Abstract

We present a machine-learning-based method for single-shot imaging through scattering media. The inverse scattering process was calculated based on a nonlinear regression algorithm by learning a number of training object-speckle pairs. In the experimental demonstration, multilayer phase objects between scattering plates were reconstructed from intensity measurements. Our approach enables model-free sensing, where it is not necessary to know the sensing processes/models.

© 2016 Optical Society of America

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References

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  1. A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photonics 6, 283–292 (2012).
    [Crossref]
  2. Y. Choi, C. Yoon, M. Kim, W. Choi, and W. Choi, “Optical imaging with the use of a scattering lens,” IEEE J. Sel. Top. Quantum Electron. 20, 6800213 (2014).
  3. R. Horstmeyer, H. Ruan, and C. Yang, “Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue,” Nat. Photonics 9, 563–571 (2015).
    [Crossref]
  4. 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, 12648–12668 (2015).
    [Crossref] [PubMed]
  5. S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Image transmission through an opaque material,” Nat. Commun. 1, 1–5 (2010).
    [Crossref]
  6. A. Liutkus, D. Martina, S. Popoff, G. Chardon, O. Katz, G. Lerosey, S. Gigan, L. Daudet, and I. Carron, “Imaging with nature: compressive imaging using a multiply scattering medium,” Sci. Rep. 4, 5552 (2014).
    [Crossref] [PubMed]
  7. A. Drémeau, A. Liutkus, D. Martina, O. Katz, C. Schülke, F. Krzakala, S. Gigan, and L. Daudet, “Referenceless measurement of the transmission matrix of a highly scattering material using a DMD and phase retrieval techniques,” Opt. Express 23, 11898–11911 (2015).
    [Crossref]
  8. T. Nakamura, R. Horisaki, and J. Tanida, “Compact wide-field-of-view imager with a designed disordered medium,” Opt. Rev. 22, 19–24 (2015).
    [Crossref]
  9. 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, 232–234 (2012).
    [Crossref] [PubMed]
  10. 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, 784–790 (2014).
    [Crossref]
  11. G. E. Hinton and R. R. Salakhutdinov, “Reducing the dimensionality of data with neural networks,” Science 313, 504–507 (2006).
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  12. D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. van den Driessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, S. Dieleman, D. Grewe, J. Nham, N. Kalchbrenner, I. Sutskever, T. Lillicrap, M. Leach, K. Kavukcuoglu, T. Graepel, and D. Hassabis, “Mastering the game of Go with deep neural networks and tree search,” Nature 529, 484–489 (2016).
    [Crossref] [PubMed]
  13. T. Ando, R. Horisaki, and J. Tanida, “Speckle-learning-based object recognition through scattering media,” Opt. Express 23, 33902–33910 (2015).
    [Crossref]
  14. A. Saade, F. Caltagirone, I. Carron, L. Daudet, A. Drémeau, S. Gigan, and F. Krzakala, “Random projections through multiple optical scattering: Approximating kernels at the speed of light,” in IEEE International Conference on Acoustics, Speech and Signal Processing (2016), pp. BD–P1.5.
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    [Crossref]
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2016 (1)

D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. van den Driessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, S. Dieleman, D. Grewe, J. Nham, N. Kalchbrenner, I. Sutskever, T. Lillicrap, M. Leach, K. Kavukcuoglu, T. Graepel, and D. Hassabis, “Mastering the game of Go with deep neural networks and tree search,” Nature 529, 484–489 (2016).
[Crossref] [PubMed]

2015 (5)

2014 (3)

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, 784–790 (2014).
[Crossref]

Y. Choi, C. Yoon, M. Kim, W. Choi, and W. Choi, “Optical imaging with the use of a scattering lens,” IEEE J. Sel. Top. Quantum Electron. 20, 6800213 (2014).

A. Liutkus, D. Martina, S. Popoff, G. Chardon, O. Katz, G. Lerosey, S. Gigan, L. Daudet, and I. Carron, “Imaging with nature: compressive imaging using a multiply scattering medium,” Sci. Rep. 4, 5552 (2014).
[Crossref] [PubMed]

2012 (2)

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photonics 6, 283–292 (2012).
[Crossref]

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, 232–234 (2012).
[Crossref] [PubMed]

2010 (1)

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Image transmission through an opaque material,” Nat. Commun. 1, 1–5 (2010).
[Crossref]

2008 (1)

T. Hofmann, B. Schölkopf, and A. J. Smola, “Kernel methods in machine learning,” Ann. Statistics 36, 1171–1220 (2008).
[Crossref]

2006 (1)

G. E. Hinton and R. R. Salakhutdinov, “Reducing the dimensionality of data with neural networks,” Science 313, 504–507 (2006).
[Crossref] [PubMed]

Ando, T.

Antonoglou, I.

D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. van den Driessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, S. Dieleman, D. Grewe, J. Nham, N. Kalchbrenner, I. Sutskever, T. Lillicrap, M. Leach, K. Kavukcuoglu, T. Graepel, and D. Hassabis, “Mastering the game of Go with deep neural networks and tree search,” Nature 529, 484–489 (2016).
[Crossref] [PubMed]

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, 232–234 (2012).
[Crossref] [PubMed]

Bishop, C. M.

C. M. Bishop, Pattern Recognition and Machine Learning (Springer-Verlag New York, Inc., 2006).

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, 232–234 (2012).
[Crossref] [PubMed]

Boccara, A. C.

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Image transmission through an opaque material,” Nat. Commun. 1, 1–5 (2010).
[Crossref]

Caltagirone, F.

A. Saade, F. Caltagirone, I. Carron, L. Daudet, A. Drémeau, S. Gigan, and F. Krzakala, “Random projections through multiple optical scattering: Approximating kernels at the speed of light,” in IEEE International Conference on Acoustics, Speech and Signal Processing (2016), pp. BD–P1.5.

Carron, I.

A. Liutkus, D. Martina, S. Popoff, G. Chardon, O. Katz, G. Lerosey, S. Gigan, L. Daudet, and I. Carron, “Imaging with nature: compressive imaging using a multiply scattering medium,” Sci. Rep. 4, 5552 (2014).
[Crossref] [PubMed]

A. Saade, F. Caltagirone, I. Carron, L. Daudet, A. Drémeau, S. Gigan, and F. Krzakala, “Random projections through multiple optical scattering: Approximating kernels at the speed of light,” in IEEE International Conference on Acoustics, Speech and Signal Processing (2016), pp. BD–P1.5.

Chardon, G.

A. Liutkus, D. Martina, S. Popoff, G. Chardon, O. Katz, G. Lerosey, S. Gigan, L. Daudet, and I. Carron, “Imaging with nature: compressive imaging using a multiply scattering medium,” Sci. Rep. 4, 5552 (2014).
[Crossref] [PubMed]

Choi, W.

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, 12648–12668 (2015).
[Crossref] [PubMed]

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, 12648–12668 (2015).
[Crossref] [PubMed]

Y. Choi, C. Yoon, M. Kim, W. Choi, and W. Choi, “Optical imaging with the use of a scattering lens,” IEEE J. Sel. Top. Quantum Electron. 20, 6800213 (2014).

Y. Choi, C. Yoon, M. Kim, W. Choi, and W. Choi, “Optical imaging with the use of a scattering lens,” IEEE J. Sel. Top. Quantum Electron. 20, 6800213 (2014).

Choi, Y.

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, 12648–12668 (2015).
[Crossref] [PubMed]

Y. Choi, C. Yoon, M. Kim, W. Choi, and W. Choi, “Optical imaging with the use of a scattering lens,” IEEE J. Sel. Top. Quantum Electron. 20, 6800213 (2014).

Daudet, L.

A. Drémeau, A. Liutkus, D. Martina, O. Katz, C. Schülke, F. Krzakala, S. Gigan, and L. Daudet, “Referenceless measurement of the transmission matrix of a highly scattering material using a DMD and phase retrieval techniques,” Opt. Express 23, 11898–11911 (2015).
[Crossref]

A. Liutkus, D. Martina, S. Popoff, G. Chardon, O. Katz, G. Lerosey, S. Gigan, L. Daudet, and I. Carron, “Imaging with nature: compressive imaging using a multiply scattering medium,” Sci. Rep. 4, 5552 (2014).
[Crossref] [PubMed]

A. Saade, F. Caltagirone, I. Carron, L. Daudet, A. Drémeau, S. Gigan, and F. Krzakala, “Random projections through multiple optical scattering: Approximating kernels at the speed of light,” in IEEE International Conference on Acoustics, Speech and Signal Processing (2016), pp. BD–P1.5.

Dieleman, S.

D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. van den Driessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, S. Dieleman, D. Grewe, J. Nham, N. Kalchbrenner, I. Sutskever, T. Lillicrap, M. Leach, K. Kavukcuoglu, T. Graepel, and D. Hassabis, “Mastering the game of Go with deep neural networks and tree search,” Nature 529, 484–489 (2016).
[Crossref] [PubMed]

Drémeau, A.

A. Drémeau, A. Liutkus, D. Martina, O. Katz, C. Schülke, F. Krzakala, S. Gigan, and L. Daudet, “Referenceless measurement of the transmission matrix of a highly scattering material using a DMD and phase retrieval techniques,” Opt. Express 23, 11898–11911 (2015).
[Crossref]

A. Saade, F. Caltagirone, I. Carron, L. Daudet, A. Drémeau, S. Gigan, and F. Krzakala, “Random projections through multiple optical scattering: Approximating kernels at the speed of light,” in IEEE International Conference on Acoustics, Speech and Signal Processing (2016), pp. BD–P1.5.

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, 784–790 (2014).
[Crossref]

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photonics 6, 283–292 (2012).
[Crossref]

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Image transmission through an opaque material,” Nat. Commun. 1, 1–5 (2010).
[Crossref]

Gigan, S.

A. Drémeau, A. Liutkus, D. Martina, O. Katz, C. Schülke, F. Krzakala, S. Gigan, and L. Daudet, “Referenceless measurement of the transmission matrix of a highly scattering material using a DMD and phase retrieval techniques,” Opt. Express 23, 11898–11911 (2015).
[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, 784–790 (2014).
[Crossref]

A. Liutkus, D. Martina, S. Popoff, G. Chardon, O. Katz, G. Lerosey, S. Gigan, L. Daudet, and I. Carron, “Imaging with nature: compressive imaging using a multiply scattering medium,” Sci. Rep. 4, 5552 (2014).
[Crossref] [PubMed]

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Image transmission through an opaque material,” Nat. Commun. 1, 1–5 (2010).
[Crossref]

A. Saade, F. Caltagirone, I. Carron, L. Daudet, A. Drémeau, S. Gigan, and F. Krzakala, “Random projections through multiple optical scattering: Approximating kernels at the speed of light,” in IEEE International Conference on Acoustics, Speech and Signal Processing (2016), pp. BD–P1.5.

Graepel, T.

D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. van den Driessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, S. Dieleman, D. Grewe, J. Nham, N. Kalchbrenner, I. Sutskever, T. Lillicrap, M. Leach, K. Kavukcuoglu, T. Graepel, and D. Hassabis, “Mastering the game of Go with deep neural networks and tree search,” Nature 529, 484–489 (2016).
[Crossref] [PubMed]

Grewe, D.

D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. van den Driessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, S. Dieleman, D. Grewe, J. Nham, N. Kalchbrenner, I. Sutskever, T. Lillicrap, M. Leach, K. Kavukcuoglu, T. Graepel, and D. Hassabis, “Mastering the game of Go with deep neural networks and tree search,” Nature 529, 484–489 (2016).
[Crossref] [PubMed]

Guez, A.

D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. van den Driessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, S. Dieleman, D. Grewe, J. Nham, N. Kalchbrenner, I. Sutskever, T. Lillicrap, M. Leach, K. Kavukcuoglu, T. Graepel, and D. Hassabis, “Mastering the game of Go with deep neural networks and tree search,” Nature 529, 484–489 (2016).
[Crossref] [PubMed]

Hassabis, D.

D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. van den Driessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, S. Dieleman, D. Grewe, J. Nham, N. Kalchbrenner, I. Sutskever, T. Lillicrap, M. Leach, K. Kavukcuoglu, T. Graepel, and D. Hassabis, “Mastering the game of Go with deep neural networks and tree search,” Nature 529, 484–489 (2016).
[Crossref] [PubMed]

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, 784–790 (2014).
[Crossref]

Hinton, G. E.

G. E. Hinton and R. R. Salakhutdinov, “Reducing the dimensionality of data with neural networks,” Science 313, 504–507 (2006).
[Crossref] [PubMed]

Hofmann, T.

T. Hofmann, B. Schölkopf, and A. J. Smola, “Kernel methods in machine learning,” Ann. Statistics 36, 1171–1220 (2008).
[Crossref]

Horisaki, R.

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

T. Nakamura, R. Horisaki, and J. Tanida, “Compact wide-field-of-view imager with a designed disordered medium,” Opt. Rev. 22, 19–24 (2015).
[Crossref]

Horstmeyer, R.

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

Huang, A.

D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. van den Driessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, S. Dieleman, D. Grewe, J. Nham, N. Kalchbrenner, I. Sutskever, T. Lillicrap, M. Leach, K. Kavukcuoglu, T. Graepel, and D. Hassabis, “Mastering the game of Go with deep neural networks and tree search,” Nature 529, 484–489 (2016).
[Crossref] [PubMed]

Huang, G.

G. Huang, M. Mattar, H. Lee, and E. G. Learned-Miller, “Learning to align from scratch,” in Advances in Neural Information Processing Systems 25, (Curran Associates, Inc., 2012), pp. 764–772.

Kalchbrenner, N.

D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. van den Driessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, S. Dieleman, D. Grewe, J. Nham, N. Kalchbrenner, I. Sutskever, T. Lillicrap, M. Leach, K. Kavukcuoglu, T. Graepel, and D. Hassabis, “Mastering the game of Go with deep neural networks and tree search,” Nature 529, 484–489 (2016).
[Crossref] [PubMed]

Katz, O.

A. Drémeau, A. Liutkus, D. Martina, O. Katz, C. Schülke, F. Krzakala, S. Gigan, and L. Daudet, “Referenceless measurement of the transmission matrix of a highly scattering material using a DMD and phase retrieval techniques,” Opt. Express 23, 11898–11911 (2015).
[Crossref]

A. Liutkus, D. Martina, S. Popoff, G. Chardon, O. Katz, G. Lerosey, S. Gigan, L. Daudet, and I. Carron, “Imaging with nature: compressive imaging using a multiply scattering medium,” Sci. Rep. 4, 5552 (2014).
[Crossref] [PubMed]

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, 784–790 (2014).
[Crossref]

Kavukcuoglu, K.

D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. van den Driessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, S. Dieleman, D. Grewe, J. Nham, N. Kalchbrenner, I. Sutskever, T. Lillicrap, M. Leach, K. Kavukcuoglu, T. Graepel, and D. Hassabis, “Mastering the game of Go with deep neural networks and tree search,” Nature 529, 484–489 (2016).
[Crossref] [PubMed]

Kim, M.

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, 12648–12668 (2015).
[Crossref] [PubMed]

Y. Choi, C. Yoon, M. Kim, W. Choi, and W. Choi, “Optical imaging with the use of a scattering lens,” IEEE J. Sel. Top. Quantum Electron. 20, 6800213 (2014).

Krzakala, F.

A. Drémeau, A. Liutkus, D. Martina, O. Katz, C. Schülke, F. Krzakala, S. Gigan, and L. Daudet, “Referenceless measurement of the transmission matrix of a highly scattering material using a DMD and phase retrieval techniques,” Opt. Express 23, 11898–11911 (2015).
[Crossref]

A. Saade, F. Caltagirone, I. Carron, L. Daudet, A. Drémeau, S. Gigan, and F. Krzakala, “Random projections through multiple optical scattering: Approximating kernels at the speed of light,” in IEEE International Conference on Acoustics, Speech and Signal Processing (2016), pp. BD–P1.5.

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, 232–234 (2012).
[Crossref] [PubMed]

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photonics 6, 283–292 (2012).
[Crossref]

Lanctot, M.

D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. van den Driessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, S. Dieleman, D. Grewe, J. Nham, N. Kalchbrenner, I. Sutskever, T. Lillicrap, M. Leach, K. Kavukcuoglu, T. Graepel, and D. Hassabis, “Mastering the game of Go with deep neural networks and tree search,” Nature 529, 484–489 (2016).
[Crossref] [PubMed]

Leach, M.

D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. van den Driessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, S. Dieleman, D. Grewe, J. Nham, N. Kalchbrenner, I. Sutskever, T. Lillicrap, M. Leach, K. Kavukcuoglu, T. Graepel, and D. Hassabis, “Mastering the game of Go with deep neural networks and tree search,” Nature 529, 484–489 (2016).
[Crossref] [PubMed]

Learned-Miller, E. G.

G. Huang, M. Mattar, H. Lee, and E. G. Learned-Miller, “Learning to align from scratch,” in Advances in Neural Information Processing Systems 25, (Curran Associates, Inc., 2012), pp. 764–772.

Lee, H.

G. Huang, M. Mattar, H. Lee, and E. G. Learned-Miller, “Learning to align from scratch,” in Advances in Neural Information Processing Systems 25, (Curran Associates, Inc., 2012), pp. 764–772.

Lerosey, G.

A. Liutkus, D. Martina, S. Popoff, G. Chardon, O. Katz, G. Lerosey, S. Gigan, L. Daudet, and I. Carron, “Imaging with nature: compressive imaging using a multiply scattering medium,” Sci. Rep. 4, 5552 (2014).
[Crossref] [PubMed]

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photonics 6, 283–292 (2012).
[Crossref]

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Image transmission through an opaque material,” Nat. Commun. 1, 1–5 (2010).
[Crossref]

Lillicrap, T.

D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. van den Driessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, S. Dieleman, D. Grewe, J. Nham, N. Kalchbrenner, I. Sutskever, T. Lillicrap, M. Leach, K. Kavukcuoglu, T. Graepel, and D. Hassabis, “Mastering the game of Go with deep neural networks and tree search,” Nature 529, 484–489 (2016).
[Crossref] [PubMed]

Liutkus, A.

A. Drémeau, A. Liutkus, D. Martina, O. Katz, C. Schülke, F. Krzakala, S. Gigan, and L. Daudet, “Referenceless measurement of the transmission matrix of a highly scattering material using a DMD and phase retrieval techniques,” Opt. Express 23, 11898–11911 (2015).
[Crossref]

A. Liutkus, D. Martina, S. Popoff, G. Chardon, O. Katz, G. Lerosey, S. Gigan, L. Daudet, and I. Carron, “Imaging with nature: compressive imaging using a multiply scattering medium,” Sci. Rep. 4, 5552 (2014).
[Crossref] [PubMed]

Maddison, C. J.

D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. van den Driessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, S. Dieleman, D. Grewe, J. Nham, N. Kalchbrenner, I. Sutskever, T. Lillicrap, M. Leach, K. Kavukcuoglu, T. Graepel, and D. Hassabis, “Mastering the game of Go with deep neural networks and tree search,” Nature 529, 484–489 (2016).
[Crossref] [PubMed]

Martina, D.

A. Drémeau, A. Liutkus, D. Martina, O. Katz, C. Schülke, F. Krzakala, S. Gigan, and L. Daudet, “Referenceless measurement of the transmission matrix of a highly scattering material using a DMD and phase retrieval techniques,” Opt. Express 23, 11898–11911 (2015).
[Crossref]

A. Liutkus, D. Martina, S. Popoff, G. Chardon, O. Katz, G. Lerosey, S. Gigan, L. Daudet, and I. Carron, “Imaging with nature: compressive imaging using a multiply scattering medium,” Sci. Rep. 4, 5552 (2014).
[Crossref] [PubMed]

Mattar, M.

G. Huang, M. Mattar, H. Lee, and E. G. Learned-Miller, “Learning to align from scratch,” in Advances in Neural Information Processing Systems 25, (Curran Associates, Inc., 2012), pp. 764–772.

Mosk, A. P.

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photonics 6, 283–292 (2012).
[Crossref]

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, 232–234 (2012).
[Crossref] [PubMed]

Nakamura, T.

T. Nakamura, R. Horisaki, and J. Tanida, “Compact wide-field-of-view imager with a designed disordered medium,” Opt. Rev. 22, 19–24 (2015).
[Crossref]

Nham, J.

D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. van den Driessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, S. Dieleman, D. Grewe, J. Nham, N. Kalchbrenner, I. Sutskever, T. Lillicrap, M. Leach, K. Kavukcuoglu, T. Graepel, and D. Hassabis, “Mastering the game of Go with deep neural networks and tree search,” Nature 529, 484–489 (2016).
[Crossref] [PubMed]

Panneershelvam, V.

D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. van den Driessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, S. Dieleman, D. Grewe, J. Nham, N. Kalchbrenner, I. Sutskever, T. Lillicrap, M. Leach, K. Kavukcuoglu, T. Graepel, and D. Hassabis, “Mastering the game of Go with deep neural networks and tree search,” Nature 529, 484–489 (2016).
[Crossref] [PubMed]

Popoff, S.

A. Liutkus, D. Martina, S. Popoff, G. Chardon, O. Katz, G. Lerosey, S. Gigan, L. Daudet, and I. Carron, “Imaging with nature: compressive imaging using a multiply scattering medium,” Sci. Rep. 4, 5552 (2014).
[Crossref] [PubMed]

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Image transmission through an opaque material,” Nat. Commun. 1, 1–5 (2010).
[Crossref]

Ruan, H.

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

Saade, A.

A. Saade, F. Caltagirone, I. Carron, L. Daudet, A. Drémeau, S. Gigan, and F. Krzakala, “Random projections through multiple optical scattering: Approximating kernels at the speed of light,” in IEEE International Conference on Acoustics, Speech and Signal Processing (2016), pp. BD–P1.5.

Salakhutdinov, R. R.

G. E. Hinton and R. R. Salakhutdinov, “Reducing the dimensionality of data with neural networks,” Science 313, 504–507 (2006).
[Crossref] [PubMed]

Schölkopf, B.

T. Hofmann, B. Schölkopf, and A. J. Smola, “Kernel methods in machine learning,” Ann. Statistics 36, 1171–1220 (2008).
[Crossref]

Schrittwieser, J.

D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. van den Driessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, S. Dieleman, D. Grewe, J. Nham, N. Kalchbrenner, I. Sutskever, T. Lillicrap, M. Leach, K. Kavukcuoglu, T. Graepel, and D. Hassabis, “Mastering the game of Go with deep neural networks and tree search,” Nature 529, 484–489 (2016).
[Crossref] [PubMed]

Schülke, C.

Sifre, L.

D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. van den Driessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, S. Dieleman, D. Grewe, J. Nham, N. Kalchbrenner, I. Sutskever, T. Lillicrap, M. Leach, K. Kavukcuoglu, T. Graepel, and D. Hassabis, “Mastering the game of Go with deep neural networks and tree search,” Nature 529, 484–489 (2016).
[Crossref] [PubMed]

Silver, D.

D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. van den Driessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, S. Dieleman, D. Grewe, J. Nham, N. Kalchbrenner, I. Sutskever, T. Lillicrap, M. Leach, K. Kavukcuoglu, T. Graepel, and D. Hassabis, “Mastering the game of Go with deep neural networks and tree search,” Nature 529, 484–489 (2016).
[Crossref] [PubMed]

Smola, A. J.

T. Hofmann, B. Schölkopf, and A. J. Smola, “Kernel methods in machine learning,” Ann. Statistics 36, 1171–1220 (2008).
[Crossref]

Sutskever, I.

D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. van den Driessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, S. Dieleman, D. Grewe, J. Nham, N. Kalchbrenner, I. Sutskever, T. Lillicrap, M. Leach, K. Kavukcuoglu, T. Graepel, and D. Hassabis, “Mastering the game of Go with deep neural networks and tree search,” Nature 529, 484–489 (2016).
[Crossref] [PubMed]

Tanida, J.

T. Nakamura, R. Horisaki, and J. Tanida, “Compact wide-field-of-view imager with a designed disordered medium,” Opt. Rev. 22, 19–24 (2015).
[Crossref]

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

van den Driessche, G.

D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. van den Driessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, S. Dieleman, D. Grewe, J. Nham, N. Kalchbrenner, I. Sutskever, T. Lillicrap, M. Leach, K. Kavukcuoglu, T. Graepel, and D. Hassabis, “Mastering the game of Go with deep neural networks and tree search,” Nature 529, 484–489 (2016).
[Crossref] [PubMed]

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, 232–234 (2012).
[Crossref] [PubMed]

Vapnik, V. N.

V. N. Vapnik, The Nature of Statistical Learning Theory (Springer-VerlagNew York, 1995).
[Crossref]

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, 232–234 (2012).
[Crossref] [PubMed]

Yang, C.

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

Yoon, C.

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, 12648–12668 (2015).
[Crossref] [PubMed]

Y. Choi, C. Yoon, M. Kim, W. Choi, and W. Choi, “Optical imaging with the use of a scattering lens,” IEEE J. Sel. Top. Quantum Electron. 20, 6800213 (2014).

Ann. Statistics (1)

T. Hofmann, B. Schölkopf, and A. J. Smola, “Kernel methods in machine learning,” Ann. Statistics 36, 1171–1220 (2008).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

Y. Choi, C. Yoon, M. Kim, W. Choi, and W. Choi, “Optical imaging with the use of a scattering lens,” IEEE J. Sel. Top. Quantum Electron. 20, 6800213 (2014).

Nat. Commun. (1)

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Image transmission through an opaque material,” Nat. Commun. 1, 1–5 (2010).
[Crossref]

Nat. Photonics (3)

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

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photonics 6, 283–292 (2012).
[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, 784–790 (2014).
[Crossref]

Nature (2)

D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. van den Driessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, S. Dieleman, D. Grewe, J. Nham, N. Kalchbrenner, I. Sutskever, T. Lillicrap, M. Leach, K. Kavukcuoglu, T. Graepel, and D. Hassabis, “Mastering the game of Go with deep neural networks and tree search,” Nature 529, 484–489 (2016).
[Crossref] [PubMed]

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, 232–234 (2012).
[Crossref] [PubMed]

Opt. Express (3)

Opt. Rev. (1)

T. Nakamura, R. Horisaki, and J. Tanida, “Compact wide-field-of-view imager with a designed disordered medium,” Opt. Rev. 22, 19–24 (2015).
[Crossref]

Sci. Rep. (1)

A. Liutkus, D. Martina, S. Popoff, G. Chardon, O. Katz, G. Lerosey, S. Gigan, L. Daudet, and I. Carron, “Imaging with nature: compressive imaging using a multiply scattering medium,” Sci. Rep. 4, 5552 (2014).
[Crossref] [PubMed]

Science (1)

G. E. Hinton and R. R. Salakhutdinov, “Reducing the dimensionality of data with neural networks,” Science 313, 504–507 (2006).
[Crossref] [PubMed]

Other (5)

G. Huang, M. Mattar, H. Lee, and E. G. Learned-Miller, “Learning to align from scratch,” in Advances in Neural Information Processing Systems 25, (Curran Associates, Inc., 2012), pp. 764–772.

“Caltech computer vision database”, http://www.vision.caltech.edu/archive.html .

A. Saade, F. Caltagirone, I. Carron, L. Daudet, A. Drémeau, S. Gigan, and F. Krzakala, “Random projections through multiple optical scattering: Approximating kernels at the speed of light,” in IEEE International Conference on Acoustics, Speech and Signal Processing (2016), pp. BD–P1.5.

C. M. Bishop, Pattern Recognition and Machine Learning (Springer-Verlag New York, Inc., 2006).

V. N. Vapnik, The Nature of Statistical Learning Theory (Springer-VerlagNew York, 1995).
[Crossref]

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Figures (5)

Fig. 1
Fig. 1

Schematic diagram illustrating the inversion of scattering.

Fig. 2
Fig. 2

Setup for the experimental demonstration. (a) The optical setup (SP: scattering plate, SLM: spatial light modulator) and (b) the scattering plates (left: FV-102, right: FV-103).

Fig. 3
Fig. 3

Experimental results. Ten examples of the training pairs of (a) the object images and (b) their measured speckle patterns. Ten examples of the test pairs of (c) the object images and (d) their measured speckle patterns. The reconstructions of the face test images from Fig. (d) with (e) the SVR method and (f) the pattern matching method.

Fig. 4
Fig. 4

Relationship between the PSNR, the number of sampling pixels (Ny), and the number of training pairs (M).

Fig. 5
Fig. 5

Specificity analysis. Ten examples of the test pairs of (a) the non-face object images and (b) their measured speckles. (c) The SVR-based reconstructions from Fig. (b) with the inverse function for the face images, whose ten impulse responses are shown in Fig. (d).

Equations (6)

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

y = ( x ) ,
x = 1 ( y ) ,
x k = k 1 ( y ) ,
k 1 ( y ) = w k y + b k ,
min w k , b k m = 1 M ξ ( x k , m k 1 ( y m ) ) + λ 2 w k 2 ,
𝒦 ( y m , y n ) = exp ( y m y n 2 2 h 2 ) ,

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