Abstract

Imaging under ultra-weak light conditions is affected by Poisson noise heavily. The problem becomes worse if a scattering media is present in the optical path. Speckle patterns detected under ultra-weak light condition carry very little information which makes it difficult to reconstruct the image. Off-the-shelf methods are no longer available in this condition. In this paper, we experimentally demonstrate the use of a deep learning network to reconstruct images through scattering media under ultra-weak light illumination. The weak light limitation of this method is analyzed. The random Poisson detection under weak light condition obtains partial information of the object. Based on this property, we demonstrated better performance of our method by enlarging the training dataset with multiple detections of the speckle patterns. Our results demonstrate that our approach can reconstruct images through scattering media from close to $1$ detected signal photon per pixel (PPP) per image.

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

Full Article  |  PDF Article
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References

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2019 (3)

H. Wang, Y. Rivenson, Y. Jin, Z. Wei, R. Gao, H. Gunaydin, L. Bentolila, and A. Ozcan, “Deep learning achieves super-resolution in fluorescence microscopy,” Nat. Methods 16(1), 103–110 (2019).
[Crossref]

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[Crossref]

Y. Sun, J. Shi, L. Sun, J. Fan, and G. Zeng, “Image reconstruction through dynamic scattering media based on deep learning,” Opt. Express 27(11), 16032–16046 (2019).
[Crossref]

2018 (7)

2017 (4)

2016 (2)

2015 (4)

R. Horstmeyer, H. Ruan, and C. Yang, “Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue,” Nat. Photonics 9(9), 563–571 (2015).
[Crossref]

P. A. Morris, R. S. Aspden, J. E. Bell, R. W. Boyd, and M. J. Padgett, “Imaging with a small number of photons,” Nat. Commun. 6(1), 5913 (2015).
[Crossref]

M. Kim, W. Choi, Y. Choi, C. Yoon, and W. Choi, “Transmission matrix of a scattering medium and its applications in biophotonics,” Opt. Express 23(10), 12648–12668 (2015).
[Crossref]

T. Ando, R. Horisaki, and J. Tanida, “Speckle-learning-based object recognition through scattering media,” Opt. Express 23(26), 33902–33910 (2015).
[Crossref]

2014 (3)

D. Bronzi, F. Villa, S. Tisa, A. Tosi, F. Zappa, D. Durini, S. Weyers, and W. Brockherde, “100 000 frames/s 64$\times$× 32 single-photon detector array for 2-d imaging and 3-d ranging,” IEEE J. Sel. Top. Quantum Electron. 20(6), 354–363 (2014).
[Crossref]

O. Katz, P. Heidmann, M. Fink, and S. Gigan, “Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations,” Nat. Photonics 8(10), 784–790 (2014).
[Crossref]

J. Salmon, Z. Harmany, C.-A. Deledalle, and R. Willett, “Poisson noise reduction with non-local pca,” J. Math. Imaging Vis. 48(2), 279–294 (2014).
[Crossref]

2012 (1)

J. Bertolotti, E. G. Van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491(7423), 232–234 (2012).
[Crossref]

2010 (2)

S. Popoff, G. Lerosey, R. Carminati, M. Fink, A. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104(10), 100601 (2010).
[Crossref]

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Image transmission through an opaque material,” Nat. Commun. 1(1), 81 (2010).
[Crossref]

2003 (1)

E. Waks, K. Inoue, W. D. Oliver, E. Diamanti, and Y. Yamamoto, “High-efficiency photon-number detection for quantum information processing,” IEEE J. Sel. Top. Quantum Electron. 9(6), 1502–1511 (2003).
[Crossref]

1999 (1)

K. Timmerman and R. D. Nowak, “Multiscale modeling and estimation of poisson processes with application to photon-limited imaging,” IEEE Trans. Inf. Theory 45(3), 846–862 (1999).
[Crossref]

1995 (1)

1968 (1)

Alfano, R.

Ando, T.

Andresen, E. R.

Arthur, K.

A. Goy, K. Arthur, S. Li, and G. Barbastathis, “Low photon count phase retrieval using deep learning,” Phys. Rev. Lett. 121(24), 243902 (2018).
[Crossref]

Aspden, R. S.

P. A. Morris, R. S. Aspden, J. E. Bell, R. W. Boyd, and M. J. Padgett, “Imaging with a small number of photons,” Nat. Commun. 6(1), 5913 (2015).
[Crossref]

Avidan, S.

D. Berman and S. Avidan, “Non-local image dehazing,” in Proceedings of the IEEE conference on computer vision and pattern recognition, (2016), pp. 1674–1682.

Barbastathis, G.

Bell, J. E.

P. A. Morris, R. S. Aspden, J. E. Bell, R. W. Boyd, and M. J. Padgett, “Imaging with a small number of photons,” Nat. Commun. 6(1), 5913 (2015).
[Crossref]

Bentolila, L.

H. Wang, Y. Rivenson, Y. Jin, Z. Wei, R. Gao, H. Gunaydin, L. Bentolila, and A. Ozcan, “Deep learning achieves super-resolution in fluorescence microscopy,” Nat. Methods 16(1), 103–110 (2019).
[Crossref]

Berman, D.

D. Berman and S. Avidan, “Non-local image dehazing,” in Proceedings of the IEEE conference on computer vision and pattern recognition, (2016), pp. 1674–1682.

Bertolotti, J.

J. Bertolotti, E. G. Van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491(7423), 232–234 (2012).
[Crossref]

Blum, C.

J. Bertolotti, E. G. Van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491(7423), 232–234 (2012).
[Crossref]

Boccara, A.

S. Popoff, G. Lerosey, R. Carminati, M. Fink, A. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104(10), 100601 (2010).
[Crossref]

Boccara, A. C.

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Image transmission through an opaque material,” Nat. Commun. 1(1), 81 (2010).
[Crossref]

Borhani, N.

Boyd, R. W.

P. A. Morris, R. S. Aspden, J. E. Bell, R. W. Boyd, and M. J. Padgett, “Imaging with a small number of photons,” Nat. Commun. 6(1), 5913 (2015).
[Crossref]

Brockherde, W.

D. Bronzi, F. Villa, S. Tisa, A. Tosi, F. Zappa, D. Durini, S. Weyers, and W. Brockherde, “100 000 frames/s 64$\times$× 32 single-photon detector array for 2-d imaging and 3-d ranging,” IEEE J. Sel. Top. Quantum Electron. 20(6), 354–363 (2014).
[Crossref]

Bronstein, A. M.

T. Remez, O. Litany, R. Giryes, and A. M. Bronstein, “Class-aware fully convolutional gaussian and poisson denoising,” IEEE Trans. on Image Process. 27(11), 5707–5722 (2018).
[Crossref]

T. Remez, O. Litany, R. Giryes, and A. M. Bronstein, “Deep convolutional denoising of low-light images,” arXiv preprint arXiv:1701.01687 (2017).

Bronzi, D.

D. Bronzi, F. Villa, S. Tisa, A. Tosi, F. Zappa, D. Durini, S. Weyers, and W. Brockherde, “100 000 frames/s 64$\times$× 32 single-photon detector array for 2-d imaging and 3-d ranging,” IEEE J. Sel. Top. Quantum Electron. 20(6), 354–363 (2014).
[Crossref]

Brox, T.

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.

Caramazza, P.

P. Caramazza, O. Moran, R. Murray-Smith, and D. Faccio, “Transmission of natural scene images through a multimode fibre,” Nat. Commun. 10(1), 2029 (2019).
[Crossref]

Carminati, R.

S. Popoff, G. Lerosey, R. Carminati, M. Fink, A. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104(10), 100601 (2010).
[Crossref]

Choi, W.

Choi, Y.

d Seelig, J.

Deledalle, C.-A.

J. Salmon, Z. Harmany, C.-A. Deledalle, and R. Willett, “Poisson noise reduction with non-local pca,” J. Math. Imaging Vis. 48(2), 279–294 (2014).
[Crossref]

Deng, M.

Diamanti, E.

E. Waks, K. Inoue, W. D. Oliver, E. Diamanti, and Y. Yamamoto, “High-efficiency photon-number detection for quantum information processing,” IEEE J. Sel. Top. Quantum Electron. 9(6), 1502–1511 (2003).
[Crossref]

Durini, D.

D. Bronzi, F. Villa, S. Tisa, A. Tosi, F. Zappa, D. Durini, S. Weyers, and W. Brockherde, “100 000 frames/s 64$\times$× 32 single-photon detector array for 2-d imaging and 3-d ranging,” IEEE J. Sel. Top. Quantum Electron. 20(6), 354–363 (2014).
[Crossref]

Engheta, N.

Faccio, D.

P. Caramazza, O. Moran, R. Murray-Smith, and D. Faccio, “Transmission of natural scene images through a multimode fibre,” Nat. Commun. 10(1), 2029 (2019).
[Crossref]

Fan, J.

Fantoni, I.

A. M. Neto, A. C. Victorino, I. Fantoni, D. E. Zampieri, J. V. Ferreira, and D. A. Lima, “Image processing using pearson’s correlation coefficient: Applications on autonomous robotics,” in 2013 13th International Conference on Autonomous Robot Systems, (IEEE, 2013), pp. 1–6.

Ferreira, J. V.

A. M. Neto, A. C. Victorino, I. Fantoni, D. E. Zampieri, J. V. Ferreira, and D. A. Lima, “Image processing using pearson’s correlation coefficient: Applications on autonomous robotics,” in 2013 13th International Conference on Autonomous Robot Systems, (IEEE, 2013), pp. 1–6.

Fink, M.

O. Katz, P. Heidmann, M. Fink, and S. Gigan, “Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations,” Nat. Photonics 8(10), 784–790 (2014).
[Crossref]

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Image transmission through an opaque material,” Nat. Commun. 1(1), 81 (2010).
[Crossref]

S. Popoff, G. Lerosey, R. Carminati, M. Fink, A. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104(10), 100601 (2010).
[Crossref]

Fischer, P.

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.

Gao, R.

H. Wang, Y. Rivenson, Y. Jin, Z. Wei, R. Gao, H. Gunaydin, L. Bentolila, and A. Ozcan, “Deep learning achieves super-resolution in fluorescence microscopy,” Nat. Methods 16(1), 103–110 (2019).
[Crossref]

Gigan, S.

A. Porat, E. R. Andresen, H. Rigneault, D. Oron, S. Gigan, and O. Katz, “Widefield lensless imaging through a fiber bundle via speckle correlations,” Opt. Express 24(15), 16835–16855 (2016).
[Crossref]

O. Katz, P. Heidmann, M. Fink, and S. Gigan, “Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations,” Nat. Photonics 8(10), 784–790 (2014).
[Crossref]

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Image transmission through an opaque material,” Nat. Commun. 1(1), 81 (2010).
[Crossref]

S. Popoff, G. Lerosey, R. Carminati, M. Fink, A. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104(10), 100601 (2010).
[Crossref]

Giryes, R.

T. Remez, O. Litany, R. Giryes, and A. M. Bronstein, “Class-aware fully convolutional gaussian and poisson denoising,” IEEE Trans. on Image Process. 27(11), 5707–5722 (2018).
[Crossref]

T. Remez, O. Litany, R. Giryes, and A. M. Bronstein, “Deep convolutional denoising of low-light images,” arXiv preprint arXiv:1701.01687 (2017).

Göröcs, Z.

Goy, A.

A. Goy, K. Arthur, S. Li, and G. Barbastathis, “Low photon count phase retrieval using deep learning,” Phys. Rev. Lett. 121(24), 243902 (2018).
[Crossref]

Gunaydin, H.

H. Wang, Y. Rivenson, Y. Jin, Z. Wei, R. Gao, H. Gunaydin, L. Bentolila, and A. Ozcan, “Deep learning achieves super-resolution in fluorescence microscopy,” Nat. Methods 16(1), 103–110 (2019).
[Crossref]

Günaydin, H.

Gupta, O.

Harmany, Z.

J. Salmon, Z. Harmany, C.-A. Deledalle, and R. Willett, “Poisson noise reduction with non-local pca,” J. Math. Imaging Vis. 48(2), 279–294 (2014).
[Crossref]

He, K.

K. He, X. Zhang, S. Ren, and J. Sun, “Deep residual learning for image recognition,” in Proceedings of the IEEE conference on computer vision and pattern recognition, (2016), pp. 770–778.

Heidmann, P.

O. Katz, P. Heidmann, M. Fink, and S. Gigan, “Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations,” Nat. Photonics 8(10), 784–790 (2014).
[Crossref]

Heshmat, B.

Horisaki, R.

Horstmeyer, R.

G. Osnabrugge, R. Horstmeyer, I. N. Papadopoulos, B. Judkewitz, and I. M. Vellekoop, “Generalized optical memory effect,” Optica 4(8), 886–892 (2017).
[Crossref]

R. Horstmeyer, H. Ruan, and C. Yang, “Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue,” Nat. Photonics 9(9), 563–571 (2015).
[Crossref]

Huang, G.

G. Huang, Z. Liu, L. Van Der Maaten, and K. Q. Weinberger, “Densely connected convolutional networks,” in Proceedings of the IEEE conference on computer vision and pattern recognition, (2017), pp. 4700–4708.

Inoue, K.

E. Waks, K. Inoue, W. D. Oliver, E. Diamanti, and Y. Yamamoto, “High-efficiency photon-number detection for quantum information processing,” IEEE J. Sel. Top. Quantum Electron. 9(6), 1502–1511 (2003).
[Crossref]

Jin, Y.

H. Wang, Y. Rivenson, Y. Jin, Z. Wei, R. Gao, H. Gunaydin, L. Bentolila, and A. Ozcan, “Deep learning achieves super-resolution in fluorescence microscopy,” Nat. Methods 16(1), 103–110 (2019).
[Crossref]

Judkewitz, B.

Kakkava, E.

Katz, O.

A. Porat, E. R. Andresen, H. Rigneault, D. Oron, S. Gigan, and O. Katz, “Widefield lensless imaging through a fiber bundle via speckle correlations,” Opt. Express 24(15), 16835–16855 (2016).
[Crossref]

O. Katz, P. Heidmann, M. Fink, and S. Gigan, “Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations,” Nat. Photonics 8(10), 784–790 (2014).
[Crossref]

Kim, M.

Koltun, V.

F. Yu and V. Koltun, “Multi-scale context aggregation by dilated convolutions,” arXiv preprint arXiv:1511.07122 (2015).

Lagendijk, A.

J. Bertolotti, E. G. Van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491(7423), 232–234 (2012).
[Crossref]

Lee, J.

Lerosey, G.

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Image transmission through an opaque material,” Nat. Commun. 1(1), 81 (2010).
[Crossref]

S. Popoff, G. Lerosey, R. Carminati, M. Fink, A. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104(10), 100601 (2010).
[Crossref]

Li, S.

Li, Y.

Lima, D. A.

A. M. Neto, A. C. Victorino, I. Fantoni, D. E. Zampieri, J. V. Ferreira, and D. A. Lima, “Image processing using pearson’s correlation coefficient: Applications on autonomous robotics,” in 2013 13th International Conference on Autonomous Robot Systems, (IEEE, 2013), pp. 1–6.

Litany, O.

T. Remez, O. Litany, R. Giryes, and A. M. Bronstein, “Class-aware fully convolutional gaussian and poisson denoising,” IEEE Trans. on Image Process. 27(11), 5707–5722 (2018).
[Crossref]

T. Remez, O. Litany, R. Giryes, and A. M. Bronstein, “Deep convolutional denoising of low-light images,” arXiv preprint arXiv:1701.01687 (2017).

Liu, Z.

G. Huang, Z. Liu, L. Van Der Maaten, and K. Q. Weinberger, “Densely connected convolutional networks,” in Proceedings of the IEEE conference on computer vision and pattern recognition, (2017), pp. 4700–4708.

Moran, O.

P. Caramazza, O. Moran, R. Murray-Smith, and D. Faccio, “Transmission of natural scene images through a multimode fibre,” Nat. Commun. 10(1), 2029 (2019).
[Crossref]

Morris, P. A.

P. A. Morris, R. S. Aspden, J. E. Bell, R. W. Boyd, and M. J. Padgett, “Imaging with a small number of photons,” Nat. Commun. 6(1), 5913 (2015).
[Crossref]

Moser, C.

Mosk, A. P.

J. Bertolotti, E. G. Van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491(7423), 232–234 (2012).
[Crossref]

Murray-Smith, R.

P. Caramazza, O. Moran, R. Murray-Smith, and D. Faccio, “Transmission of natural scene images through a multimode fibre,” Nat. Commun. 10(1), 2029 (2019).
[Crossref]

Neto, A. M.

A. M. Neto, A. C. Victorino, I. Fantoni, D. E. Zampieri, J. V. Ferreira, and D. A. Lima, “Image processing using pearson’s correlation coefficient: Applications on autonomous robotics,” in 2013 13th International Conference on Autonomous Robot Systems, (IEEE, 2013), pp. 1–6.

Niu, Z.

Nowak, R. D.

K. Timmerman and R. D. Nowak, “Multiscale modeling and estimation of poisson processes with application to photon-limited imaging,” IEEE Trans. Inf. Theory 45(3), 846–862 (1999).
[Crossref]

Ockman, N.

Oliver, W. D.

E. Waks, K. Inoue, W. D. Oliver, E. Diamanti, and Y. Yamamoto, “High-efficiency photon-number detection for quantum information processing,” IEEE J. Sel. Top. Quantum Electron. 9(6), 1502–1511 (2003).
[Crossref]

Oron, D.

Osnabrugge, G.

Ozcan, A.

H. Wang, Y. Rivenson, Y. Jin, Z. Wei, R. Gao, H. Gunaydin, L. Bentolila, and A. Ozcan, “Deep learning achieves super-resolution in fluorescence microscopy,” Nat. Methods 16(1), 103–110 (2019).
[Crossref]

Y. Rivenson, Z. Göröcs, H. Günaydin, Y. Zhang, H. Wang, and A. Ozcan, “Deep learning microscopy,” Optica 4(11), 1437–1443 (2017).
[Crossref]

Padgett, M. J.

P. A. Morris, R. S. Aspden, J. E. Bell, R. W. Boyd, and M. J. Padgett, “Imaging with a small number of photons,” Nat. Commun. 6(1), 5913 (2015).
[Crossref]

Papadopoulos, I. N.

Perez, L.

L. Perez and J. Wang, “The effectiveness of data augmentation in image classification using deep learning,” arXiv preprint arXiv:1712.04621 (2017).

Popoff, S.

S. Popoff, G. Lerosey, R. Carminati, M. Fink, A. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104(10), 100601 (2010).
[Crossref]

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Image transmission through an opaque material,” Nat. Commun. 1(1), 81 (2010).
[Crossref]

Porat, A.

Psaltis, D.

Pugh, E.

Raskar, R.

G. Satat, M. Tancik, O. Gupta, B. Heshmat, and R. Raskar, “Object classification through scattering media with deep learning on time resolved measurement,” Opt. Express 25(15), 17466–17479 (2017).
[Crossref]

G. Satat, M. Tancik, and R. Raskar, “Towards photography through realistic fog,” in Computational Photography (ICCP), 2018 IEEE International Conference on, (IEEE, 2018), pp. 1–10.

Remez, T.

T. Remez, O. Litany, R. Giryes, and A. M. Bronstein, “Class-aware fully convolutional gaussian and poisson denoising,” IEEE Trans. on Image Process. 27(11), 5707–5722 (2018).
[Crossref]

T. Remez, O. Litany, R. Giryes, and A. M. Bronstein, “Deep convolutional denoising of low-light images,” arXiv preprint arXiv:1701.01687 (2017).

Ren, S.

K. He, X. Zhang, S. Ren, and J. Sun, “Deep residual learning for image recognition,” in Proceedings of the IEEE conference on computer vision and pattern recognition, (2016), pp. 770–778.

Rigneault, H.

Rivenson, Y.

H. Wang, Y. Rivenson, Y. Jin, Z. Wei, R. Gao, H. Gunaydin, L. Bentolila, and A. Ozcan, “Deep learning achieves super-resolution in fluorescence microscopy,” Nat. Methods 16(1), 103–110 (2019).
[Crossref]

Y. Rivenson, Z. Göröcs, H. Günaydin, Y. Zhang, H. Wang, and A. Ozcan, “Deep learning microscopy,” Optica 4(11), 1437–1443 (2017).
[Crossref]

Ronneberger, O.

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.

Rowe, M.

Ruan, H.

R. Horstmeyer, H. Ruan, and C. Yang, “Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue,” Nat. Photonics 9(9), 563–571 (2015).
[Crossref]

Salmon, J.

J. Salmon, Z. Harmany, C.-A. Deledalle, and R. Willett, “Poisson noise reduction with non-local pca,” J. Math. Imaging Vis. 48(2), 279–294 (2014).
[Crossref]

Satat, G.

G. Satat, M. Tancik, O. Gupta, B. Heshmat, and R. Raskar, “Object classification through scattering media with deep learning on time resolved measurement,” Opt. Express 25(15), 17466–17479 (2017).
[Crossref]

G. Satat, M. Tancik, and R. Raskar, “Towards photography through realistic fog,” in Computational Photography (ICCP), 2018 IEEE International Conference on, (IEEE, 2018), pp. 1–10.

Schechner, Y. Y.

M. Sheinin and Y. Y. Schechner, “The next best underwater view,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, (2016), pp. 3764–3773.

Sheinin, M.

M. Sheinin and Y. Y. Schechner, “The next best underwater view,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, (2016), pp. 3764–3773.

Shi, J.

Sinha, A.

Sun, J.

K. He, X. Zhang, S. Ren, and J. Sun, “Deep residual learning for image recognition,” in Proceedings of the IEEE conference on computer vision and pattern recognition, (2016), pp. 770–778.

Sun, L.

Sun, Y.

Takagi, R.

Tancik, M.

G. Satat, M. Tancik, O. Gupta, B. Heshmat, and R. Raskar, “Object classification through scattering media with deep learning on time resolved measurement,” Opt. Express 25(15), 17466–17479 (2017).
[Crossref]

G. Satat, M. Tancik, and R. Raskar, “Towards photography through realistic fog,” in Computational Photography (ICCP), 2018 IEEE International Conference on, (IEEE, 2018), pp. 1–10.

Tanida, J.

Tian, L.

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K. Timmerman and R. D. Nowak, “Multiscale modeling and estimation of poisson processes with application to photon-limited imaging,” IEEE Trans. Inf. Theory 45(3), 846–862 (1999).
[Crossref]

Tisa, S.

D. Bronzi, F. Villa, S. Tisa, A. Tosi, F. Zappa, D. Durini, S. Weyers, and W. Brockherde, “100 000 frames/s 64$\times$× 32 single-photon detector array for 2-d imaging and 3-d ranging,” IEEE J. Sel. Top. Quantum Electron. 20(6), 354–363 (2014).
[Crossref]

Tosi, A.

D. Bronzi, F. Villa, S. Tisa, A. Tosi, F. Zappa, D. Durini, S. Weyers, and W. Brockherde, “100 000 frames/s 64$\times$× 32 single-photon detector array for 2-d imaging and 3-d ranging,” IEEE J. Sel. Top. Quantum Electron. 20(6), 354–363 (2014).
[Crossref]

Turpin, A.

Tyo, J. S.

Van Der Maaten, L.

G. Huang, Z. Liu, L. Van Der Maaten, and K. Q. Weinberger, “Densely connected convolutional networks,” in Proceedings of the IEEE conference on computer vision and pattern recognition, (2017), pp. 4700–4708.

Van Putten, E. G.

J. Bertolotti, E. G. Van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491(7423), 232–234 (2012).
[Crossref]

Vellekoop, I. M.

Victorino, A. C.

A. M. Neto, A. C. Victorino, I. Fantoni, D. E. Zampieri, J. V. Ferreira, and D. A. Lima, “Image processing using pearson’s correlation coefficient: Applications on autonomous robotics,” in 2013 13th International Conference on Autonomous Robot Systems, (IEEE, 2013), pp. 1–6.

Villa, F.

D. Bronzi, F. Villa, S. Tisa, A. Tosi, F. Zappa, D. Durini, S. Weyers, and W. Brockherde, “100 000 frames/s 64$\times$× 32 single-photon detector array for 2-d imaging and 3-d ranging,” IEEE J. Sel. Top. Quantum Electron. 20(6), 354–363 (2014).
[Crossref]

Vishniakou, I.

Vos, W. L.

J. Bertolotti, E. G. Van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491(7423), 232–234 (2012).
[Crossref]

Waks, E.

E. Waks, K. Inoue, W. D. Oliver, E. Diamanti, and Y. Yamamoto, “High-efficiency photon-number detection for quantum information processing,” IEEE J. Sel. Top. Quantum Electron. 9(6), 1502–1511 (2003).
[Crossref]

Wang, H.

H. Wang, Y. Rivenson, Y. Jin, Z. Wei, R. Gao, H. Gunaydin, L. Bentolila, and A. Ozcan, “Deep learning achieves super-resolution in fluorescence microscopy,” Nat. Methods 16(1), 103–110 (2019).
[Crossref]

Y. Rivenson, Z. Göröcs, H. Günaydin, Y. Zhang, H. Wang, and A. Ozcan, “Deep learning microscopy,” Optica 4(11), 1437–1443 (2017).
[Crossref]

Wang, J.

L. Perez and J. Wang, “The effectiveness of data augmentation in image classification using deep learning,” arXiv preprint arXiv:1712.04621 (2017).

Wei, Z.

H. Wang, Y. Rivenson, Y. Jin, Z. Wei, R. Gao, H. Gunaydin, L. Bentolila, and A. Ozcan, “Deep learning achieves super-resolution in fluorescence microscopy,” Nat. Methods 16(1), 103–110 (2019).
[Crossref]

Weinberger, K. Q.

G. Huang, Z. Liu, L. Van Der Maaten, and K. Q. Weinberger, “Densely connected convolutional networks,” in Proceedings of the IEEE conference on computer vision and pattern recognition, (2017), pp. 4700–4708.

Weyers, S.

D. Bronzi, F. Villa, S. Tisa, A. Tosi, F. Zappa, D. Durini, S. Weyers, and W. Brockherde, “100 000 frames/s 64$\times$× 32 single-photon detector array for 2-d imaging and 3-d ranging,” IEEE J. Sel. Top. Quantum Electron. 20(6), 354–363 (2014).
[Crossref]

Willett, R.

J. Salmon, Z. Harmany, C.-A. Deledalle, and R. Willett, “Poisson noise reduction with non-local pca,” J. Math. Imaging Vis. 48(2), 279–294 (2014).
[Crossref]

Xue, Y.

Yamamoto, Y.

E. Waks, K. Inoue, W. D. Oliver, E. Diamanti, and Y. Yamamoto, “High-efficiency photon-number detection for quantum information processing,” IEEE J. Sel. Top. Quantum Electron. 9(6), 1502–1511 (2003).
[Crossref]

Yang, C.

R. Horstmeyer, H. Ruan, and C. Yang, “Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue,” Nat. Photonics 9(9), 563–571 (2015).
[Crossref]

Yoon, C.

Yu, F.

F. Yu and V. Koltun, “Multi-scale context aggregation by dilated convolutions,” arXiv preprint arXiv:1511.07122 (2015).

Zampieri, D. E.

A. M. Neto, A. C. Victorino, I. Fantoni, D. E. Zampieri, J. V. Ferreira, and D. A. Lima, “Image processing using pearson’s correlation coefficient: Applications on autonomous robotics,” in 2013 13th International Conference on Autonomous Robot Systems, (IEEE, 2013), pp. 1–6.

Zappa, F.

D. Bronzi, F. Villa, S. Tisa, A. Tosi, F. Zappa, D. Durini, S. Weyers, and W. Brockherde, “100 000 frames/s 64$\times$× 32 single-photon detector array for 2-d imaging and 3-d ranging,” IEEE J. Sel. Top. Quantum Electron. 20(6), 354–363 (2014).
[Crossref]

Zeng, G.

Zhang, X.

K. He, X. Zhang, S. Ren, and J. Sun, “Deep residual learning for image recognition,” in Proceedings of the IEEE conference on computer vision and pattern recognition, (2016), pp. 770–778.

Zhang, Y.

Zhu, Y.

IEEE J. Sel. Top. Quantum Electron. (2)

E. Waks, K. Inoue, W. D. Oliver, E. Diamanti, and Y. Yamamoto, “High-efficiency photon-number detection for quantum information processing,” IEEE J. Sel. Top. Quantum Electron. 9(6), 1502–1511 (2003).
[Crossref]

D. Bronzi, F. Villa, S. Tisa, A. Tosi, F. Zappa, D. Durini, S. Weyers, and W. Brockherde, “100 000 frames/s 64$\times$× 32 single-photon detector array for 2-d imaging and 3-d ranging,” IEEE J. Sel. Top. Quantum Electron. 20(6), 354–363 (2014).
[Crossref]

IEEE Trans. Inf. Theory (1)

K. Timmerman and R. D. Nowak, “Multiscale modeling and estimation of poisson processes with application to photon-limited imaging,” IEEE Trans. Inf. Theory 45(3), 846–862 (1999).
[Crossref]

IEEE Trans. on Image Process. (1)

T. Remez, O. Litany, R. Giryes, and A. M. Bronstein, “Class-aware fully convolutional gaussian and poisson denoising,” IEEE Trans. on Image Process. 27(11), 5707–5722 (2018).
[Crossref]

J. Math. Imaging Vis. (1)

J. Salmon, Z. Harmany, C.-A. Deledalle, and R. Willett, “Poisson noise reduction with non-local pca,” J. Math. Imaging Vis. 48(2), 279–294 (2014).
[Crossref]

J. Opt. Soc. Am. (1)

Nat. Commun. (3)

P. A. Morris, R. S. Aspden, J. E. Bell, R. W. Boyd, and M. J. Padgett, “Imaging with a small number of photons,” Nat. Commun. 6(1), 5913 (2015).
[Crossref]

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Image transmission through an opaque material,” Nat. Commun. 1(1), 81 (2010).
[Crossref]

P. Caramazza, O. Moran, R. Murray-Smith, and D. Faccio, “Transmission of natural scene images through a multimode fibre,” Nat. Commun. 10(1), 2029 (2019).
[Crossref]

Nat. Methods (1)

H. Wang, Y. Rivenson, Y. Jin, Z. Wei, R. Gao, H. Gunaydin, L. Bentolila, and A. Ozcan, “Deep learning achieves super-resolution in fluorescence microscopy,” Nat. Methods 16(1), 103–110 (2019).
[Crossref]

Nat. Photonics (2)

O. Katz, P. Heidmann, M. Fink, and S. Gigan, “Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations,” Nat. Photonics 8(10), 784–790 (2014).
[Crossref]

R. Horstmeyer, H. Ruan, and C. Yang, “Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue,” Nat. Photonics 9(9), 563–571 (2015).
[Crossref]

Nature (1)

J. Bertolotti, E. G. Van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491(7423), 232–234 (2012).
[Crossref]

Opt. Express (8)

Opt. Lett. (1)

Optica (6)

Phys. Rev. Lett. (2)

S. Popoff, G. Lerosey, R. Carminati, M. Fink, A. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104(10), 100601 (2010).
[Crossref]

A. Goy, K. Arthur, S. Li, and G. Barbastathis, “Low photon count phase retrieval using deep learning,” Phys. Rev. Lett. 121(24), 243902 (2018).
[Crossref]

Other (10)

D. Berman and S. Avidan, “Non-local image dehazing,” in Proceedings of the IEEE conference on computer vision and pattern recognition, (2016), pp. 1674–1682.

G. Satat, M. Tancik, and R. Raskar, “Towards photography through realistic fog,” in Computational Photography (ICCP), 2018 IEEE International Conference on, (IEEE, 2018), pp. 1–10.

M. Sheinin and Y. Y. Schechner, “The next best underwater view,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, (2016), pp. 3764–3773.

L. Perez and J. Wang, “The effectiveness of data augmentation in image classification using deep learning,” arXiv preprint arXiv:1712.04621 (2017).

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.

G. Huang, Z. Liu, L. Van Der Maaten, and K. Q. Weinberger, “Densely connected convolutional networks,” in Proceedings of the IEEE conference on computer vision and pattern recognition, (2017), pp. 4700–4708.

K. He, X. Zhang, S. Ren, and J. Sun, “Deep residual learning for image recognition,” in Proceedings of the IEEE conference on computer vision and pattern recognition, (2016), pp. 770–778.

F. Yu and V. Koltun, “Multi-scale context aggregation by dilated convolutions,” arXiv preprint arXiv:1511.07122 (2015).

A. M. Neto, A. C. Victorino, I. Fantoni, D. E. Zampieri, J. V. Ferreira, and D. A. Lima, “Image processing using pearson’s correlation coefficient: Applications on autonomous robotics,” in 2013 13th International Conference on Autonomous Robot Systems, (IEEE, 2013), pp. 1–6.

T. Remez, O. Litany, R. Giryes, and A. M. Bronstein, “Deep convolutional denoising of low-light images,” arXiv preprint arXiv:1701.01687 (2017).

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Figures (16)

Fig. 1.
Fig. 1. Schematic diagram of the experimental setup.
Fig. 2.
Fig. 2. Our network structure that consists of fully connected network and DenseNet.
Fig. 3.
Fig. 3. Comparison of reconstruction results from speckle correlation and deep learning method. (a) is the ground truth of ten digits. (b) is the speckle pattern of photon numbers. (c) shows the reconstruction results of the speckle correlation method. (d) shows the reconstruction results of deep learning method.
Fig. 4.
Fig. 4. Experimental results of strong light and weak light. (a) shows the original images. (b) shows the speckle patterns of test images under strong light. (c) shows the reconstructed images of (b). (d)(f) show two different speckle patterns under ultra-weak light. (e)(g) show the reconstructed images of (d)(f).
Fig. 5.
Fig. 5. Cross-correlation of same digit different detection and different digit different detection under strong light condition.
Fig. 6.
Fig. 6. Cross-correlation of same digit different detection and different digit different detection under ultra-weak light condition.
Fig. 7.
Fig. 7. Speckle patterns from different digits and different detection. The speckles patterns show the photon number of each pixel. The color bar at the right show the color corresponding to the number of photons.
Fig. 8.
Fig. 8. Experimental results of our network for three different sizes of datasets. (a) are ground-truth of digits. (b) are speckle patterns of test digits. (c) are the results of the dataset of 1950. (d) are the results of the dataset of 9750. (e) are the result of the dataset of 19500.
Fig. 9.
Fig. 9. Quantitative analysis of our network trained using NPCC as the loss function. The training and testing error curves of three dataset size of 1950, 9750 and 19500.
Fig. 10.
Fig. 10. Randomized noise realizations for data augmentation. (a) ground-truth. (b) speckle patterns. (c) results of adding Gaussian noise. (d) results of adding Poisson noise. (e) results of multiple detection.
Fig. 11.
Fig. 11. Experimental results of eight examples of the testing digits and letters samples. (a) shows the original images. (b)(d) show the speckle patterns of test images. (c) show the reconstructed images of (b).
Fig. 12.
Fig. 12. Structure of fully connected network with 5 layers.
Fig. 13.
Fig. 13. Reconstruction results of fully connection neural network of different number of layers. (a) is the ground truth of eight digits. (b) is the speckle patterns of photon numbers. The number of photons per pixel (PPP) is shown under each speckle pattern. (c)-(h) shows the reconstruction results of one-layer to six-layer fully connection neural network.
Fig. 14.
Fig. 14. Scheme of DenseNet used as contrast in our experiment.
Fig. 15.
Fig. 15. Experimental results of three different networks. (a) ground truth of origin digits. (b) shows the speckle patterns of photon numbers. (c) shows the reconstruction results of fully connected neural network. (d) shows the reconstruction results of DenseNet. (e) shows the reconstruction results of our network.
Fig. 16.
Fig. 16. Quantitative analysis of our network trained using NPCC as the loss function. The networks are fully connected neural network (FCNN), DenseNet (D), and our network (FCD).

Equations (5)

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

N P C C = c o v ( I , I ^ ) σ I σ I ^ = i = 1 N x j = 1 N y ( I ( i , j ) I ¯ ) ( I ^ ( i , j ) I ^ ¯ ) i = 1 N x j = 1 N y ( I ( i , j ) I ) ¯ 2 i = 1 N x j = 1 N y ( I ^ ( i , j ) I ^ ¯ ) 2
P P P = 1 N x × N y [ i = 1 N x j = 1 N y I ( i , j ) H ]
P S N R ( d B ) = 10 × lg 255 2 M S E
M S E = 1 N x × N y i = 1 N x j = 1 N y [ I ( i , j ) I ^ ( i , j ) ] 2
S S I M ( X , Y ) = ( 2 μ x μ y + c 1 ) ( 2 σ x y + c 2 ) ( μ x 2 + μ y 2 + c 1 ) ( σ x 2 + σ y 2 + c 2 )

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