Abstract

Fourier ptychographic microscopy (FPM) is a novel computational microscopy technique that provides intensity images with both wide field-of-view (FOV) and high-resolution (HR). By combining ideas from synthetic aperture and phase retrieval, FPM iteratively stitches together a number of variably illuminated, low-resolution (LR) intensity images in Fourier space to reconstruct an HR complex sample image. In practice, however, the reconstruction of FPM is sensitive to the input noise, including Gaussian noise, Poisson shot noise or mixed Poisson-Gaussian noise. To efficiently address these noises, we developed a novel FPM reconstruction method termed generalized Anscombe transform approximation Fourier ptychographic (GATFP) reconstruction. The method utilizes the generalized Anscombe transform (GAT) approximation for the noise model, and a maximum likelihood theory is employed for formulating the FPM optimization problem. We validated the proposed method with both simulated data for quantitative evaluation and real experimental data captured using FPM setup. The results show that the proposed method achieves state-of-the-art performance in comparison with other approaches.

© 2017 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Accelerated and high-quality Fourier ptychographic method using a double truncated Wirtinger criteria

Jian Liu, Yong Li, Weibo Wang, Jiubin Tan, and Chenguang Liu
Opt. Express 26(20) 26556-26565 (2018)

Apodized coherent transfer function constraint for partially coherent Fourier ptychographic microscopy

Xiong Chen, Youqiang Zhu, Minglu Sun, Dayu Li, Quanquan Mu, and Li Xuan
Opt. Express 27(10) 14099-14111 (2019)

Fourier ptychographic reconstruction using Wirtinger flow optimization

Liheng Bian, Jinli Suo, Guoan Zheng, Kaikai Guo, Feng Chen, and Qionghai Dai
Opt. Express 23(4) 4856-4866 (2015)

References

  • View by:
  • |
  • |
  • |

  1. G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics 7(9), 739–745 (2013).
    [Crossref]
  2. X. Ou, R. Horstmeyer, G. Zheng, and C. Yang, “High numerical aperture Fourier ptychography: principle, implementation and characterization,” Opt. Express 23(3), 3472–3491 (2015).
    [Crossref] [PubMed]
  3. L.-H. Yeh, J. Dong, J. Zhong, L. Tian, M. Chen, G. Tang, M. Soltanolkotabi, and L. Waller, “Experimental robustness of Fourier ptychography phase retrieval algorithms,” Opt. Express 23(26), 33214–33240 (2015).
    [Crossref]
  4. T. M. Turpin, L. H. Gesell, J. Lapides, and C. H. Price, “Theory of the synthetic aperture microscope,” Proc. SPIE 2566, 230–240(1995).
    [Crossref]
  5. J. Di, J. Zhao, H. Jiang, P. Zhang, Q. Fan, and W. Sun, “High resolution digital holographic microscopy with a wide field of view based on a synthetic aperture technique and use of linear CCD scanning,” Appl. Opt. 47(30), 5654–5659 (2008).
    [Crossref] [PubMed]
  6. T. R. Hillman, T Gutzler, S. A. Alexandrov, and D. D. Sampson, “High-resolution, wide-field object reconstruction with synthetic aperture Fourier holographic optical microscopy,” Opt. Express 17(10), 7873–7892 (2009).
    [Crossref] [PubMed]
  7. L. Granero, V. Micó, Z. Zalevsky, and J. García, “Synthetic aperture superresolved microscopy in digital lensless Fourier holography by time and angular multiplexing of the object information,” Appl. Opt. 49(5), 845–857 (2010).
    [Crossref] [PubMed]
  8. M. Kim, Y. Choi, C. Fang-Yen, Y. Sung, R. R. Dasari, M. S. Feld, and W. Choi, “High-speed synthetic aperture microscopy for live cell imaging,” Opt. Lett. 36(2), 148–150(2011).
    [Crossref] [PubMed]
  9. J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Phys. 21(15), 2758–2769 (1982).
  10. J. R. Fienup, “Reconstruction of a complex-valued object from the modulus of its Fourier transform using a support constraint,” J. Opt. Soc. Am. A 4, (1)118–123 (1987).
    [Crossref]
  11. X. Ou, R. Horstmeyer, C. Yang, and G. Zheng, “Quantitative phase imaging via Fourier ptychographic microscopy,” Opt. Lett. 38(22), 4845–4848 (2013).
    [Crossref] [PubMed]
  12. Y. Shechtman, Y. C. Eldar, O. Cohen, H. N. Chapman, J. Miao, and M. Segev, “Phase retrieval with application to optical imaging: a contemporary overview,” IEEE Signal Processing Magazine 32(3), 87–109 (2015).
    [Crossref]
  13. L. Bian, J. Suo, G. Zheng, K. Guo, F. Chen, and Q. Dai, “Fourier ptychographic reconstruction using Wirtinger flow optimization,” Opt. Express 23(4), 4856–4866 (2015).
    [Crossref] [PubMed]
  14. E. J. Candes, X. Li, and W. Soltanolkotabi, “Phase retrieval via Wirtinger flow: Theory and algorithms,” IEEE Transactions on Information Theory 61(4), 1985–2007 (2015).
    [Crossref]
  15. X. Ou, G. Zheng, and C. Yang, “Embedded pupil function recovery for Fourier ptychographic microscopy,” Opt. Express 22(5), 4960–4972 (2014).
    [Crossref] [PubMed]
  16. M. Guizar-Sicairos and J. R. Fienup, “Phase retrieval with transverse translation diversity: a nonlinear optimization approach,” Opt. Express 16(10), 7264–7278(2008).
    [Crossref] [PubMed]
  17. Y. Zhang, W. Jiang, and Q. Dai, “Nonlinear optimization approach for Fourier ptychographic microscopy,” Opt. Express 23(26), 33822–33835 (2015).
    [Crossref]
  18. L. Tian, X. Li, K. Ramchandran, and L. Waller, “Multiplexed coded illumination for Fourier Ptychography with an LED array microscope,” Biomed. Opt. Express 5(7), 2376–2389 (2014).
    [Crossref] [PubMed]
  19. R. Horstmeyer, R. Y. Chen, X. Ou, B. Ames, J. A. Tropp, and C. Yang, “Solving ptychography with a convex relaxation,” New journal of physics 17(5), 053044 (2015).
    [Crossref] [PubMed]
  20. L. Bian, J. Suo, J. Chung, X. Ou, C. Yang, F. Chen, and Q. Dai, “Fourier ptychographic reconstruction using Poisson maximum likelihood and truncated Wirtinger gradient,” https://arxiv.org/abs/1603.04746 (2016).
  21. Y. Chen and E. Candes, “Solving random quadratic systems of equations is nearly as easy as solving linear systems,” Advances in Neural Information Processing Systems, https://arxiv.org/abs/1505.05114 (2015).
  22. M. Makitalo and A. Foi, “Optimal inversion of the generalized Anscombe transformation for Poisson-Gaussian noise,” IEEE transactions on image processing 22(1), 91–103 (2013).
    [Crossref]
  23. J. L. Starck, F. D. Murtagh, and A. Bijaoui, Image Processing and Data Analysis: The Multiscale Approach (Cambridge University Press, 1998).
    [Crossref]
  24. F. J. Anscombe, “The transformation of Poisson, binomial and negative-binomial data,” Biometrika 35(3/4), 246–254 (1948).
    [Crossref]
  25. Y. Marnissi, Y. Zheng, and J. C. Pesquei, “Fast variational Bayesian signal recovery in the presence of Poisson-Gaussian noise,” IEEE International Conference on Acoustics, Speech and Signal Processing (IEEE, 2016), pp. 3964–3968.
  26. E. Chouzenoux, A. Jezierska, J. C. Pesquet, and H. Talbot, “A Convex Approach for Image Restoration with Exact Poisson–Gaussian Likelihood,” SIAM Journal on Imaging Sciences 8(4), 2662–2682 (2015).
    [Crossref]
  27. B. Zhang, M. J. Fadili, J.-L. Starck, and J.-C. Olivo-Marin, “Multiscale variance-stabilizaing transform for mixed-Poisson-Gaussian process and its application in bioimaging,” IEEE International Conference on Image Processing (IEEE, 2007), 6: VI-233–VI-236.
  28. University of Southern California, “The USC-SIPI Image Database,” http://sipi.usc.edu./database .
  29. J. Zhang, K. Hirakawa, and X. Jin, “Quantile analysis of image sensor noise distribution,” IEEE International Conference on Acoustics, Speech and Signal Processing (IEEE, 2015), pp. 1598–1602.

2015 (8)

X. Ou, R. Horstmeyer, G. Zheng, and C. Yang, “High numerical aperture Fourier ptychography: principle, implementation and characterization,” Opt. Express 23(3), 3472–3491 (2015).
[Crossref] [PubMed]

L.-H. Yeh, J. Dong, J. Zhong, L. Tian, M. Chen, G. Tang, M. Soltanolkotabi, and L. Waller, “Experimental robustness of Fourier ptychography phase retrieval algorithms,” Opt. Express 23(26), 33214–33240 (2015).
[Crossref]

Y. Shechtman, Y. C. Eldar, O. Cohen, H. N. Chapman, J. Miao, and M. Segev, “Phase retrieval with application to optical imaging: a contemporary overview,” IEEE Signal Processing Magazine 32(3), 87–109 (2015).
[Crossref]

L. Bian, J. Suo, G. Zheng, K. Guo, F. Chen, and Q. Dai, “Fourier ptychographic reconstruction using Wirtinger flow optimization,” Opt. Express 23(4), 4856–4866 (2015).
[Crossref] [PubMed]

E. J. Candes, X. Li, and W. Soltanolkotabi, “Phase retrieval via Wirtinger flow: Theory and algorithms,” IEEE Transactions on Information Theory 61(4), 1985–2007 (2015).
[Crossref]

Y. Zhang, W. Jiang, and Q. Dai, “Nonlinear optimization approach for Fourier ptychographic microscopy,” Opt. Express 23(26), 33822–33835 (2015).
[Crossref]

R. Horstmeyer, R. Y. Chen, X. Ou, B. Ames, J. A. Tropp, and C. Yang, “Solving ptychography with a convex relaxation,” New journal of physics 17(5), 053044 (2015).
[Crossref] [PubMed]

E. Chouzenoux, A. Jezierska, J. C. Pesquet, and H. Talbot, “A Convex Approach for Image Restoration with Exact Poisson–Gaussian Likelihood,” SIAM Journal on Imaging Sciences 8(4), 2662–2682 (2015).
[Crossref]

2014 (2)

2013 (3)

X. Ou, R. Horstmeyer, C. Yang, and G. Zheng, “Quantitative phase imaging via Fourier ptychographic microscopy,” Opt. Lett. 38(22), 4845–4848 (2013).
[Crossref] [PubMed]

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics 7(9), 739–745 (2013).
[Crossref]

M. Makitalo and A. Foi, “Optimal inversion of the generalized Anscombe transformation for Poisson-Gaussian noise,” IEEE transactions on image processing 22(1), 91–103 (2013).
[Crossref]

2011 (1)

2010 (1)

2009 (1)

2008 (2)

1995 (1)

T. M. Turpin, L. H. Gesell, J. Lapides, and C. H. Price, “Theory of the synthetic aperture microscope,” Proc. SPIE 2566, 230–240(1995).
[Crossref]

1987 (1)

1982 (1)

J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Phys. 21(15), 2758–2769 (1982).

1948 (1)

F. J. Anscombe, “The transformation of Poisson, binomial and negative-binomial data,” Biometrika 35(3/4), 246–254 (1948).
[Crossref]

Alexandrov, S. A.

Ames, B.

R. Horstmeyer, R. Y. Chen, X. Ou, B. Ames, J. A. Tropp, and C. Yang, “Solving ptychography with a convex relaxation,” New journal of physics 17(5), 053044 (2015).
[Crossref] [PubMed]

Anscombe, F. J.

F. J. Anscombe, “The transformation of Poisson, binomial and negative-binomial data,” Biometrika 35(3/4), 246–254 (1948).
[Crossref]

Bian, L.

L. Bian, J. Suo, G. Zheng, K. Guo, F. Chen, and Q. Dai, “Fourier ptychographic reconstruction using Wirtinger flow optimization,” Opt. Express 23(4), 4856–4866 (2015).
[Crossref] [PubMed]

L. Bian, J. Suo, J. Chung, X. Ou, C. Yang, F. Chen, and Q. Dai, “Fourier ptychographic reconstruction using Poisson maximum likelihood and truncated Wirtinger gradient,” https://arxiv.org/abs/1603.04746 (2016).

Bijaoui, A.

J. L. Starck, F. D. Murtagh, and A. Bijaoui, Image Processing and Data Analysis: The Multiscale Approach (Cambridge University Press, 1998).
[Crossref]

Candes, E.

Y. Chen and E. Candes, “Solving random quadratic systems of equations is nearly as easy as solving linear systems,” Advances in Neural Information Processing Systems, https://arxiv.org/abs/1505.05114 (2015).

Candes, E. J.

E. J. Candes, X. Li, and W. Soltanolkotabi, “Phase retrieval via Wirtinger flow: Theory and algorithms,” IEEE Transactions on Information Theory 61(4), 1985–2007 (2015).
[Crossref]

Chapman, H. N.

Y. Shechtman, Y. C. Eldar, O. Cohen, H. N. Chapman, J. Miao, and M. Segev, “Phase retrieval with application to optical imaging: a contemporary overview,” IEEE Signal Processing Magazine 32(3), 87–109 (2015).
[Crossref]

Chen, F.

L. Bian, J. Suo, G. Zheng, K. Guo, F. Chen, and Q. Dai, “Fourier ptychographic reconstruction using Wirtinger flow optimization,” Opt. Express 23(4), 4856–4866 (2015).
[Crossref] [PubMed]

L. Bian, J. Suo, J. Chung, X. Ou, C. Yang, F. Chen, and Q. Dai, “Fourier ptychographic reconstruction using Poisson maximum likelihood and truncated Wirtinger gradient,” https://arxiv.org/abs/1603.04746 (2016).

Chen, M.

Chen, R. Y.

R. Horstmeyer, R. Y. Chen, X. Ou, B. Ames, J. A. Tropp, and C. Yang, “Solving ptychography with a convex relaxation,” New journal of physics 17(5), 053044 (2015).
[Crossref] [PubMed]

Chen, Y.

Y. Chen and E. Candes, “Solving random quadratic systems of equations is nearly as easy as solving linear systems,” Advances in Neural Information Processing Systems, https://arxiv.org/abs/1505.05114 (2015).

Choi, W.

Choi, Y.

Chouzenoux, E.

E. Chouzenoux, A. Jezierska, J. C. Pesquet, and H. Talbot, “A Convex Approach for Image Restoration with Exact Poisson–Gaussian Likelihood,” SIAM Journal on Imaging Sciences 8(4), 2662–2682 (2015).
[Crossref]

Chung, J.

L. Bian, J. Suo, J. Chung, X. Ou, C. Yang, F. Chen, and Q. Dai, “Fourier ptychographic reconstruction using Poisson maximum likelihood and truncated Wirtinger gradient,” https://arxiv.org/abs/1603.04746 (2016).

Cohen, O.

Y. Shechtman, Y. C. Eldar, O. Cohen, H. N. Chapman, J. Miao, and M. Segev, “Phase retrieval with application to optical imaging: a contemporary overview,” IEEE Signal Processing Magazine 32(3), 87–109 (2015).
[Crossref]

Dai, Q.

Dasari, R. R.

Di, J.

Dong, J.

Eldar, Y. C.

Y. Shechtman, Y. C. Eldar, O. Cohen, H. N. Chapman, J. Miao, and M. Segev, “Phase retrieval with application to optical imaging: a contemporary overview,” IEEE Signal Processing Magazine 32(3), 87–109 (2015).
[Crossref]

Fadili, M. J.

B. Zhang, M. J. Fadili, J.-L. Starck, and J.-C. Olivo-Marin, “Multiscale variance-stabilizaing transform for mixed-Poisson-Gaussian process and its application in bioimaging,” IEEE International Conference on Image Processing (IEEE, 2007), 6: VI-233–VI-236.

Fan, Q.

Fang-Yen, C.

Feld, M. S.

Fienup, J. R.

Foi, A.

M. Makitalo and A. Foi, “Optimal inversion of the generalized Anscombe transformation for Poisson-Gaussian noise,” IEEE transactions on image processing 22(1), 91–103 (2013).
[Crossref]

García, J.

Gesell, L. H.

T. M. Turpin, L. H. Gesell, J. Lapides, and C. H. Price, “Theory of the synthetic aperture microscope,” Proc. SPIE 2566, 230–240(1995).
[Crossref]

Granero, L.

Guizar-Sicairos, M.

Guo, K.

Gutzler, T

Hillman, T. R.

Hirakawa, K.

J. Zhang, K. Hirakawa, and X. Jin, “Quantile analysis of image sensor noise distribution,” IEEE International Conference on Acoustics, Speech and Signal Processing (IEEE, 2015), pp. 1598–1602.

Horstmeyer, R.

R. Horstmeyer, R. Y. Chen, X. Ou, B. Ames, J. A. Tropp, and C. Yang, “Solving ptychography with a convex relaxation,” New journal of physics 17(5), 053044 (2015).
[Crossref] [PubMed]

X. Ou, R. Horstmeyer, G. Zheng, and C. Yang, “High numerical aperture Fourier ptychography: principle, implementation and characterization,” Opt. Express 23(3), 3472–3491 (2015).
[Crossref] [PubMed]

X. Ou, R. Horstmeyer, C. Yang, and G. Zheng, “Quantitative phase imaging via Fourier ptychographic microscopy,” Opt. Lett. 38(22), 4845–4848 (2013).
[Crossref] [PubMed]

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics 7(9), 739–745 (2013).
[Crossref]

Jezierska, A.

E. Chouzenoux, A. Jezierska, J. C. Pesquet, and H. Talbot, “A Convex Approach for Image Restoration with Exact Poisson–Gaussian Likelihood,” SIAM Journal on Imaging Sciences 8(4), 2662–2682 (2015).
[Crossref]

Jiang, H.

Jiang, W.

Jin, X.

J. Zhang, K. Hirakawa, and X. Jin, “Quantile analysis of image sensor noise distribution,” IEEE International Conference on Acoustics, Speech and Signal Processing (IEEE, 2015), pp. 1598–1602.

Kim, M.

Lapides, J.

T. M. Turpin, L. H. Gesell, J. Lapides, and C. H. Price, “Theory of the synthetic aperture microscope,” Proc. SPIE 2566, 230–240(1995).
[Crossref]

Li, X.

E. J. Candes, X. Li, and W. Soltanolkotabi, “Phase retrieval via Wirtinger flow: Theory and algorithms,” IEEE Transactions on Information Theory 61(4), 1985–2007 (2015).
[Crossref]

L. Tian, X. Li, K. Ramchandran, and L. Waller, “Multiplexed coded illumination for Fourier Ptychography with an LED array microscope,” Biomed. Opt. Express 5(7), 2376–2389 (2014).
[Crossref] [PubMed]

Makitalo, M.

M. Makitalo and A. Foi, “Optimal inversion of the generalized Anscombe transformation for Poisson-Gaussian noise,” IEEE transactions on image processing 22(1), 91–103 (2013).
[Crossref]

Marnissi, Y.

Y. Marnissi, Y. Zheng, and J. C. Pesquei, “Fast variational Bayesian signal recovery in the presence of Poisson-Gaussian noise,” IEEE International Conference on Acoustics, Speech and Signal Processing (IEEE, 2016), pp. 3964–3968.

Miao, J.

Y. Shechtman, Y. C. Eldar, O. Cohen, H. N. Chapman, J. Miao, and M. Segev, “Phase retrieval with application to optical imaging: a contemporary overview,” IEEE Signal Processing Magazine 32(3), 87–109 (2015).
[Crossref]

Micó, V.

Murtagh, F. D.

J. L. Starck, F. D. Murtagh, and A. Bijaoui, Image Processing and Data Analysis: The Multiscale Approach (Cambridge University Press, 1998).
[Crossref]

Olivo-Marin, J.-C.

B. Zhang, M. J. Fadili, J.-L. Starck, and J.-C. Olivo-Marin, “Multiscale variance-stabilizaing transform for mixed-Poisson-Gaussian process and its application in bioimaging,” IEEE International Conference on Image Processing (IEEE, 2007), 6: VI-233–VI-236.

Ou, X.

R. Horstmeyer, R. Y. Chen, X. Ou, B. Ames, J. A. Tropp, and C. Yang, “Solving ptychography with a convex relaxation,” New journal of physics 17(5), 053044 (2015).
[Crossref] [PubMed]

X. Ou, R. Horstmeyer, G. Zheng, and C. Yang, “High numerical aperture Fourier ptychography: principle, implementation and characterization,” Opt. Express 23(3), 3472–3491 (2015).
[Crossref] [PubMed]

X. Ou, G. Zheng, and C. Yang, “Embedded pupil function recovery for Fourier ptychographic microscopy,” Opt. Express 22(5), 4960–4972 (2014).
[Crossref] [PubMed]

X. Ou, R. Horstmeyer, C. Yang, and G. Zheng, “Quantitative phase imaging via Fourier ptychographic microscopy,” Opt. Lett. 38(22), 4845–4848 (2013).
[Crossref] [PubMed]

L. Bian, J. Suo, J. Chung, X. Ou, C. Yang, F. Chen, and Q. Dai, “Fourier ptychographic reconstruction using Poisson maximum likelihood and truncated Wirtinger gradient,” https://arxiv.org/abs/1603.04746 (2016).

Pesquei, J. C.

Y. Marnissi, Y. Zheng, and J. C. Pesquei, “Fast variational Bayesian signal recovery in the presence of Poisson-Gaussian noise,” IEEE International Conference on Acoustics, Speech and Signal Processing (IEEE, 2016), pp. 3964–3968.

Pesquet, J. C.

E. Chouzenoux, A. Jezierska, J. C. Pesquet, and H. Talbot, “A Convex Approach for Image Restoration with Exact Poisson–Gaussian Likelihood,” SIAM Journal on Imaging Sciences 8(4), 2662–2682 (2015).
[Crossref]

Price, C. H.

T. M. Turpin, L. H. Gesell, J. Lapides, and C. H. Price, “Theory of the synthetic aperture microscope,” Proc. SPIE 2566, 230–240(1995).
[Crossref]

Ramchandran, K.

Sampson, D. D.

Segev, M.

Y. Shechtman, Y. C. Eldar, O. Cohen, H. N. Chapman, J. Miao, and M. Segev, “Phase retrieval with application to optical imaging: a contemporary overview,” IEEE Signal Processing Magazine 32(3), 87–109 (2015).
[Crossref]

Shechtman, Y.

Y. Shechtman, Y. C. Eldar, O. Cohen, H. N. Chapman, J. Miao, and M. Segev, “Phase retrieval with application to optical imaging: a contemporary overview,” IEEE Signal Processing Magazine 32(3), 87–109 (2015).
[Crossref]

Soltanolkotabi, M.

Soltanolkotabi, W.

E. J. Candes, X. Li, and W. Soltanolkotabi, “Phase retrieval via Wirtinger flow: Theory and algorithms,” IEEE Transactions on Information Theory 61(4), 1985–2007 (2015).
[Crossref]

Starck, J. L.

J. L. Starck, F. D. Murtagh, and A. Bijaoui, Image Processing and Data Analysis: The Multiscale Approach (Cambridge University Press, 1998).
[Crossref]

Starck, J.-L.

B. Zhang, M. J. Fadili, J.-L. Starck, and J.-C. Olivo-Marin, “Multiscale variance-stabilizaing transform for mixed-Poisson-Gaussian process and its application in bioimaging,” IEEE International Conference on Image Processing (IEEE, 2007), 6: VI-233–VI-236.

Sun, W.

Sung, Y.

Suo, J.

L. Bian, J. Suo, G. Zheng, K. Guo, F. Chen, and Q. Dai, “Fourier ptychographic reconstruction using Wirtinger flow optimization,” Opt. Express 23(4), 4856–4866 (2015).
[Crossref] [PubMed]

L. Bian, J. Suo, J. Chung, X. Ou, C. Yang, F. Chen, and Q. Dai, “Fourier ptychographic reconstruction using Poisson maximum likelihood and truncated Wirtinger gradient,” https://arxiv.org/abs/1603.04746 (2016).

Talbot, H.

E. Chouzenoux, A. Jezierska, J. C. Pesquet, and H. Talbot, “A Convex Approach for Image Restoration with Exact Poisson–Gaussian Likelihood,” SIAM Journal on Imaging Sciences 8(4), 2662–2682 (2015).
[Crossref]

Tang, G.

Tian, L.

Tropp, J. A.

R. Horstmeyer, R. Y. Chen, X. Ou, B. Ames, J. A. Tropp, and C. Yang, “Solving ptychography with a convex relaxation,” New journal of physics 17(5), 053044 (2015).
[Crossref] [PubMed]

Turpin, T. M.

T. M. Turpin, L. H. Gesell, J. Lapides, and C. H. Price, “Theory of the synthetic aperture microscope,” Proc. SPIE 2566, 230–240(1995).
[Crossref]

Waller, L.

Yang, C.

X. Ou, R. Horstmeyer, G. Zheng, and C. Yang, “High numerical aperture Fourier ptychography: principle, implementation and characterization,” Opt. Express 23(3), 3472–3491 (2015).
[Crossref] [PubMed]

R. Horstmeyer, R. Y. Chen, X. Ou, B. Ames, J. A. Tropp, and C. Yang, “Solving ptychography with a convex relaxation,” New journal of physics 17(5), 053044 (2015).
[Crossref] [PubMed]

X. Ou, G. Zheng, and C. Yang, “Embedded pupil function recovery for Fourier ptychographic microscopy,” Opt. Express 22(5), 4960–4972 (2014).
[Crossref] [PubMed]

X. Ou, R. Horstmeyer, C. Yang, and G. Zheng, “Quantitative phase imaging via Fourier ptychographic microscopy,” Opt. Lett. 38(22), 4845–4848 (2013).
[Crossref] [PubMed]

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics 7(9), 739–745 (2013).
[Crossref]

L. Bian, J. Suo, J. Chung, X. Ou, C. Yang, F. Chen, and Q. Dai, “Fourier ptychographic reconstruction using Poisson maximum likelihood and truncated Wirtinger gradient,” https://arxiv.org/abs/1603.04746 (2016).

Yeh, L.-H.

Zalevsky, Z.

Zhang, B.

B. Zhang, M. J. Fadili, J.-L. Starck, and J.-C. Olivo-Marin, “Multiscale variance-stabilizaing transform for mixed-Poisson-Gaussian process and its application in bioimaging,” IEEE International Conference on Image Processing (IEEE, 2007), 6: VI-233–VI-236.

Zhang, J.

J. Zhang, K. Hirakawa, and X. Jin, “Quantile analysis of image sensor noise distribution,” IEEE International Conference on Acoustics, Speech and Signal Processing (IEEE, 2015), pp. 1598–1602.

Zhang, P.

Zhang, Y.

Zhao, J.

Zheng, G.

Zheng, Y.

Y. Marnissi, Y. Zheng, and J. C. Pesquei, “Fast variational Bayesian signal recovery in the presence of Poisson-Gaussian noise,” IEEE International Conference on Acoustics, Speech and Signal Processing (IEEE, 2016), pp. 3964–3968.

Zhong, J.

Appl. Opt. (2)

Appl. Phys. (1)

J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Phys. 21(15), 2758–2769 (1982).

Biomed. Opt. Express (1)

Biometrika (1)

F. J. Anscombe, “The transformation of Poisson, binomial and negative-binomial data,” Biometrika 35(3/4), 246–254 (1948).
[Crossref]

IEEE Signal Processing Magazine (1)

Y. Shechtman, Y. C. Eldar, O. Cohen, H. N. Chapman, J. Miao, and M. Segev, “Phase retrieval with application to optical imaging: a contemporary overview,” IEEE Signal Processing Magazine 32(3), 87–109 (2015).
[Crossref]

IEEE transactions on image processing (1)

M. Makitalo and A. Foi, “Optimal inversion of the generalized Anscombe transformation for Poisson-Gaussian noise,” IEEE transactions on image processing 22(1), 91–103 (2013).
[Crossref]

IEEE Transactions on Information Theory (1)

E. J. Candes, X. Li, and W. Soltanolkotabi, “Phase retrieval via Wirtinger flow: Theory and algorithms,” IEEE Transactions on Information Theory 61(4), 1985–2007 (2015).
[Crossref]

J. Opt. Soc. Am. A (1)

Nat. Photonics (1)

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics 7(9), 739–745 (2013).
[Crossref]

New journal of physics (1)

R. Horstmeyer, R. Y. Chen, X. Ou, B. Ames, J. A. Tropp, and C. Yang, “Solving ptychography with a convex relaxation,” New journal of physics 17(5), 053044 (2015).
[Crossref] [PubMed]

Opt. Express (7)

Opt. Lett. (2)

Proc. SPIE (1)

T. M. Turpin, L. H. Gesell, J. Lapides, and C. H. Price, “Theory of the synthetic aperture microscope,” Proc. SPIE 2566, 230–240(1995).
[Crossref]

SIAM Journal on Imaging Sciences (1)

E. Chouzenoux, A. Jezierska, J. C. Pesquet, and H. Talbot, “A Convex Approach for Image Restoration with Exact Poisson–Gaussian Likelihood,” SIAM Journal on Imaging Sciences 8(4), 2662–2682 (2015).
[Crossref]

Other (7)

B. Zhang, M. J. Fadili, J.-L. Starck, and J.-C. Olivo-Marin, “Multiscale variance-stabilizaing transform for mixed-Poisson-Gaussian process and its application in bioimaging,” IEEE International Conference on Image Processing (IEEE, 2007), 6: VI-233–VI-236.

University of Southern California, “The USC-SIPI Image Database,” http://sipi.usc.edu./database .

J. Zhang, K. Hirakawa, and X. Jin, “Quantile analysis of image sensor noise distribution,” IEEE International Conference on Acoustics, Speech and Signal Processing (IEEE, 2015), pp. 1598–1602.

L. Bian, J. Suo, J. Chung, X. Ou, C. Yang, F. Chen, and Q. Dai, “Fourier ptychographic reconstruction using Poisson maximum likelihood and truncated Wirtinger gradient,” https://arxiv.org/abs/1603.04746 (2016).

Y. Chen and E. Candes, “Solving random quadratic systems of equations is nearly as easy as solving linear systems,” Advances in Neural Information Processing Systems, https://arxiv.org/abs/1505.05114 (2015).

J. L. Starck, F. D. Murtagh, and A. Bijaoui, Image Processing and Data Analysis: The Multiscale Approach (Cambridge University Press, 1998).
[Crossref]

Y. Marnissi, Y. Zheng, and J. C. Pesquei, “Fast variational Bayesian signal recovery in the presence of Poisson-Gaussian noise,” IEEE International Conference on Acoustics, Speech and Signal Processing (IEEE, 2016), pp. 3964–3968.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1 A set of images captured by FPM stacking together into a long data vector.
Fig. 2
Fig. 2 Reconstruction results with three types of noises (Poisson noise, Gaussian noise and mixed Poisson-Gaussian noise), using different algorithms (TPWFP, Newton method and GATFP).
Fig. 3
Fig. 3 Reconstruction results under Bloodsmear dataset using different algorithms (TPWFP, Newton method and GATFP).
Fig. 4
Fig. 4 Reconstruction results under USAF dataset using different algorithms (TPWFP, Newton method and GATFP).

Equations (19)

Equations on this page are rendered with MathJax. Learn more.

I j = | 1 { P ( k ) S ( k k j ) } | 2 ,
I j = | F 1 d i a g ( P ) Q j S | 2 ,
b = | F ^ 1 P ^ Q S | 2 = | DS | 2 ,
z q = b ˜ q + n q , q = 1 , , N ,
z q ˜ = { 2 z q + 3 8 + σ 2 , z q > 3 8 σ 2 0 , z q 3 8 σ 2
p ( z q | b q ) = i = 1 m 2 ( j = 1 + e [ b q ] i ( [ b q ] i j j ! e 1 2 σ 2 ( [ z q ] i j ) 2 2 π σ 2 ) ,
[ b q ] i = | [ F 1 d i a g ( P ) Q q ] i S | 2 = | [ D q ] i S | 2 ,
p ( z q ˜ | b q ) = i = 1 m 2 1 2 π exp ( 1 2 ( z q ˜ 2 | [ D q ] i S | 2 + 3 8 + σ 2 ) 2 ) .
max q = 1 N p ( z q ˜ ) .
min f ( S ) = log ( q = 1 N p ( z q ˜ ) ) = log ( q = 1 N i = 1 m 2 1 2 π exp ( 1 2 ( z q ˜ 2 | [ D q ] i S | 2 + 3 8 + σ 2 ) 2 ) ) = 1 2 q = 1 N i = 1 m 2 ( log 2 π z q ˜ 2 + 4 z q ˜ | [ D q ] i S | 2 + 3 8 + σ 2 4 ( | [ D q ] i S | 2 + 3 8 + σ 2 ) ) .
min f ( S ) = 1 2 q = 1 N i = 1 m 2 ( 4 z q ˜ | [ D q ] i S | 2 + 3 8 + σ 2 4 ( | [ D q ] i S | 2 + 3 8 + σ 2 ) ) .
f ( S ) = d f ( S ) d S * = d { 2 q = 1 N i = 1 m 2 ( z q ˜ | [ D q ] i S | 2 + 3 8 + σ 2 ( | [ D q ] i S | 2 + 3 8 + σ 2 ) ) } d S * = 2 q = 1 N i = 1 m 2 d { ( z q ˜ | [ D q ] i S | 2 + 3 8 + σ 2 ( | [ D q ] i S | 2 + 3 8 + σ 2 ) ) } d S * = 2 q = 1 N i = 1 m 2 { 1 2 z q ˜ [ D q ] i H [ D q ] i S | [ D q ] i S | 2 + 3 8 + σ 2 [ D q ] i H [ D q ] i S } ,
ζ q ( S ) = { | z q D q S | 2 α h z | DS | 2 1 N | D q S | 2 S } ,
t r f ( S ) = 2 q = 1 N i = 1 m 2 { 1 2 z q ˜ [ D q ] i H [ D q ] i S | [ D q ] i S | 2 + 3 8 + σ 2 [ D q ] i H [ D q ] i S } ζ q ( S ) .
S ( k + 1 ) = S ( k ) β ( k ) t r f ( S ) ,
β ( k ) = min ( 1 e k / k 0 , β max ) N m 2 ,
S ( k + 1 ) = S ( k ) β S ( k ) d f ( S ( k ) ) d S * = S ( k ) β S ( k ) d { 2 q = 1 N z q ˜ | 1 { P ( k + k q ) S ( k ) } | 2 + 3 8 + σ 2 ( | 1 { P ( k + k q ) S ( k ) } | 2 + 3 8 + σ 2 ) } d S * = S ( k ) + 2 β S ( k ) q = 1 N d { z q ˜ | 1 { P ( k + k q ) S ( k ) } | 2 + 3 8 + σ 2 ( | 1 { P ( k + k q ) S ( k ) } | 2 + 3 8 + σ 2 ) } d S * = S ( k ) + 2 β S ( k ) q = 1 N [ P ( k + k q ) ] * { z q ˜ 1 { P ( k + k q ) S ( k ) } 2 | 1 { P ( k + k q ) S ( k ) } | 2 + 3 8 + σ 2 1 { P ( k + k q ) S ( k ) } } ,
P ( k + 1 ) = P ( k ) β P ( k ) d f ( P ( k ) ) d P * = P ( k ) + 2 β P ( k ) q = 1 N [ S ( k k q ) ] * { z q ˜ 1 { P ( k ) S ( k k q ) } 2 | 1 { P ( k ) S ( k k q ) } | 2 + 3 8 + σ 2 1 { P ( k ) S ( k k q ) } } ,
R E = min ϕ [ 0 , 2 π ) e j ϕ S S t 2 S t 2 ,

Metrics