Abstract

Fourier ptychographic microscopy allows for the collection of images with a high space-bandwidth product at the cost of temporal resolution. In Fourier ptychographic microscopy, the light source of a conventional widefield microscope is replaced with a light-emitting diode (LED) matrix, and multiple images are collected with different LED illumination patterns. From these images, a higher-resolution image can be computationally reconstructed without sacrificing field-of-view. We use deep learning to achieve single-shot imaging without sacrificing the space-bandwidth product, reducing the acquisition time in Fourier ptychographic microscopy by a factor of 69. In our deep learning approach, a training dataset of high-resolution images is used to jointly optimize a single LED illumination pattern with the parameters of a reconstruction algorithm. Our work paves the way for high-throughput imaging in biological studies.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (4)

2015 (3)

2014 (3)

2013 (1)

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

2010 (1)

S. J. Pan and Q. Yang, “A Survey on Transfer Learning,” IEEE Transactions on Knowl. Data Eng. 22, 1345–1359 (2010).
[Crossref]

Abadi, M.

M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Jozefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mane, R. Monga, S. Moore, D. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. Tucker, V. Vanhoucke, V. Vasudevan, F. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems,” arXiv:1603.04467 [cs] (2016).

Agarwal, A.

M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Jozefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mane, R. Monga, S. Moore, D. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. Tucker, V. Vanhoucke, V. Vasudevan, F. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems,” arXiv:1603.04467 [cs] (2016).

Ba, J.

D. P. Kingma and J. Ba, “Adam: A Method for Stochastic Optimization,” arXiv:1412.6980 [cs] (2014).

Baburajan, R.

L. Boominathan, M. Maniparambil, H. Gupta, R. Baburajan, and K. Mitra, “Phase retrieval for Fourier Ptychography under varying amount of measurements,” arXiv:1805.03593 [cs] (2018).

Barham, P.

M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Jozefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mane, R. Monga, S. Moore, D. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. Tucker, V. Vanhoucke, V. Vasudevan, F. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems,” arXiv:1603.04467 [cs] (2016).

Bengio, Y.

Y. LeCun, P. Haffner, L. Bottou, and Y. Bengio, “Object Recognition with Gradient-Based Learning,” in Shape, Contour and Grouping in Computer Vision, (Springer-Verlag, London, UK, UK, 1999), pp. 319–347.
[Crossref]

Bian, Z.

Boominathan, L.

L. Boominathan, M. Maniparambil, H. Gupta, R. Baburajan, and K. Mitra, “Phase retrieval for Fourier Ptychography under varying amount of measurements,” arXiv:1805.03593 [cs] (2018).

Bostan, E.

M. R. Kellman, E. Bostan, N. Repina, M. Lustig, and L. Waller, “Physics-based Learned Design: Optimized Coded-Illumination for Quantitative Phase Imaging,” arXiv:1808.03571 [cs, eess] (2018).

Bottou, L.

Y. LeCun, P. Haffner, L. Bottou, and Y. Bengio, “Object Recognition with Gradient-Based Learning,” in Shape, Contour and Grouping in Computer Vision, (Springer-Verlag, London, UK, UK, 1999), pp. 319–347.
[Crossref]

Brevdo, E.

M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Jozefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mane, R. Monga, S. Moore, D. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. Tucker, V. Vanhoucke, V. Vasudevan, F. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems,” arXiv:1603.04467 [cs] (2016).

Bronstein, A.

H. Haim, S. Elmalem, R. Giryes, A. Bronstein, and E. Marom, “Depth Estimation from a Single Image using Deep Learned Phase Coded Mask,” IEEE Transactions on Comput. Imaging pp. 1 (2018).

Chakrabarti, A.

A. Chakrabarti, “Learning Sensor Multiplexing Design Through Back-propagation,” in Proceedings of the 30th International Conference on Neural Information Processing Systems, (Curran Associates Inc., USA, 2016), NIPS’16, pp. 3089–3097.

Chen, M.

Chen, R. Y.

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

Chen, Z.

M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Jozefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mane, R. Monga, S. Moore, D. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. Tucker, V. Vanhoucke, V. Vasudevan, F. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems,” arXiv:1603.04467 [cs] (2016).

Citro, C.

M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Jozefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mane, R. Monga, S. Moore, D. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. Tucker, V. Vanhoucke, V. Vasudevan, F. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems,” arXiv:1603.04467 [cs] (2016).

Corrado, G. S.

M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Jozefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mane, R. Monga, S. Moore, D. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. Tucker, V. Vanhoucke, V. Vasudevan, F. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems,” arXiv:1603.04467 [cs] (2016).

Cossairt, O.

S. Ghosh, Y. S. G. Nashed, O. Cossairt, and A. Katsaggelos, “ADP: Automatic differentiation ptychography,” in 2018 IEEE International Conference on Computational Photography (ICCP), (2018), pp. 1–10.

A. Kappeler, S. Ghosh, J. Holloway, O. Cossairt, and A. Katsaggelos, “Ptychnet: CNN based fourier ptychography,” in 2017 IEEE International Conference on Image Processing (ICIP), (IEEE, Beijing, 2017), pp. 1712–1716.
[Crossref]

Dai, Q.

Davis, A.

M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Jozefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mane, R. Monga, S. Moore, D. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. Tucker, V. Vanhoucke, V. Vasudevan, F. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems,” arXiv:1603.04467 [cs] (2016).

Dean, J.

M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Jozefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mane, R. Monga, S. Moore, D. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. Tucker, V. Vanhoucke, V. Vasudevan, F. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems,” arXiv:1603.04467 [cs] (2016).

Devin, M.

M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Jozefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mane, R. Monga, S. Moore, D. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. Tucker, V. Vanhoucke, V. Vasudevan, F. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems,” arXiv:1603.04467 [cs] (2016).

Diederich, B.

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] [PubMed]

Dong, J.

Dong, S.

Elmalem, S.

S. Elmalem, R. Giryes, and E. Marom, “Learned phase coded aperture for the benefit of depth of field extension,” Opt. Express 26, 15316–15331 (2018).
[Crossref] [PubMed]

H. Haim, S. Elmalem, R. Giryes, A. Bronstein, and E. Marom, “Depth Estimation from a Single Image using Deep Learned Phase Coded Mask,” IEEE Transactions on Comput. Imaging pp. 1 (2018).

Ganapati, V.

Ghemawat, S.

M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Jozefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mane, R. Monga, S. Moore, D. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. Tucker, V. Vanhoucke, V. Vasudevan, F. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems,” arXiv:1603.04467 [cs] (2016).

Ghosh, S.

S. Ghosh, Y. S. G. Nashed, O. Cossairt, and A. Katsaggelos, “ADP: Automatic differentiation ptychography,” in 2018 IEEE International Conference on Computational Photography (ICCP), (2018), pp. 1–10.

A. Kappeler, S. Ghosh, J. Holloway, O. Cossairt, and A. Katsaggelos, “Ptychnet: CNN based fourier ptychography,” in 2017 IEEE International Conference on Image Processing (ICIP), (IEEE, Beijing, 2017), pp. 1712–1716.
[Crossref]

Giryes, R.

S. Elmalem, R. Giryes, and E. Marom, “Learned phase coded aperture for the benefit of depth of field extension,” Opt. Express 26, 15316–15331 (2018).
[Crossref] [PubMed]

H. Haim, S. Elmalem, R. Giryes, A. Bronstein, and E. Marom, “Depth Estimation from a Single Image using Deep Learned Phase Coded Mask,” IEEE Transactions on Comput. Imaging pp. 1 (2018).

Goodfellow, I.

M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Jozefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mane, R. Monga, S. Moore, D. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. Tucker, V. Vanhoucke, V. Vasudevan, F. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems,” arXiv:1603.04467 [cs] (2016).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (Roberts and Company Publishers, 2005).

Guo, K.

Gupta, H.

L. Boominathan, M. Maniparambil, H. Gupta, R. Baburajan, and K. Mitra, “Phase retrieval for Fourier Ptychography under varying amount of measurements,” arXiv:1805.03593 [cs] (2018).

Haffner, P.

Y. LeCun, P. Haffner, L. Bottou, and Y. Bengio, “Object Recognition with Gradient-Based Learning,” in Shape, Contour and Grouping in Computer Vision, (Springer-Verlag, London, UK, UK, 1999), pp. 319–347.
[Crossref]

Haim, H.

H. Haim, S. Elmalem, R. Giryes, A. Bronstein, and E. Marom, “Depth Estimation from a Single Image using Deep Learned Phase Coded Mask,” IEEE Transactions on Comput. Imaging pp. 1 (2018).

Harp, A.

M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Jozefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mane, R. Monga, S. Moore, D. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. Tucker, V. Vanhoucke, V. Vasudevan, F. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems,” arXiv:1603.04467 [cs] (2016).

Heintzmann, R.

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] [PubMed]

Hershko, E.

E. Hershko, L. E. Weiss, T. Michaeli, and Y. Shechtman, “Multicolor localization microscopy by deep learning,” arXiv:1807.01637 [physics] (2018).

Holloway, J.

A. Kappeler, S. Ghosh, J. Holloway, O. Cossairt, and A. Katsaggelos, “Ptychnet: CNN based fourier ptychography,” in 2017 IEEE International Conference on Image Processing (ICIP), (IEEE, Beijing, 2017), pp. 1712–1716.
[Crossref]

Horstmeyer, R.

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 [physics] (2017).

Irving, G.

M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Jozefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mane, R. Monga, S. Moore, D. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. Tucker, V. Vanhoucke, V. Vasudevan, F. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems,” arXiv:1603.04467 [cs] (2016).

Isard, M.

M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Jozefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mane, R. Monga, S. Moore, D. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. Tucker, V. Vanhoucke, V. Vasudevan, F. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems,” arXiv:1603.04467 [cs] (2016).

Jia, Y.

M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Jozefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mane, R. Monga, S. Moore, D. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. Tucker, V. Vanhoucke, V. Vasudevan, F. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems,” arXiv:1603.04467 [cs] (2016).

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M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Jozefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mane, R. Monga, S. Moore, D. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. Tucker, V. Vanhoucke, V. Vasudevan, F. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems,” arXiv:1603.04467 [cs] (2016).

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M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Jozefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mane, R. Monga, S. Moore, D. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. Tucker, V. Vanhoucke, V. Vasudevan, F. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems,” arXiv:1603.04467 [cs] (2016).

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M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Jozefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mane, R. Monga, S. Moore, D. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. Tucker, V. Vanhoucke, V. Vasudevan, F. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems,” arXiv:1603.04467 [cs] (2016).

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Li, Y.

T. Nguyen, Y. Xue, Y. Li, L. Tian, and G. Nehmetallah, “Deep learning approach to Fourier ptychographic microscopy,” arXiv:1805.00334 [physics] (2018).

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M. R. Kellman, E. Bostan, N. Repina, M. Lustig, and L. Waller, “Physics-based Learned Design: Optimized Coded-Illumination for Quantitative Phase Imaging,” arXiv:1808.03571 [cs, eess] (2018).

Mane, D.

M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Jozefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mane, R. Monga, S. Moore, D. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. Tucker, V. Vanhoucke, V. Vasudevan, F. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems,” arXiv:1603.04467 [cs] (2016).

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L. Boominathan, M. Maniparambil, H. Gupta, R. Baburajan, and K. Mitra, “Phase retrieval for Fourier Ptychography under varying amount of measurements,” arXiv:1805.03593 [cs] (2018).

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X.-J. Mao, C. Shen, and Y.-B. Yang, “Image Restoration Using Convolutional Auto-encoders with Symmetric Skip Connections,” arXiv:1606.08921 [cs] (2016).

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E. Hershko, L. E. Weiss, T. Michaeli, and Y. Shechtman, “Multicolor localization microscopy by deep learning,” arXiv:1807.01637 [physics] (2018).

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L. Boominathan, M. Maniparambil, H. Gupta, R. Baburajan, and K. Mitra, “Phase retrieval for Fourier Ptychography under varying amount of measurements,” arXiv:1805.03593 [cs] (2018).

Monga, R.

M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Jozefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mane, R. Monga, S. Moore, D. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. Tucker, V. Vanhoucke, V. Vasudevan, F. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems,” arXiv:1603.04467 [cs] (2016).

Moore, S.

M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Jozefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mane, R. Monga, S. Moore, D. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. Tucker, V. Vanhoucke, V. Vasudevan, F. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems,” arXiv:1603.04467 [cs] (2016).

Murray, D.

M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Jozefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mane, R. Monga, S. Moore, D. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. Tucker, V. Vanhoucke, V. Vasudevan, F. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems,” arXiv:1603.04467 [cs] (2016).

Nashed, Y. S. G.

S. Ghosh, Y. S. G. Nashed, O. Cossairt, and A. Katsaggelos, “ADP: Automatic differentiation ptychography,” in 2018 IEEE International Conference on Computational Photography (ICCP), (2018), pp. 1–10.

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T. Nguyen, Y. Xue, Y. Li, L. Tian, and G. Nehmetallah, “Deep learning approach to Fourier ptychographic microscopy,” arXiv:1805.00334 [physics] (2018).

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T. Nguyen, Y. Xue, Y. Li, L. Tian, and G. Nehmetallah, “Deep learning approach to Fourier ptychographic microscopy,” arXiv:1805.00334 [physics] (2018).

Olah, C.

M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Jozefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mane, R. Monga, S. Moore, D. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. Tucker, V. Vanhoucke, V. Vasudevan, F. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems,” arXiv:1603.04467 [cs] (2016).

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Repina, N.

M. R. Kellman, E. Bostan, N. Repina, M. Lustig, and L. Waller, “Physics-based Learned Design: Optimized Coded-Illumination for Quantitative Phase Imaging,” arXiv:1808.03571 [cs, eess] (2018).

Robey, A.

Schadwinkel, H.

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).
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Schuster, M.

M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Jozefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mane, R. Monga, S. Moore, D. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. Tucker, V. Vanhoucke, V. Vasudevan, F. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems,” arXiv:1603.04467 [cs] (2016).

Shechtman, Y.

E. Hershko, L. E. Weiss, T. Michaeli, and Y. Shechtman, “Multicolor localization microscopy by deep learning,” arXiv:1807.01637 [physics] (2018).

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X.-J. Mao, C. Shen, and Y.-B. Yang, “Image Restoration Using Convolutional Auto-encoders with Symmetric Skip Connections,” arXiv:1606.08921 [cs] (2016).

Shiradkar, R.

Shlens, J.

M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Jozefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mane, R. Monga, S. Moore, D. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. Tucker, V. Vanhoucke, V. Vasudevan, F. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems,” arXiv:1603.04467 [cs] (2016).

Soltanolkotabi, M.

Steiner, B.

M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Jozefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mane, R. Monga, S. Moore, D. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. Tucker, V. Vanhoucke, V. Vasudevan, F. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems,” arXiv:1603.04467 [cs] (2016).

Sutskever, I.

M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Jozefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mane, R. Monga, S. Moore, D. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. Tucker, V. Vanhoucke, V. Vasudevan, F. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems,” arXiv:1603.04467 [cs] (2016).

Talwar, K.

M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Jozefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mane, R. Monga, S. Moore, D. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. Tucker, V. Vanhoucke, V. Vasudevan, F. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems,” arXiv:1603.04467 [cs] (2016).

Tang, G.

Tian, L.

Tucker, P.

M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Jozefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mane, R. Monga, S. Moore, D. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. Tucker, V. Vanhoucke, V. Vasudevan, F. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems,” arXiv:1603.04467 [cs] (2016).

Vanhoucke, V.

M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Jozefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mane, R. Monga, S. Moore, D. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. Tucker, V. Vanhoucke, V. Vasudevan, F. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems,” arXiv:1603.04467 [cs] (2016).

Vasudevan, V.

M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Jozefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mane, R. Monga, S. Moore, D. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. Tucker, V. Vanhoucke, V. Vasudevan, F. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems,” arXiv:1603.04467 [cs] (2016).

Viegas, F.

M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Jozefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mane, R. Monga, S. Moore, D. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. Tucker, V. Vanhoucke, V. Vasudevan, F. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems,” arXiv:1603.04467 [cs] (2016).

Vinyals, O.

M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Jozefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mane, R. Monga, S. Moore, D. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. Tucker, V. Vanhoucke, V. Vasudevan, F. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems,” arXiv:1603.04467 [cs] (2016).

Waller, L.

Warden, P.

M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Jozefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mane, R. Monga, S. Moore, D. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. Tucker, V. Vanhoucke, V. Vasudevan, F. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems,” arXiv:1603.04467 [cs] (2016).

Wartmann, R.

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).
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Wattenberg, M.

M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Jozefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mane, R. Monga, S. Moore, D. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. Tucker, V. Vanhoucke, V. Vasudevan, F. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems,” arXiv:1603.04467 [cs] (2016).

Weiss, L. E.

E. Hershko, L. E. Weiss, T. Michaeli, and Y. Shechtman, “Multicolor localization microscopy by deep learning,” arXiv:1807.01637 [physics] (2018).

Wicke, M.

M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Jozefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mane, R. Monga, S. Moore, D. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. Tucker, V. Vanhoucke, V. Vasudevan, F. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems,” arXiv:1603.04467 [cs] (2016).

Xue, Y.

T. Nguyen, Y. Xue, Y. Li, L. Tian, and G. Nehmetallah, “Deep learning approach to Fourier ptychographic microscopy,” arXiv:1805.00334 [physics] (2018).

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

S. J. Pan and Q. Yang, “A Survey on Transfer Learning,” IEEE Transactions on Knowl. Data Eng. 22, 1345–1359 (2010).
[Crossref]

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X.-J. Mao, C. Shen, and Y.-B. Yang, “Image Restoration Using Convolutional Auto-encoders with Symmetric Skip Connections,” arXiv:1606.08921 [cs] (2016).

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Figures (8)

Fig. 1
Fig. 1 Fourier ptychographic microscopy setup. (a) Schematic of the Fourier ptychographic microscopy setup. An LED matrix replaces the illumination source of a conventional microscope. (b) Experimental Fourier ptychographic microscopy setup. We utilize a 20× magnification objective with a numerical aperture of 0.5 in our setup.
Fig. 2
Fig. 2 Brightfield image intensity (top) and intensity of the iterative Fourier ptychographic (FP) reconstruction (bottom) of a target slide. We see improved image quality in the iterative Fourier ptychographic reconstruction. The zoomed in region has a resolution of 228.0 line pairs per millimeter.
Fig. 3
Fig. 3 Overview of the training and evaluation steps in our data-driven joint hardware and software optimization.
Fig. 4
Fig. 4 We include a Gaussian approximation of Poisson noise in our computational model of the Fourier ptychographic microscope. To estimate m in Eq. (7), we took 100 images with the center LED illuminated. This plot shows the square root of the sample mean vs. the sample standard deviation at every point of the image stack. The slope s = 1 m.
Fig. 5
Fig. 5 An image patch from the evaluation dataset. From left to right: the amplitude and phase of the iterative Fourier ptychographic (FP) reconstruction, 3 images from the 69 low-resolution image stack each with single LED illumination, the collected image with the optimized LED illumination pattern, and the amplitude and phase of the neural network reconstruction. In the 3 images from the low-resolution stack, there is a circular artifact corresponding to the image of the single source LED.
Fig. 6
Fig. 6 Initial and final LED illumination patterns with the corresponding emulated image patches. The exposures for the initial and final images are 200 and 1140 milliseconds, respectively. We visually see an increase in contrast and information content in the final image with the optimized LED illumination pattern.
Fig. 7
Fig. 7 Examples from the evaluation dataset, comparing amplitude of the iterative Fourier ptychographic (FP) reconstruction (the ground truth) and the neural network output. We see high fidelity between the two reconstructions. The neural network output requires only 1 collected image, representing a factor of 69 decrease in acquisition time. Linescans cut through cells in different phases of the cell cycle; cells are in (a) anaphase, (b) prophase, and (c) interphase.
Fig. 8
Fig. 8 Example from the evaluation dataset, comparing phase of the iterative Fourier ptychographic (FP) reconstruction (the ground truth) and the neural network output. The corresponding amplitude is given in Fig. 7(b). We see similar features in the two phase maps. It appears that much of the phase noise in Fourier ptychographic reconstruction is filtered out by the neural network.

Equations (7)

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o ( x , y ) e i 2 π ( u l , x x + u l , y y ) .
I = | 1 { P ( u x , u y ) O ( u x u l , x , u y u l , y ) } | 2 ,
I = l = 1 n c l | { P ( u x , u y ) O ( u x u l , x , u y u l , y ) } | 2 ,
o ( x , y ) = 1 69 l = 0 68 I l ( x , y ) ,
L = l = 0 68 ( I l ( x , y ) I l g ( x , y ) ) 2 ,
I s ( x , y ) = l = 0 68 c l I l ( x , y )
max ( I low × m × g + I low × m m , 0 ) ,

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