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M. Weigert, U. Schmidt, T. Boothe, A. Müller, A. Dibrov, A. Jain, B. Wilhelm, D. Schmidt, C. Broaddus, S. Culley, and M. Rocha-Martins, “Content-aware image restoration: pushing the limits of fluorescence microscopy,” Nat. Methods 15, 1090–1097 (2018).

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L. Tian, Z. Liu, L.-H. Yeh, M. Chen, J. Zhong, and L. Waller, “Computational illumination for high-speed in vitro Fourier ptychographic microscopy,” Optica 2, 904–911 (2015).

[Crossref]

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, 33214–33240 (2015).

[Crossref]

P. Chen and A. Fannjiang, “Coded aperture ptychography: uniqueness and reconstruction,” Inverse Probl. 34, 025003 (2018).

[Crossref]

J. Sun, Q. Chen, Y. Zhang, and C. Zuo, “Efficient positional misalignment correction method for Fourier ptychographic microscopy,” Biomed. Opt. Express 7, 1336–1350 (2016).

[Crossref]

Y. Fan, J. Sun, Q. Chen, X. Pan, L. Tian, and C. Zuo, “Optimal illumination scheme for isotropic quantitative differential phase contrast microscopy,” arXiv:1903.10718 (2019).

R. Horstmeyer, R. Y. Chen, B. Kappes, and B. Judkewitz, “Convolutional neural networks that teach microscopes how to image,” arXiv:1709.07223 (2017).

M. Weigert, U. Schmidt, T. Boothe, A. Müller, A. Dibrov, A. Jain, B. Wilhelm, D. Schmidt, C. Broaddus, S. Culley, and M. Rocha-Martins, “Content-aware image restoration: pushing the limits of fluorescence microscopy,” Nat. Methods 15, 1090–1097 (2018).

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M. Weigert, U. Schmidt, T. Boothe, A. Müller, A. Dibrov, A. Jain, B. Wilhelm, D. Schmidt, C. Broaddus, S. Culley, and M. Rocha-Martins, “Content-aware image restoration: pushing the limits of fluorescence microscopy,” Nat. Methods 15, 1090–1097 (2018).

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Y. Fan, J. Sun, Q. Chen, X. Pan, L. Tian, and C. Zuo, “Optimal illumination scheme for isotropic quantitative differential phase contrast microscopy,” arXiv:1903.10718 (2019).

P. Chen and A. Fannjiang, “Coded aperture ptychography: uniqueness and reconstruction,” Inverse Probl. 34, 025003 (2018).

[Crossref]

V. Kuleshov, N. Fenner, and S. Ermon, “Accurate uncertainties for deep learning using calibrated regression,” arXiv:1807.00263 (2018).

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[Crossref]

Y. Gal and Z. Ghahramani, “Dropout as a Bayesian approximation: representing model uncertainty in deep learning,” in International Conference on Machine Learning (2016), pp. 1050–1059.

X. Glorot and Y. Bengio, “Understanding the difficulty of training deep feedforward neural networks,” in International Conference on Artificial Intelligence and Statistics (2010), Vol. 9, pp. 249–256.

Y. Rivenson, Y. Zhang, H. Günaydn, D. Teng, and A. Ozcan, “Phase recovery and holographic image reconstruction using deep learning in neural networks,” Light Sci. Appl. 7, 17141–17149 (2018).

[Crossref]

B. Diederich, R. Wartmann, H. Schadwinkel, and R. Heintzmann, “Using machine-learning to optimize phase contrast in a low-cost cellphone microscope,” PLoS One 13, e0192937 (2018).

[Crossref]

K. Wicker and R. Heintzmann, “Resolving a misconception about structured illumination,” Nat. Photonics 8, 342–344 (2014).

[Crossref]

N. Srivastava, G. Hinton, A. Krizhevsky, I. Sutskevar, and R. Salakhutdinov, “Dropout: a simple way to prevent neural networks from overfitting,” J. Mach. Learn. Res. 15, 1929–1958 (2014).

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

[Crossref]

R. Horstmeyer, R. Y. Chen, B. Kappes, and B. Judkewitz, “Convolutional neural networks that teach microscopes how to image,” arXiv:1709.07223 (2017).

P. Isola, J. Zhu, T. Zhou, and A. A. Efros, “Image-to-image translation with conditional adversarial networks,” CoRR abs/1611.07004 (2016).

M. Weigert, U. Schmidt, T. Boothe, A. Müller, A. Dibrov, A. Jain, B. Wilhelm, D. Schmidt, C. Broaddus, S. Culley, and M. Rocha-Martins, “Content-aware image restoration: pushing the limits of fluorescence microscopy,” Nat. Methods 15, 1090–1097 (2018).

[Crossref]

R. Horstmeyer, R. Y. Chen, B. Kappes, and B. Judkewitz, “Convolutional neural networks that teach microscopes how to image,” arXiv:1709.07223 (2017).

R. Horstmeyer, R. Y. Chen, B. Kappes, and B. Judkewitz, “Convolutional neural networks that teach microscopes how to image,” arXiv:1709.07223 (2017).

M. Kellman, E. Bostan, N. Repina, and L. Waller, “Physics-based learned design: optimized coded-illumination for quantitative phase imaging,” IEEE Transactions on Computational Imaging (Early Access) (2019), https://doi.org/10.1109/TCI.2019.2905434.

A. Kendall and Y. Gal, “What uncertainties do we need in Bayesian deep learning for computer vision?” in Advances in Neural Information Processing Systems (2017), pp. 5580–5590.

A. D. Kiureghian and O. Ditlevsen, “Aleatory or epistemic? Does it matter?” Struct. Saf. 31, 105–112 (2009).

[Crossref]

N. Srivastava, G. Hinton, A. Krizhevsky, I. Sutskevar, and R. Salakhutdinov, “Dropout: a simple way to prevent neural networks from overfitting,” J. Mach. Learn. Res. 15, 1929–1958 (2014).

V. Kuleshov, N. Fenner, and S. Ermon, “Accurate uncertainties for deep learning using calibrated regression,” arXiv:1807.00263 (2018).

B. Lakshminarayanan, A. Pritzel, and C. Blundell, “Simple and scalable predictive uncertainty estimation using deep ensembles,” in Advances in Neural Information Processing Systems (2017), pp. 6402–6413.

S. Li, M. Deng, J. Lee, A. Sinha, and G. Barbastathis, “Imaging through glass diffusers using densely connected convolutional networks,” Optica 5, 803–813 (2018).

[Crossref]

A. Sinha, J. Lee, S. Li, and G. Barbastathis, “Lensless computational imaging through deep learning,” Optica 4, 1117–1125 (2017).

[Crossref]

S. Li, M. Deng, J. Lee, A. Sinha, and G. Barbastathis, “Imaging through glass diffusers using densely connected convolutional networks,” Optica 5, 803–813 (2018).

[Crossref]

A. Sinha, J. Lee, S. Li, and G. Barbastathis, “Lensless computational imaging through deep learning,” Optica 4, 1117–1125 (2017).

[Crossref]

Y. Li, Y. Xue, and L. Tian, “Deep speckle correlation: a deep learning approach toward scalable imaging through scattering media,” Optica 5, 1181–1190 (2018).

[Crossref]

T. Nguyen, Y. Xue, Y. Li, L. Tian, and G. Nehmetallah, “Deep learning approach for Fourier ptychography microscopy,” Opt. Express 26, 26470–26484 (2018).

[Crossref]

A. W. Lohmann, R. G. Dorsch, D. Mendlovic, Z. Zalevsky, and C. Ferreira, “Space–bandwidth product of optical signals and systems,” J. Opt. Soc. Am. A 13, 470–473 (1996).

[Crossref]

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[Crossref]

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[Crossref]

A. Niculescu-Mizil and R. Caruana, “Predicting good probabilities with supervised learning,” in Proceedings of the 22nd International Conference on Machine Learning (2005).

Y. Wu, Y. Rivenson, Y. Zhang, Z. Wei, H. Günaydin, X. Lin, and A. Ozcan, “Extended depth-of-field in holographic imaging using deep-learning-based autofocusing and phase recovery,” Optica 5, 704–710 (2018).

[Crossref]

Y. Rivenson, Y. Zhang, H. Günaydn, D. Teng, and A. Ozcan, “Phase recovery and holographic image reconstruction using deep learning in neural networks,” Light Sci. Appl. 7, 17141–17149 (2018).

[Crossref]

Y. Fan, J. Sun, Q. Chen, X. Pan, L. Tian, and C. Zuo, “Optimal illumination scheme for isotropic quantitative differential phase contrast microscopy,” arXiv:1903.10718 (2019).

B. Lakshminarayanan, A. Pritzel, and C. Blundell, “Simple and scalable predictive uncertainty estimation using deep ensembles,” in Advances in Neural Information Processing Systems (2017), pp. 6402–6413.

E. Bostan, M. Soltanolkotabi, D. Ren, and L. Waller, “Accelerated Wirtinger flow for multiplexed Fourier ptychographic microscopy,” arXiv:1803.03714 (2018).

M. Kellman, E. Bostan, N. Repina, and L. Waller, “Physics-based learned design: optimized coded-illumination for quantitative phase imaging,” IEEE Transactions on Computational Imaging (Early Access) (2019), https://doi.org/10.1109/TCI.2019.2905434.

Y. Rivenson, Y. Zhang, H. Günaydn, D. Teng, and A. Ozcan, “Phase recovery and holographic image reconstruction using deep learning in neural networks,” Light Sci. Appl. 7, 17141–17149 (2018).

[Crossref]

Y. Wu, Y. Rivenson, Y. Zhang, Z. Wei, H. Günaydin, X. Lin, and A. Ozcan, “Extended depth-of-field in holographic imaging using deep-learning-based autofocusing and phase recovery,” Optica 5, 704–710 (2018).

[Crossref]

M. Weigert, U. Schmidt, T. Boothe, A. Müller, A. Dibrov, A. Jain, B. Wilhelm, D. Schmidt, C. Broaddus, S. Culley, and M. Rocha-Martins, “Content-aware image restoration: pushing the limits of fluorescence microscopy,” Nat. Methods 15, 1090–1097 (2018).

[Crossref]

O. Ronneberger, P. Fischer, and T. Brox, “U-Net: convolutional networks for biomedical image segmentation,” in International Conference on Medical Image Computing and Computer-Assisted Intervention (Springer, 2015), pp. 234–241.

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B. Diederich, R. Wartmann, H. Schadwinkel, and R. Heintzmann, “Using machine-learning to optimize phase contrast in a low-cost cellphone microscope,” PLoS One 13, e0192937 (2018).

[Crossref]

M. Weigert, U. Schmidt, T. Boothe, A. Müller, A. Dibrov, A. Jain, B. Wilhelm, D. Schmidt, C. Broaddus, S. Culley, and M. Rocha-Martins, “Content-aware image restoration: pushing the limits of fluorescence microscopy,” Nat. Methods 15, 1090–1097 (2018).

[Crossref]

M. Weigert, U. Schmidt, T. Boothe, A. Müller, A. Dibrov, A. Jain, B. Wilhelm, D. Schmidt, C. Broaddus, S. Culley, and M. Rocha-Martins, “Content-aware image restoration: pushing the limits of fluorescence microscopy,” Nat. Methods 15, 1090–1097 (2018).

[Crossref]

S. Li, M. Deng, J. Lee, A. Sinha, and G. Barbastathis, “Imaging through glass diffusers using densely connected convolutional networks,” Optica 5, 803–813 (2018).

[Crossref]

A. Sinha, J. Lee, S. Li, and G. Barbastathis, “Lensless computational imaging through deep learning,” Optica 4, 1117–1125 (2017).

[Crossref]

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, 33214–33240 (2015).

[Crossref]

E. Bostan, M. Soltanolkotabi, D. Ren, and L. Waller, “Accelerated Wirtinger flow for multiplexed Fourier ptychographic microscopy,” arXiv:1803.03714 (2018).

N. Srivastava, G. Hinton, A. Krizhevsky, I. Sutskevar, and R. Salakhutdinov, “Dropout: a simple way to prevent neural networks from overfitting,” J. Mach. Learn. Res. 15, 1929–1958 (2014).

J. Sun, Q. Chen, Y. Zhang, and C. Zuo, “Efficient positional misalignment correction method for Fourier ptychographic microscopy,” Biomed. Opt. Express 7, 1336–1350 (2016).

[Crossref]

Y. Fan, J. Sun, Q. Chen, X. Pan, L. Tian, and C. Zuo, “Optimal illumination scheme for isotropic quantitative differential phase contrast microscopy,” arXiv:1903.10718 (2019).

N. Srivastava, G. Hinton, A. Krizhevsky, I. Sutskevar, and R. Salakhutdinov, “Dropout: a simple way to prevent neural networks from overfitting,” J. Mach. Learn. Res. 15, 1929–1958 (2014).

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, 33214–33240 (2015).

[Crossref]

Y. Rivenson, Y. Zhang, H. Günaydn, D. Teng, and A. Ozcan, “Phase recovery and holographic image reconstruction using deep learning in neural networks,” Light Sci. Appl. 7, 17141–17149 (2018).

[Crossref]

R. Ling, W. Tahir, H.-Y. Lin, H. Lee, and L. Tian, “High-throughput intensity diffraction tomography with a computational microscope,” Biomed. Opt. Express 9, 2130–2141 (2018).

[Crossref]

T. Nguyen, Y. Xue, Y. Li, L. Tian, and G. Nehmetallah, “Deep learning approach for Fourier ptychography microscopy,” Opt. Express 26, 26470–26484 (2018).

[Crossref]

Y. Li, Y. Xue, and L. Tian, “Deep speckle correlation: a deep learning approach toward scalable imaging through scattering media,” Optica 5, 1181–1190 (2018).

[Crossref]

L. Tian and L. Waller, “Quantitative differential phase contrast imaging in an LED array microscope,” Opt. Express 23, 11394–11403 (2015).

[Crossref]

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, 33214–33240 (2015).

[Crossref]

L. Tian, Z. Liu, L.-H. Yeh, M. Chen, J. Zhong, and L. Waller, “Computational illumination for high-speed in vitro Fourier ptychographic microscopy,” Optica 2, 904–911 (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, 2376–2389 (2014).

[Crossref]

Y. Fan, J. Sun, Q. Chen, X. Pan, L. Tian, and C. Zuo, “Optimal illumination scheme for isotropic quantitative differential phase contrast microscopy,” arXiv:1903.10718 (2019).

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[Crossref]

L. Tian, Z. Liu, L.-H. Yeh, M. Chen, J. Zhong, and L. Waller, “Computational illumination for high-speed in vitro Fourier ptychographic microscopy,” Optica 2, 904–911 (2015).

[Crossref]

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, 33214–33240 (2015).

[Crossref]

L. Tian and L. Waller, “Quantitative differential phase contrast imaging in an LED array microscope,” Opt. Express 23, 11394–11403 (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, 2376–2389 (2014).

[Crossref]

M. Kellman, E. Bostan, N. Repina, and L. Waller, “Physics-based learned design: optimized coded-illumination for quantitative phase imaging,” IEEE Transactions on Computational Imaging (Early Access) (2019), https://doi.org/10.1109/TCI.2019.2905434.

E. Bostan, M. Soltanolkotabi, D. Ren, and L. Waller, “Accelerated Wirtinger flow for multiplexed Fourier ptychographic microscopy,” arXiv:1803.03714 (2018).

B. Diederich, R. Wartmann, H. Schadwinkel, and R. Heintzmann, “Using machine-learning to optimize phase contrast in a low-cost cellphone microscope,” PLoS One 13, e0192937 (2018).

[Crossref]

M. Weigert, U. Schmidt, T. Boothe, A. Müller, A. Dibrov, A. Jain, B. Wilhelm, D. Schmidt, C. Broaddus, S. Culley, and M. Rocha-Martins, “Content-aware image restoration: pushing the limits of fluorescence microscopy,” Nat. Methods 15, 1090–1097 (2018).

[Crossref]

K. Wicker and R. Heintzmann, “Resolving a misconception about structured illumination,” Nat. Photonics 8, 342–344 (2014).

[Crossref]

M. Weigert, U. Schmidt, T. Boothe, A. Müller, A. Dibrov, A. Jain, B. Wilhelm, D. Schmidt, C. Broaddus, S. Culley, and M. Rocha-Martins, “Content-aware image restoration: pushing the limits of fluorescence microscopy,” Nat. Methods 15, 1090–1097 (2018).

[Crossref]

Y. Li, Y. Xue, and L. Tian, “Deep speckle correlation: a deep learning approach toward scalable imaging through scattering media,” Optica 5, 1181–1190 (2018).

[Crossref]

T. Nguyen, Y. Xue, Y. Li, L. Tian, and G. Nehmetallah, “Deep learning approach for Fourier ptychography microscopy,” Opt. Express 26, 26470–26484 (2018).

[Crossref]

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

[Crossref]

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

[Crossref]

L. Tian, Z. Liu, L.-H. Yeh, M. Chen, J. Zhong, and L. Waller, “Computational illumination for high-speed in vitro Fourier ptychographic microscopy,” Optica 2, 904–911 (2015).

[Crossref]

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, 33214–33240 (2015).

[Crossref]

Y. Rivenson, Y. Zhang, H. Günaydn, D. Teng, and A. Ozcan, “Phase recovery and holographic image reconstruction using deep learning in neural networks,” Light Sci. Appl. 7, 17141–17149 (2018).

[Crossref]

Y. Wu, Y. Rivenson, Y. Zhang, Z. Wei, H. Günaydin, X. Lin, and A. Ozcan, “Extended depth-of-field in holographic imaging using deep-learning-based autofocusing and phase recovery,” Optica 5, 704–710 (2018).

[Crossref]

J. Sun, Q. Chen, Y. Zhang, and C. Zuo, “Efficient positional misalignment correction method for Fourier ptychographic microscopy,” Biomed. Opt. Express 7, 1336–1350 (2016).

[Crossref]

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

[Crossref]

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

[Crossref]

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, 33214–33240 (2015).

[Crossref]

L. Tian, Z. Liu, L.-H. Yeh, M. Chen, J. Zhong, and L. Waller, “Computational illumination for high-speed in vitro Fourier ptychographic microscopy,” Optica 2, 904–911 (2015).

[Crossref]

P. Isola, J. Zhu, T. Zhou, and A. A. Efros, “Image-to-image translation with conditional adversarial networks,” CoRR abs/1611.07004 (2016).

P. Isola, J. Zhu, T. Zhou, and A. A. Efros, “Image-to-image translation with conditional adversarial networks,” CoRR abs/1611.07004 (2016).

J. Sun, Q. Chen, Y. Zhang, and C. Zuo, “Efficient positional misalignment correction method for Fourier ptychographic microscopy,” Biomed. Opt. Express 7, 1336–1350 (2016).

[Crossref]

Y. Fan, J. Sun, Q. Chen, X. Pan, L. Tian, and C. Zuo, “Optimal illumination scheme for isotropic quantitative differential phase contrast microscopy,” arXiv:1903.10718 (2019).

R. Ling, W. Tahir, H.-Y. Lin, H. Lee, and L. Tian, “High-throughput intensity diffraction tomography with a computational microscope,” Biomed. Opt. Express 9, 2130–2141 (2018).

[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, 2376–2389 (2014).

[Crossref]

J. Sun, Q. Chen, Y. Zhang, and C. Zuo, “Efficient positional misalignment correction method for Fourier ptychographic microscopy,” Biomed. Opt. Express 7, 1336–1350 (2016).

[Crossref]

P. Chen and A. Fannjiang, “Coded aperture ptychography: uniqueness and reconstruction,” Inverse Probl. 34, 025003 (2018).

[Crossref]

N. Srivastava, G. Hinton, A. Krizhevsky, I. Sutskevar, and R. Salakhutdinov, “Dropout: a simple way to prevent neural networks from overfitting,” J. Mach. Learn. Res. 15, 1929–1958 (2014).

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[Crossref]

Y. Rivenson, Y. Zhang, H. Günaydn, D. Teng, and A. Ozcan, “Phase recovery and holographic image reconstruction using deep learning in neural networks,” Light Sci. Appl. 7, 17141–17149 (2018).

[Crossref]

M. Weigert, U. Schmidt, T. Boothe, A. Müller, A. Dibrov, A. Jain, B. Wilhelm, D. Schmidt, C. Broaddus, S. Culley, and M. Rocha-Martins, “Content-aware image restoration: pushing the limits of fluorescence microscopy,” Nat. Methods 15, 1090–1097 (2018).

[Crossref]

K. Wicker and R. Heintzmann, “Resolving a misconception about structured illumination,” Nat. Photonics 8, 342–344 (2014).

[Crossref]

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

[Crossref]

Z. Ghahramani, “Probabilistic machine learning and artificial intelligence,” Nature 521, 452–459 (2015).

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

[Crossref]

L. Tian and L. Waller, “Quantitative differential phase contrast imaging in an LED array microscope,” Opt. Express 23, 11394–11403 (2015).

[Crossref]

T. Nguyen, Y. Xue, Y. Li, L. Tian, and G. Nehmetallah, “Deep learning approach for Fourier ptychography microscopy,” Opt. Express 26, 26470–26484 (2018).

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