using dynamic graph cuts: Application to neurosurgery,” Med. Image Anal. 18, 1132–1142 (2014).
[Crossref]

Darga, D.

de Souza, J.

Desse, J.-M.

Dong, J.

J. Dong, F. Chen, D. Zhou, T. Liu, Z. Yu, and Y. Wang, “Phase unwrapping with graph cuts optimization and dual decomposition acceleration for 3D high-resolution MRI data,” Magn. Reson. Med. 77, 1353–1358 (2017).
[Crossref]

dos Santos, P.

Doubre, C.

R. Schlögel, C. Doubre, J. P. Malet, and F. Masson, “Landslide deformation monitoring with ALOS/PALSAR imagery: a D-InSAR geomorphological interpretation method,” Geomorphology 231, 314–330 (2015).
[Crossref]

Drobnjakand, I.

P. Daga, T. Pendse, M. Modat, M. White, L. Mancini, G. P. Winston, A. W. McEvoy, J. Thornton, T. Yousry, I. Drobnjakand, and J. S. Duncan, “Susceptibility artifact correction using dynamic graph cuts: Application to neurosurgery,” Med. Image Anal. 18, 1132–1142 (2014).
[Crossref]

Du, G.

G. Du, C. Zhang, C. Zhou, S. Si, H. Li, and Y. Li, “Iterative two-step temporal phase-unwrapping applied to high sensitivity three-dimensional profilometry,” Opt. Lasers Eng. 79, 22–28 (2016).
[Crossref]

Duncan, J. S.

P. Daga, T. Pendse, M. Modat, M. White, L. Mancini, G. P. Winston, A. W. McEvoy, J. Thornton, T. Yousry, I. Drobnjakand, and J. S. Duncan, “Susceptibility artifact correction using dynamic graph cuts: Application to neurosurgery,” Med. Image Anal. 18, 1132–1142 (2014).
[Crossref]

Durand, J. C.

H. Xia, P. Picart, S. Montresor, R. Guo, J. C. Li, O. Yusuf-Solieman, J. C. Durand, and M. Fages, “Mechanical behavior of CAD/CAM occlusal ceramic reconstruction assessed by digital color holography,” Dent. Mater. 34, 1222–1234 (2018).
[Crossref]

Estrada, J. C.

J. C. Estrada, J. L. Marroquin, and O. M. Medina, “Reconstruction of local frequencies for recovering the unwrapped phase in optical interferometry,” Sci. Rep. 7, 6727 (2017).
[Crossref]

Fages, M.

H. Xia, P. Picart, S. Montresor, R. Guo, J. C. Li, O. Yusuf-Solieman, J. C. Durand, and M. Fages, “Mechanical behavior of CAD/CAM occlusal ceramic reconstruction assessed by digital color holography,” Dent. Mater. 34, 1222–1234 (2018).
[Crossref]

Fan, Z.

H. Xia, R. Guo, Z. Fan, H. Cheng, and B. Yang, “Non-invasive mechanical measurement for transparent objects by digital holographic interferometry based on iterative least-squares phase unwrapping,” Exp. Mech. 52, 439–445 (2012).
[Crossref]

Feng, S.

Gao, J.

J. Gao, “Reliability-map-guided phase unwrapping method,” IEEE Geosci. Remote Sens. Lett. 13, 716–720 (2016).
[Crossref]

Garnica, G.

Gdeisat, M. A.

M. Arevalillo-Herráez, F. R. Villatoro, and M. A. Gdeisat, “A robust and simple measure for quality-guided 2D phase unwrapping algorithms,” IEEE Trans. Image Process. 25, 2601–2609 (2016).
[Crossref]

Ghiglia, D. C.

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, 1998).

Gonzalez, A.

M. Rivera, F. J. Hernandez-Lopez, and A. Gonzalez, “Phase unwrapping by accumulation of residual maps,” Opt. Laser Eng. 64, 51–58 (2015).
[Crossref]

Goodman, J. W.

J. W. Goodman, Speckle Phenomena in Optics (Roberts and Company Publishers, 2006).

Guo, R.

H. Xia, S. Montresor, P. Picart, R. Guo, and J. C. Li, “Comparative analysis for combination of unwrapping and de-noising of phase data with high speckle decorrelation noise,” Opt. Laser Eng. 107, 71–77 (2018).
[Crossref]

H. Xia, P. Picart, S. Montresor, R. Guo, J. C. Li, O. Yusuf-Solieman, J. C. Durand, and M. Fages, “Mechanical behavior of CAD/CAM occlusal ceramic reconstruction assessed by digital color holography,” Dent. Mater. 34, 1222–1234 (2018).
[Crossref]

H. Xia, S. Montresor, R. Guo, J. C. Li, F. Olchewsky, J.-M. Desse, and P. Picart, “Robust processing of phase dislocations based on combined unwrapping and inpainting approaches,” Opt. Lett. 42, 322–325 (2017).
[Crossref]

H. Xia, S. Montresor, R. Guo, J. C. Li, F. Yan, H. Cheng, and P. Picart, “Phase calibration unwrapping algorithm for phase data corrupted by strong decorrelation speckle noise,” Opt. Express 24, 28713–28730 (2016).
[Crossref]

H. Xia, R. Guo, Z. Fan, H. Cheng, and B. Yang, “Non-invasive mechanical measurement for transparent objects by digital holographic interferometry based on iterative least-squares phase unwrapping,” Exp. Mech. 52, 439–445 (2012).
[Crossref]

Guo, Y.

Y. Guo, X. Chen, and T. Zhang, “Robust phase unwrapping algorithm based on least squares,” Opt. Laser Eng. 63, 25–29 (2014).
[Crossref]

Har, D.

Hernandez-Lopez, F. J.

M. Rivera, F. J. Hernandez-Lopez, and A. Gonzalez, “Phase unwrapping by accumulation of residual maps,” Opt. Laser Eng. 64, 51–58 (2015).
[Crossref]

Hu, Y.

Huang, D.

Huang, L.

Huang, W.

B. N. Li, X. Shan, K. Xiang, N. An, J. Xu, W. Huang, and E. Kobayashi, “Evaluation of robust wave image processing methods for magnetic resonance elastography,” Comput. Biol. Med. 54, 100–108 (2014).
[Crossref]

Huang, X.

J. Xu, D. An, X. Huang, and P. Yi, “An efficient minimum-discontinuity phase-unwrapping method,” IEEE Geosci. Remote Sens. Lett. 13, 666–670 (2016).
[Crossref]

Huang, Y.

S. Xia, Y. Huang, S. Peng, Y. Wu, and X. Tan, “Robust phase unwrapping for phase images in Fourier domain Doppler optical coherence tomography,” J. Biomed. Opt. 22, 36014 (2017).
[Crossref]

Jafarfard, M.

Jia, Y.

M. Wang, F. Li, M. Zheng, W. Lu, Y. Jia, Q. Yu, S. Zhao, and J. Wu, “Realization of absolute-phase unwrapping and speckle suppression in laser digital holography,” Ann. Phys. (Berlin) 529, 1600378 (2017).
[Crossref]

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Z. Jiang, J. Wang, Q. Song, and Z. Zhou, “A refined cluster-analysis-based multibaseline phase-unwrapping algorithm,” IEEE Geosci. Remote Sens. Lett. 14, 1565–1569 (2017).
[Crossref]

Kemao, Q.

Kim, D.

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B. N. Li, X. Shan, K. Xiang, N. An, J. Xu, W. Huang, and E. Kobayashi, “Evaluation of robust wave image processing methods for magnetic resonance elastography,” Comput. Biol. Med. 54, 100–108 (2014).
[Crossref]

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Lan, Y.

H. Yu, Y. Lan, J. Xu, D. An, and H. Lee, “Large-scale L0-norm and L1-norm 2-D phase unwrapping,” IEEE Trans. Geosci. Remote Sensing 55, 4712–4728 (2017).
[Crossref]

H. Yu and Y. Lan, “Robust two-dimensional phase unwrapping for multibaseline SAR interferograms: A two-stage programming approach,” IEEE Trans. Geosci. Remote Sensing 54, 5217–5225 (2016).
[Crossref]

Lee, H.

H. Yu, Y. Lan, J. Xu, D. An, and H. Lee, “Large-scale L0-norm and L1-norm 2-D phase unwrapping,” IEEE Trans. Geosci. Remote Sensing 55, 4712–4728 (2017).
[Crossref]

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B. N. Li, X. Shan, K. Xiang, N. An, J. Xu, W. Huang, and E. Kobayashi, “Evaluation of robust wave image processing methods for magnetic resonance elastography,” Comput. Biol. Med. 54, 100–108 (2014).
[Crossref]

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M. Wang, F. Li, M. Zheng, W. Lu, Y. Jia, Q. Yu, S. Zhao, and J. Wu, “Realization of absolute-phase unwrapping and speckle suppression in laser digital holography,” Ann. Phys. (Berlin) 529, 1600378 (2017).
[Crossref]

Li, H.

M. Zhang, Q. Chen, T. Tao, S. Feng, Y. Hu, H. Li, and C. Zuo, “Robust and efficient multi-frequency temporal phase unwrapping: optimal fringe frequency and pattern sequence selection,” Opt. Express 25, 20381–20400 (2017).
[Crossref]

G. Du, C. Zhang, C. Zhou, S. Si, H. Li, and Y. Li, “Iterative two-step temporal phase-unwrapping applied to high sensitivity three-dimensional profilometry,” Opt. Lasers Eng. 79, 22–28 (2016).
[Crossref]

Li, J. C.

H. Xia, S. Montresor, P. Picart, R. Guo, and J. C. Li, “Comparative analysis for combination of unwrapping and de-noising of phase data with high speckle decorrelation noise,” Opt. Laser Eng. 107, 71–77 (2018).
[Crossref]

H. Xia, P. Picart, S. Montresor, R. Guo, J. C. Li, O. Yusuf-Solieman, J. C. Durand, and M. Fages, “Mechanical behavior of CAD/CAM occlusal ceramic reconstruction assessed by digital color holography,” Dent. Mater. 34, 1222–1234 (2018).
[Crossref]

H. Xia, S. Montresor, R. Guo, J. C. Li, F. Olchewsky, J.-M. Desse, and P. Picart, “Robust processing of phase dislocations based on combined unwrapping and inpainting approaches,” Opt. Lett. 42, 322–325 (2017).
[Crossref]

H. Xia, S. Montresor, R. Guo, J. C. Li, F. Yan, H. Cheng, and P. Picart, “Phase calibration unwrapping algorithm for phase data corrupted by strong decorrelation speckle noise,” Opt. Express 24, 28713–28730 (2016).
[Crossref]

Li, Y.

G. Du, C. Zhang, C. Zhou, S. Si, H. Li, and Y. Li, “Iterative two-step temporal phase-unwrapping applied to high sensitivity three-dimensional profilometry,” Opt. Lasers Eng. 79, 22–28 (2016).
[Crossref]

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J. Dong, F. Chen, D. Zhou, T. Liu, Z. Yu, and Y. Wang, “Phase unwrapping with graph cuts optimization and dual decomposition acceleration for 3D high-resolution MRI data,” Magn. Reson. Med. 77, 1353–1358 (2017).
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M. Wang, F. Li, M. Zheng, W. Lu, Y. Jia, Q. Yu, S. Zhao, and J. Wu, “Realization of absolute-phase unwrapping and speckle suppression in laser digital holography,” Ann. Phys. (Berlin) 529, 1600378 (2017).
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R. Schlögel, C. Doubre, J. P. Malet, and F. Masson, “Landslide deformation monitoring with ALOS/PALSAR imagery: a D-InSAR geomorphological interpretation method,” Geomorphology 231, 314–330 (2015).
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P. Daga, T. Pendse, M. Modat, M. White, L. Mancini, G. P. Winston, A. W. McEvoy, J. Thornton, T. Yousry, I. Drobnjakand, and J. S. Duncan, “Susceptibility artifact correction using dynamic graph cuts: Application to neurosurgery,” Med. Image Anal. 18, 1132–1142 (2014).
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P. Daga, T. Pendse, M. Modat, M. White, L. Mancini, G. P. Winston, A. W. McEvoy, J. Thornton, T. Yousry, I. Drobnjakand, and J. S. Duncan, “Susceptibility artifact correction using dynamic graph cuts: Application to neurosurgery,” Med. Image Anal. 18, 1132–1142 (2014).
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J. C. Estrada, J. L. Marroquin, and O. M. Medina, “Reconstruction of local frequencies for recovering the unwrapped phase in optical interferometry,” Sci. Rep. 7, 6727 (2017).
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P. Daga, T. Pendse, M. Modat, M. White, L. Mancini, G. P. Winston, A. W. McEvoy, J. Thornton, T. Yousry, I. Drobnjakand, and J. S. Duncan, “Susceptibility artifact correction using dynamic graph cuts: Application to neurosurgery,” Med. Image Anal. 18, 1132–1142 (2014).
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H. Xia, S. Montresor, P. Picart, R. Guo, and J. C. Li, “Comparative analysis for combination of unwrapping and de-noising of phase data with high speckle decorrelation noise,” Opt. Laser Eng. 107, 71–77 (2018).
[Crossref]

H. Xia, P. Picart, S. Montresor, R. Guo, J. C. Li, O. Yusuf-Solieman, J. C. Durand, and M. Fages, “Mechanical behavior of CAD/CAM occlusal ceramic reconstruction assessed by digital color holography,” Dent. Mater. 34, 1222–1234 (2018).
[Crossref]

H. Xia, S. Montresor, R. Guo, J. C. Li, F. Olchewsky, J.-M. Desse, and P. Picart, “Robust processing of phase dislocations based on combined unwrapping and inpainting approaches,” Opt. Lett. 42, 322–325 (2017).
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S. Montresor and P. Picart, “Quantitative appraisal for noise reduction in digital holographic phase imaging,” Opt. Express 24, 14322–14343 (2016).
[Crossref]

H. Xia, S. Montresor, R. Guo, J. C. Li, F. Yan, H. Cheng, and P. Picart, “Phase calibration unwrapping algorithm for phase data corrupted by strong decorrelation speckle noise,” Opt. Express 24, 28713–28730 (2016).
[Crossref]

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Nguyen, T.

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P. Daga, T. Pendse, M. Modat, M. White, L. Mancini, G. P. Winston, A. W. McEvoy, J. Thornton, T. Yousry, I. Drobnjakand, and J. S. Duncan, “Susceptibility artifact correction using dynamic graph cuts: Application to neurosurgery,” Med. Image Anal. 18, 1132–1142 (2014).
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S. Xia, Y. Huang, S. Peng, Y. Wu, and X. Tan, “Robust phase unwrapping for phase images in Fourier domain Doppler optical coherence tomography,” J. Biomed. Opt. 22, 36014 (2017).
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A. Criminisi, P. Pérez, and K. Toyama, “Region filling and object removal by exemplar-based image inpainting,” IEEE Trans. Image Process. 13, 1200–1212 (2004).
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H. Xia, P. Picart, S. Montresor, R. Guo, J. C. Li, O. Yusuf-Solieman, J. C. Durand, and M. Fages, “Mechanical behavior of CAD/CAM occlusal ceramic reconstruction assessed by digital color holography,” Dent. Mater. 34, 1222–1234 (2018).
[Crossref]

H. Xia, S. Montresor, P. Picart, R. Guo, and J. C. Li, “Comparative analysis for combination of unwrapping and de-noising of phase data with high speckle decorrelation noise,” Opt. Laser Eng. 107, 71–77 (2018).
[Crossref]

H. Xia, S. Montresor, R. Guo, J. C. Li, F. Olchewsky, J.-M. Desse, and P. Picart, “Robust processing of phase dislocations based on combined unwrapping and inpainting approaches,” Opt. Lett. 42, 322–325 (2017).
[Crossref]

H. Xia, S. Montresor, R. Guo, J. C. Li, F. Yan, H. Cheng, and P. Picart, “Phase calibration unwrapping algorithm for phase data corrupted by strong decorrelation speckle noise,” Opt. Express 24, 28713–28730 (2016).
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S. Montresor and P. Picart, “Quantitative appraisal for noise reduction in digital holographic phase imaging,” Opt. Express 24, 14322–14343 (2016).
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D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, 1998).

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R. Schlögel, C. Doubre, J. P. Malet, and F. Masson, “Landslide deformation monitoring with ALOS/PALSAR imagery: a D-InSAR geomorphological interpretation method,” Geomorphology 231, 314–330 (2015).
[Crossref]

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Servin, M.

Shaked, N. T.

Shan, X.

B. N. Li, X. Shan, K. Xiang, N. An, J. Xu, W. Huang, and E. Kobayashi, “Evaluation of robust wave image processing methods for magnetic resonance elastography,” Comput. Biol. Med. 54, 100–108 (2014).
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Sharif, F.

Si, S.

G. Du, C. Zhang, C. Zhou, S. Si, H. Li, and Y. Li, “Iterative two-step temporal phase-unwrapping applied to high sensitivity three-dimensional profilometry,” Opt. Lasers Eng. 79, 22–28 (2016).
[Crossref]

Smid, J.

Song, Q.

Z. Jiang, J. Wang, Q. Song, and Z. Zhou, “A refined cluster-analysis-based multibaseline phase-unwrapping algorithm,” IEEE Geosci. Remote Sens. Lett. 14, 1565–1569 (2017).
[Crossref]

Song, Y.

Su, X.

Su, Y.

Tan, X.

S. Xia, Y. Huang, S. Peng, Y. Wu, and X. Tan, “Robust phase unwrapping for phase images in Fourier domain Doppler optical coherence tomography,” J. Biomed. Opt. 22, 36014 (2017).
[Crossref]

Tao, T.

Tayebi, B.

Teh, D.

Thornton, J.

P. Daga, T. Pendse, M. Modat, M. White, L. Mancini, G. P. Winston, A. W. McEvoy, J. Thornton, T. Yousry, I. Drobnjakand, and J. S. Duncan, “Susceptibility artifact correction using dynamic graph cuts: Application to neurosurgery,” Med. Image Anal. 18, 1132–1142 (2014).
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S. A. Villar, S. Torcida, and G. G. Acosta, “Median filtering: a new insight,” J. Math. Imaging Vis. 58, 130–146 (2017).
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A. Criminisi, P. Pérez, and K. Toyama, “Region filling and object removal by exemplar-based image inpainting,” IEEE Trans. Image Process. 13, 1200–1212 (2004).
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S. A. Villar, S. Torcida, and G. G. Acosta, “Median filtering: a new insight,” J. Math. Imaging Vis. 58, 130–146 (2017).
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M. Arevalillo-Herráez, F. R. Villatoro, and M. A. Gdeisat, “A robust and simple measure for quality-guided 2D phase unwrapping algorithms,” IEEE Trans. Image Process. 25, 2601–2609 (2016).
[Crossref]

Wang, J.

Z. Jiang, J. Wang, Q. Song, and Z. Zhou, “A refined cluster-analysis-based multibaseline phase-unwrapping algorithm,” IEEE Geosci. Remote Sens. Lett. 14, 1565–1569 (2017).
[Crossref]

Wang, M.

M. Wang, F. Li, M. Zheng, W. Lu, Y. Jia, Q. Yu, S. Zhao, and J. Wu, “Realization of absolute-phase unwrapping and speckle suppression in laser digital holography,” Ann. Phys. (Berlin) 529, 1600378 (2017).
[Crossref]

Wang, Y.

J. Dong, F. Chen, D. Zhou, T. Liu, Z. Yu, and Y. Wang, “Phase unwrapping with graph cuts optimization and dual decomposition acceleration for 3D high-resolution MRI data,” Magn. Reson. Med. 77, 1353–1358 (2017).
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Y. Wang, D. Huang, Y. Su, and X. S. Yao, “Two-dimensional phase unwrapping in Doppler Fourier domain optical coherence tomography,” Opt. Express 24, 26129–26145 (2016).
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P. Daga, T. Pendse, M. Modat, M. White, L. Mancini, G. P. Winston, A. W. McEvoy, J. Thornton, T. Yousry, I. Drobnjakand, and J. S. Duncan, “Susceptibility artifact correction using dynamic graph cuts: Application to neurosurgery,” Med. Image Anal. 18, 1132–1142 (2014).
[Crossref]

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P. Daga, T. Pendse, M. Modat, M. White, L. Mancini, G. P. Winston, A. W. McEvoy, J. Thornton, T. Yousry, I. Drobnjakand, and J. S. Duncan, “Susceptibility artifact correction using dynamic graph cuts: Application to neurosurgery,” Med. Image Anal. 18, 1132–1142 (2014).
[Crossref]

Wu, J.

M. Wang, F. Li, M. Zheng, W. Lu, Y. Jia, Q. Yu, S. Zhao, and J. Wu, “Realization of absolute-phase unwrapping and speckle suppression in laser digital holography,” Ann. Phys. (Berlin) 529, 1600378 (2017).
[Crossref]

Wu, S.

Wu, Y.

S. Xia, Y. Huang, S. Peng, Y. Wu, and X. Tan, “Robust phase unwrapping for phase images in Fourier domain Doppler optical coherence tomography,” J. Biomed. Opt. 22, 36014 (2017).
[Crossref]

Xia, H.

H. Xia, S. Montresor, P. Picart, R. Guo, and J. C. Li, “Comparative analysis for combination of unwrapping and de-noising of phase data with high speckle decorrelation noise,” Opt. Laser Eng. 107, 71–77 (2018).
[Crossref]

H. Xia, P. Picart, S. Montresor, R. Guo, J. C. Li, O. Yusuf-Solieman, J. C. Durand, and M. Fages, “Mechanical behavior of CAD/CAM occlusal ceramic reconstruction assessed by digital color holography,” Dent. Mater. 34, 1222–1234 (2018).
[Crossref]

H. Xia, S. Montresor, R. Guo, J. C. Li, F. Olchewsky, J.-M. Desse, and P. Picart, “Robust processing of phase dislocations based on combined unwrapping and inpainting approaches,” Opt. Lett. 42, 322–325 (2017).
[Crossref]

H. Xia, S. Montresor, R. Guo, J. C. Li, F. Yan, H. Cheng, and P. Picart, “Phase calibration unwrapping algorithm for phase data corrupted by strong decorrelation speckle noise,” Opt. Express 24, 28713–28730 (2016).
[Crossref]

H. Xia, R. Guo, Z. Fan, H. Cheng, and B. Yang, “Non-invasive mechanical measurement for transparent objects by digital holographic interferometry based on iterative least-squares phase unwrapping,” Exp. Mech. 52, 439–445 (2012).
[Crossref]

Xia, S.

S. Xia, Y. Huang, S. Peng, Y. Wu, and X. Tan, “Robust phase unwrapping for phase images in Fourier domain Doppler optical coherence tomography,” J. Biomed. Opt. 22, 36014 (2017).
[Crossref]

Xiang, K.

B. N. Li, X. Shan, K. Xiang, N. An, J. Xu, W. Huang, and E. Kobayashi, “Evaluation of robust wave image processing methods for magnetic resonance elastography,” Comput. Biol. Med. 54, 100–108 (2014).
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Xie, X.

Xu, J.

H. Yu, Y. Lan, J. Xu, D. An, and H. Lee, “Large-scale L0-norm and L1-norm 2-D phase unwrapping,” IEEE Trans. Geosci. Remote Sensing 55, 4712–4728 (2017).
[Crossref]

J. Xu, D. An, X. Huang, and P. Yi, “An efficient minimum-discontinuity phase-unwrapping method,” IEEE Geosci. Remote Sens. Lett. 13, 666–670 (2016).
[Crossref]

B. N. Li, X. Shan, K. Xiang, N. An, J. Xu, W. Huang, and E. Kobayashi, “Evaluation of robust wave image processing methods for magnetic resonance elastography,” Comput. Biol. Med. 54, 100–108 (2014).
[Crossref]

Xu, Y.

Yan, F.

Yang, B.

H. Xia, R. Guo, Z. Fan, H. Cheng, and B. Yang, “Non-invasive mechanical measurement for transparent objects by digital holographic interferometry based on iterative least-squares phase unwrapping,” Exp. Mech. 52, 439–445 (2012).
[Crossref]

Yang, L.

Yao, X. S.

Yi, P.

J. Xu, D. An, X. Huang, and P. Yi, “An efficient minimum-discontinuity phase-unwrapping method,” IEEE Geosci. Remote Sens. Lett. 13, 666–670 (2016).
[Crossref]

Yousry, T.

P. Daga, T. Pendse, M. Modat, M. White, L. Mancini, G. P. Winston, A. W. McEvoy, J. Thornton, T. Yousry, I. Drobnjakand, and J. S. Duncan, “Susceptibility artifact correction using dynamic graph cuts: Application to neurosurgery,” Med. Image Anal. 18, 1132–1142 (2014).
[Crossref]

Yu, H.

H. Yu, Y. Lan, J. Xu, D. An, and H. Lee, “Large-scale L0-norm and L1-norm 2-D phase unwrapping,” IEEE Trans. Geosci. Remote Sensing 55, 4712–4728 (2017).
[Crossref]

H. Yu and Y. Lan, “Robust two-dimensional phase unwrapping for multibaseline SAR interferograms: A two-stage programming approach,” IEEE Trans. Geosci. Remote Sensing 54, 5217–5225 (2016).
[Crossref]

Yu, Q.

M. Wang, F. Li, M. Zheng, W. Lu, Y. Jia, Q. Yu, S. Zhao, and J. Wu, “Realization of absolute-phase unwrapping and speckle suppression in laser digital holography,” Ann. Phys. (Berlin) 529, 1600378 (2017).
[Crossref]

Yu, Z.

J. Dong, F. Chen, D. Zhou, T. Liu, Z. Yu, and Y. Wang, “Phase unwrapping with graph cuts optimization and dual decomposition acceleration for 3D high-resolution MRI data,” Magn. Reson. Med. 77, 1353–1358 (2017).
[Crossref]

Yusuf-Solieman, O.

H. Xia, P. Picart, S. Montresor, R. Guo, J. C. Li, O. Yusuf-Solieman, J. C. Durand, and M. Fages, “Mechanical behavior of CAD/CAM occlusal ceramic reconstruction assessed by digital color holography,” Dent. Mater. 34, 1222–1234 (2018).
[Crossref]

Zhang, C.

G. Du, C. Zhang, C. Zhou, S. Si, H. Li, and Y. Li, “Iterative two-step temporal phase-unwrapping applied to high sensitivity three-dimensional profilometry,” Opt. Lasers Eng. 79, 22–28 (2016).
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Zhang, M.

Zhang, Q.

Zhang, T.

Y. Guo, X. Chen, and T. Zhang, “Robust phase unwrapping algorithm based on least squares,” Opt. Laser Eng. 63, 25–29 (2014).
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Zhao, S.

M. Wang, F. Li, M. Zheng, W. Lu, Y. Jia, Q. Yu, S. Zhao, and J. Wu, “Realization of absolute-phase unwrapping and speckle suppression in laser digital holography,” Ann. Phys. (Berlin) 529, 1600378 (2017).
[Crossref]

Zheng, D.

Zheng, M.

M. Wang, F. Li, M. Zheng, W. Lu, Y. Jia, Q. Yu, S. Zhao, and J. Wu, “Realization of absolute-phase unwrapping and speckle suppression in laser digital holography,” Ann. Phys. (Berlin) 529, 1600378 (2017).
[Crossref]

Zhou, C.

G. Du, C. Zhang, C. Zhou, S. Si, H. Li, and Y. Li, “Iterative two-step temporal phase-unwrapping applied to high sensitivity three-dimensional profilometry,” Opt. Lasers Eng. 79, 22–28 (2016).
[Crossref]

Zhou, D.

J. Dong, F. Chen, D. Zhou, T. Liu, Z. Yu, and Y. Wang, “Phase unwrapping with graph cuts optimization and dual decomposition acceleration for 3D high-resolution MRI data,” Magn. Reson. Med. 77, 1353–1358 (2017).
[Crossref]

Zhou, Z.

Z. Jiang, J. Wang, Q. Song, and Z. Zhou, “A refined cluster-analysis-based multibaseline phase-unwrapping algorithm,” IEEE Geosci. Remote Sens. Lett. 14, 1565–1569 (2017).
[Crossref]

Zhu, L.

Zuo, C.

Zysk, A. M.

Ann. Phys. (Berlin) (1)

M. Wang, F. Li, M. Zheng, W. Lu, Y. Jia, Q. Yu, S. Zhao, and J. Wu, “Realization of absolute-phase unwrapping and speckle suppression in laser digital holography,” Ann. Phys. (Berlin) 529, 1600378 (2017).
[Crossref]

Appl. Opt. (2)

Comput. Biol. Med. (1)

B. N. Li, X. Shan, K. Xiang, N. An, J. Xu, W. Huang, and E. Kobayashi, “Evaluation of robust wave image processing methods for magnetic resonance elastography,” Comput. Biol. Med. 54, 100–108 (2014).
[Crossref]

Dent. Mater. (1)

H. Xia, P. Picart, S. Montresor, R. Guo, J. C. Li, O. Yusuf-Solieman, J. C. Durand, and M. Fages, “Mechanical behavior of CAD/CAM occlusal ceramic reconstruction assessed by digital color holography,” Dent. Mater. 34, 1222–1234 (2018).
[Crossref]

Exp. Mech. (1)

H. Xia, R. Guo, Z. Fan, H. Cheng, and B. Yang, “Non-invasive mechanical measurement for transparent objects by digital holographic interferometry based on iterative least-squares phase unwrapping,” Exp. Mech. 52, 439–445 (2012).
[Crossref]

Geomorphology (1)

R. Schlögel, C. Doubre, J. P. Malet, and F. Masson, “Landslide deformation monitoring with ALOS/PALSAR imagery: a D-InSAR geomorphological interpretation method,” Geomorphology 231, 314–330 (2015).
[Crossref]

IEEE Geosci. Remote Sens. Lett. (3)

Z. Jiang, J. Wang, Q. Song, and Z. Zhou, “A refined cluster-analysis-based multibaseline phase-unwrapping algorithm,” IEEE Geosci. Remote Sens. Lett. 14, 1565–1569 (2017).
[Crossref]

J. Gao, “Reliability-map-guided phase unwrapping method,” IEEE Geosci. Remote Sens. Lett. 13, 716–720 (2016).
[Crossref]

J. Xu, D. An, X. Huang, and P. Yi, “An efficient minimum-discontinuity phase-unwrapping method,” IEEE Geosci. Remote Sens. Lett. 13, 666–670 (2016).
[Crossref]

IEEE Trans. Geosci. Remote Sensing (2)

H. Yu and Y. Lan, “Robust two-dimensional phase unwrapping for multibaseline SAR interferograms: A two-stage programming approach,” IEEE Trans. Geosci. Remote Sensing 54, 5217–5225 (2016).
[Crossref]

H. Yu, Y. Lan, J. Xu, D. An, and H. Lee, “Large-scale L0-norm and L1-norm 2-D phase unwrapping,” IEEE Trans. Geosci. Remote Sensing 55, 4712–4728 (2017).
[Crossref]

IEEE Trans. Image Process. (2)

A. Criminisi, P. Pérez, and K. Toyama, “Region filling and object removal by exemplar-based image inpainting,” IEEE Trans. Image Process. 13, 1200–1212 (2004).
[Crossref]

M. Arevalillo-Herráez, F. R. Villatoro, and M. A. Gdeisat, “A robust and simple measure for quality-guided 2D phase unwrapping algorithms,” IEEE Trans. Image Process. 25, 2601–2609 (2016).
[Crossref]

J. Biomed. Opt. (1)

S. Xia, Y. Huang, S. Peng, Y. Wu, and X. Tan, “Robust phase unwrapping for phase images in Fourier domain Doppler optical coherence tomography,” J. Biomed. Opt. 22, 36014 (2017).
[Crossref]

J. Math. Imaging Vis. (1)

S. A. Villar, S. Torcida, and G. G. Acosta, “Median filtering: a new insight,” J. Math. Imaging Vis. 58, 130–146 (2017).
[Crossref]

Magn. Reson. Med. (1)

J. Dong, F. Chen, D. Zhou, T. Liu, Z. Yu, and Y. Wang, “Phase unwrapping with graph cuts optimization and dual decomposition acceleration for 3D high-resolution MRI data,” Magn. Reson. Med. 77, 1353–1358 (2017).
[Crossref]

Med. Image Anal. (1)

P. Daga, T. Pendse, M. Modat, M. White, L. Mancini, G. P. Winston, A. W. McEvoy, J. Thornton, T. Yousry, I. Drobnjakand, and J. S. Duncan, “Susceptibility artifact correction using dynamic graph cuts: Application to neurosurgery,” Med. Image Anal. 18, 1132–1142 (2014).
[Crossref]

Opt. Express (9)

B. Tayebi, M. Jafarfard, F. Sharif, Y. Song, D. Har, and D. Kim, “Large step-phase measurement by a reduced-phase triple-illumination interferometer,” Opt. Express 23, 11264–11271 (2015).
[Crossref]

Y. Wang, D. Huang, Y. Su, and X. S. Yao, “Two-dimensional phase unwrapping in Doppler Fourier domain optical coherence tomography,” Opt. Express 24, 26129–26145 (2016).
[Crossref]

H. Xia, S. Montresor, R. Guo, J. C. Li, F. Yan, H. Cheng, and P. Picart, “Phase calibration unwrapping algorithm for phase data corrupted by strong decorrelation speckle noise,” Opt. Express 24, 28713–28730 (2016).
[Crossref]

D. Zheng, F. Da, Q. Kemao, and H. S. Seah, “Phase-shifting profilometry combined with Gray-code patterns projection: unwrapping error removal by an adaptive median filter,” Opt. Express 25, 4700–4713 (2017).
[Crossref]

T. Nguyen, V. Bui, V. Lam, C. B. Raub, L.-C. Chang, and G. Nehmetallah, “Automatic phase aberration compensation for digital holographic microscopy based on deep learning background detection,” Opt. Express 25, 15043–15057 (2017).
[Crossref]

M. Zhang, Q. Chen, T. Tao, S. Feng, Y. Hu, H. Li, and C. Zuo, “Robust and efficient multi-frequency temporal phase unwrapping: optimal fringe frequency and pattern sequence selection,” Opt. Express 25, 20381–20400 (2017).
[Crossref]

M. Padilla, M. Servin, and G. Garnica, “Profilometry with digital fringe-projection at the spatial and temporal Nyquist frequencies,” Opt. Express 25, 22292–22302 (2017).
[Crossref]

S. Montresor and P. Picart, “Quantitative appraisal for noise reduction in digital holographic phase imaging,” Opt. Express 24, 14322–14343 (2016).
[Crossref]

X. Xie, “Iterated unscented Kalman filter for phase unwrapping of interferometric fringes,” Opt. Express 24, 18872–18897 (2016).
[Crossref]

Opt. Laser Eng. (4)

M. Rivera, F. J. Hernandez-Lopez, and A. Gonzalez, “Phase unwrapping by accumulation of residual maps,” Opt. Laser Eng. 64, 51–58 (2015).
[Crossref]

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[Crossref]

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[Crossref]

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[Crossref]

Opt. Lasers Eng. (1)

G. Du, C. Zhang, C. Zhou, S. Si, H. Li, and Y. Li, “Iterative two-step temporal phase-unwrapping applied to high sensitivity three-dimensional profilometry,” Opt. Lasers Eng. 79, 22–28 (2016).
[Crossref]

Opt. Lett. (5)

Sci. Rep. (1)

J. C. Estrada, J. L. Marroquin, and O. M. Medina, “Reconstruction of local frequencies for recovering the unwrapped phase in optical interferometry,” Sci. Rep. 7, 6727 (2017).
[Crossref]

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J. W. Goodman, Speckle Phenomena in Optics (Roberts and Company Publishers, 2006).

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Figures (11)

Fig. 1.
Fig. 1. Noise-free wrapped phase with dislocations. From left to right and up to down are first through tenth phase map with progressive increase of amplitude and dislocation areas.
Fig. 2.
Fig. 2. Noisy wrapped phase with dislocations. From left to right and up to down are first through tenth phase map with progressive increase of amplitude, speckle noise, and dislocation areas.
Fig. 3.
Fig. 3. Restoration of the first simulated phase. (a) Original true phase. (b) Wrapped phase with dislocations. (c) Wrapped phase with noise and dislocation and restored phases with (d) WMPI, (e) WMEP, (f) MCMI, (g) MCIM, (h) MECM, (i) MEWP.
Fig. 4.
Fig. 4. Restoration of the tenth simulated phase. (a) Original true phase. (b) Wrapped phase with dislocations. (c) Wrapped phase with noise and dislocation and restored phases with (d) WMPI, (e) WMEP, (f) MCMI, (g) MCIM, (h) MECM, (i) MEWP.
Fig. 5.
Fig. 5. Error maps obtained for the first phase map: (a) WMPI, (b) WMEP, (c) MCMI, (d) MCIM, (e) MECM, (f) MEWP.
Fig. 6.
Fig. 6. Error maps obtained for the tenth phase map: (a) WMPI, (b) WMEP, (c) MCMI, (d) MCIM, (e) MECM, (f) MEWP.
Fig. 7.
Fig. 7. Standard deviations of phase errors versus standard deviations of the decorrelation noise in phase maps; each point corresponds to one pattern of the set of fringe patterns.
Fig. 8.
Fig. 8. Ratios of peak-to-valley values versus the standard deviation of the decorrelation noise in phase maps; each point corresponds to one pattern of the set of fringe patterns.
Fig. 9.
Fig. 9. Computation times of restoration of simulated phase maps.
Fig. 10.
Fig. 10. Digital holographic setup applied to dental material investigation. (a) Tooth sample of interest. (b) Illumination geometry for the three beams. (c) General top view of the setup (PBS1-3, polarizing beam splitter; D1-2, dichroic plate; M1-5, mirrors; AL, achromatic lens; SF, spatial filter).
Fig. 11.
Fig. 11. Restoration of experimental phase data with WMPI combination. (a) Tooth specimen investigated with color digital holography. (b) Raw wrapped phase with both high noise and dislocation. (c) Denoised wrapped phase. (d) Wrapped phase with masked dislocation. (e) Unwrapped phase. (f) Final restored phase. (g) Cosine fringe of raw wrapped phase. (h) Cosine fringe of denoised wrapped phase. (i) Cosine fringe of final restored phase.

Tables (4)

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Table 1. Combination of Operations for Phase Processing

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Table 2. Standard Deviations of Phase Errors for the Different Combinations

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Table 3. Standard Deviations of Phase Errors for the Different Combinations

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Table 4. Computation Times of Restoration of Simulated Phase Maps for the Processing Schemes

Equations (10)

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f ( x , y ) = exp [ j ψ ( x , y ) ] ,
f ¯ ( x , y ) = I W F T F ( T H [ W F T F ( f ( x , y ) ) ] ) ,
ψ ¯ ( x , y ) = a tan { I m ( f ¯ ( x , y ) ) R e ( f ¯ ( x , y ) ) } ,
Δ i j x = W ( ψ ( i + 1 ) j ψ i j ) , Δ i j y = W ( ψ i ( j + 1 ) ψ i j ) ,
G i j = | φ i j | = ( Δ i j x ) 2 + ( Δ i j y ) 2 .
Δ G i j x = G ( i + 1 ) j G i j , Δ G i j y = G i ( j + 1 ) G i j .
| G i j | = ( Δ G i j x ) 2 + ( Δ G i j y ) 2 .
( φ ( i + 1 ) j 2 φ i j + φ ( i 1 ) j ) + ( φ i ( j + 1 ) 2 φ i j + φ i ( j 1 ) ) = ρ i j ,
ρ i j = ( Δ i j x Δ ( i 1 ) j x ) + ( Δ i j y Δ i ( j 1 ) y ) .
φ i j = 1 4 [ φ ( i 1 ) j + φ ( i + 1 ) j + φ i ( j 1 ) + φ i ( j + 1 ) ] .

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