Abstract

Imaging through scattering media is challenging since the signal to noise ratio (SNR) of the reflection can be heavily reduced by scatterers. Single-pixel detectors (SPD) with high sensitivities offer compelling advantages for sensing such weak signals. In this paper, we focus on the use of ghost imaging to resolve 2D spatial information using just an SPD. We prototype a polarimetric ghost imaging system that suppresses backscattering from volumetric media and leverages deep learning for fast reconstructions. In this work, we implement ghost imaging by projecting Hadamard patterns that are optimized for imaging through scattering media. We demonstrate good quality reconstructions in highly scattering conditions using a 1.6% sampling rate.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2020 (1)

H. Wu, M. Zhao, F. Li, Z. Tian, and M. Zhao, “Underwater polarization-based single pixel imaging,” J. Soc. Inf. Disp. 28(2), 157–163 (2020).
[Crossref]

2018 (6)

F. Liu, P. Han, Y. Wei, K. Yang, S. Huang, X. Li, G. Zhang, L. Bai, and X. Shao, “Deeply seeing through highly turbid water by active polarization imaging,” Opt. Lett. 43(20), 4903–4906 (2018).
[Crossref]

A. Lucas, M. Iliadis, R. Molina, and A. K. Katsaggelos, “Using deep neural networks for inverse problems in imaging: beyond analytical methods,” IEEE Signal Process. Mag. 35(1), 20–36 (2018).
[Crossref]

Y. Li, Y. Xue, and L. Tian, “Deep speckle correlation: a deep learning approach toward scalable imaging through scattering media,” Optica 5(10), 1181–1190 (2018).
[Crossref]

C. F. Higham, R. Murray-Smith, M. J. Padgett, and M. P. Edgar, “Deep learning for real-time single-pixel video,” Sci. Rep. 8(1), 2369 (2018).
[Crossref]

Y. He, G. Wang, G. Dong, S. Zhu, H. Chen, A. Zhang, and Z. Xu, “Ghost imaging based on deep learning,” Sci. Rep. 8(1), 6469 (2018).
[Crossref]

H. Gupta, K. H. Jin, H. Q. Nguyen, M. T. McCann, and M. Unser, “Cnn-based projected gradient descent for consistent ct image reconstruction,” IEEE Trans. Med. Imag. 37(6), 1440–1453 (2018).
[Crossref]

2017 (3)

2015 (3)

Y. Zhu, J. Shi, Y. Yang, and G. Zeng, “Polarization difference ghost imaging,” Appl. Opt. 54(6), 1279–1284 (2015).
[Crossref]

Y. LeCun, Y. Bengio, and G. Hinton, “Deep learning,” Nature 521(7553), 436–444 (2015).
[Crossref]

M. Zhao, J. Liu, S. Chen, C. Kang, and W. Xu, “Single-pixel imaging with deterministic complex-valued sensing matrices,” J Eur. Opt. Soc-Rapid. 10, 15041 (2015).
[Crossref]

2014 (3)

2013 (3)

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. Padgett, “3d computational imaging with single-pixel detectors,” Science 340(6134), 844–847 (2013).
[Crossref]

M. Bina, D. Magatti, M. Molteni, A. Gatti, L. Lugiato, and F. Ferri, “Backscattering differential ghost imaging in turbid media,” Phys. Rev. Lett. 110(8), 083901 (2013).
[Crossref]

J. Guan and J. Zhu, “Target detection in turbid medium using polarization-based range-gated technology,” Opt. Express 21(12), 14152–14158 (2013).
[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]

2011 (1)

2009 (3)

Y. Bromberg, O. Katz, and Y. Silberberg, “Ghost imaging with a single detector,” Phys. Rev. A 79(5), 053840 (2009).
[Crossref]

T. Treibitz and Y. Y. Schechner, “Active polarization descattering,” IEEE Trans. Pattern Anal. Mach. Intell. 31(3), 385–399 (2009).
[Crossref]

L. Mullen, B. Cochenour, W. Rabinovich, R. Mahon, and J. Muth, “Backscatter suppression for underwater modulating retroreflector links using polarization discrimination,” Appl. Opt. 48(2), 328–337 (2009).
[Crossref]

2008 (2)

J. H. Shapiro, “Computational ghost imaging,” Phys. Rev. A 78(6), 061802 (2008).
[Crossref]

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
[Crossref]

2007 (1)

J. M. Bioucas-Dias and M. A. Figueiredo, “A new twist: Two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE Trans. on Image Process. 16(12), 2992–3004 (2007).
[Crossref]

2006 (1)

2005 (1)

1997 (1)

1991 (1)

A. Ishimaru, “Wave propagation and scattering in random media and rough surfaces,” Proc. IEEE 79(10), 1359–1366 (1991).
[Crossref]

Alfano, R.

Andrés, P.

Ba, J.

D. P. Kingma and J. Ba, “Adam: A method for stochastic optimization,” arXiv preprint arXiv:1412.6980 (2014).

Bai, L.

Baraniuk, R. G.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
[Crossref]

C. A. Metzler, P. Schniter, A. Veeraraghavan, and R. G. Baraniuk, “prdeep: Robust phase retrieval with a flexible deep network,” arXiv preprint arXiv:1803.00212 (2018).

Bengio, Y.

Y. LeCun, Y. Bengio, and G. Hinton, “Deep learning,” Nature 521(7553), 436–444 (2015).
[Crossref]

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]

Bina, M.

M. Bina, D. Magatti, M. Molteni, A. Gatti, L. Lugiato, and F. Ferri, “Backscattering differential ghost imaging in turbid media,” Phys. Rev. Lett. 110(8), 083901 (2013).
[Crossref]

Bioucas-Dias, J. M.

J. M. Bioucas-Dias and M. A. Figueiredo, “A new twist: Two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE Trans. on Image Process. 16(12), 2992–3004 (2007).
[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]

Bowman, A.

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. Padgett, “3d computational imaging with single-pixel detectors,” Science 340(6134), 844–847 (2013).
[Crossref]

Bowman, R.

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. Padgett, “3d computational imaging with single-pixel detectors,” Science 340(6134), 844–847 (2013).
[Crossref]

Bromberg, Y.

Y. Bromberg, O. Katz, and Y. Silberberg, “Ghost imaging with a single detector,” Phys. Rev. A 79(5), 053840 (2009).
[Crossref]

Bruscaglioni, P.

Chen, E.

J. Xie, L. Xu, and E. Chen, “Image denoising and inpainting with deep neural networks,” in Advances in neural information processing systems, (2012), pp. 341–349.

Chen, H.

Chen, N.

M. Lyu, W. Wang, H. Wang, H. Wang, G. Li, N. Chen, and G. Situ, “Deep-learning-based ghost imaging,” Sci. Rep. 7(1), 17865 (2017).
[Crossref]

Chen, S.

M. Zhao, J. Liu, S. Chen, C. Kang, and W. Xu, “Single-pixel imaging with deterministic complex-valued sensing matrices,” J Eur. Opt. Soc-Rapid. 10, 15041 (2015).
[Crossref]

Chenault, D. B.

Clemente, P.

Coates, A.

A. Coates, A. Ng, and H. Lee, “An analysis of single-layer networks in unsupervised feature learning,” in Proceedings of the fourteenth international conference on artificial intelligence and statistics, (2011), pp. 215–223.

Cochenour, B.

Cossairt, O.

Davenport, M. A.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
[Crossref]

Devir, A.

Donelli, P.

Dong, G.

Y. He, G. Wang, G. Dong, S. Zhu, H. Chen, A. Zhang, and Z. Xu, “Ghost imaging based on deep learning,” Sci. Rep. 8(1), 6469 (2018).
[Crossref]

Dor, B. B.

Duarte, M. F.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
[Crossref]

Ducros, N.

N. Ducros, A. L. Mur, and F. Peyrin, “A completion network for reconstruction from compressed acquisition,” in 2020 IEEE 17th International Symposium on Biomedical Imaging (ISBI2020), (2020).

Durán, V.

Edgar, M. P.

C. F. Higham, R. Murray-Smith, M. J. Padgett, and M. P. Edgar, “Deep learning for real-time single-pixel video,” Sci. Rep. 8(1), 2369 (2018).
[Crossref]

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. Padgett, “3d computational imaging with single-pixel detectors,” Science 340(6134), 844–847 (2013).
[Crossref]

Ferri, F.

M. Bina, D. Magatti, M. Molteni, A. Gatti, L. Lugiato, and F. Ferri, “Backscattering differential ghost imaging in turbid media,” Phys. Rev. Lett. 110(8), 083901 (2013).
[Crossref]

Figueiredo, M. A.

J. M. Bioucas-Dias and M. A. Figueiredo, “A new twist: Two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE Trans. on Image Process. 16(12), 2992–3004 (2007).
[Crossref]

Gatti, A.

M. Bina, D. Magatti, M. Molteni, A. Gatti, L. Lugiato, and F. Ferri, “Backscattering differential ghost imaging in turbid media,” Phys. Rev. Lett. 110(8), 083901 (2013).
[Crossref]

Goldstein, D. L.

Gong, W.

Guan, J.

Guney, D. O.

Gupta, H.

H. Gupta, K. H. Jin, H. Q. Nguyen, M. T. McCann, and M. Unser, “Cnn-based projected gradient descent for consistent ct image reconstruction,” IEEE Trans. Med. Imag. 37(6), 1440–1453 (2018).
[Crossref]

Han, P.

Han, S.

Hanafy, M. E.

He, K.

F. Li, H. Chen, A. Pediredla, C. Yeh, K. He, A. Veeraraghavan, and O. Cossairt, “Cs-tof: High-resolution compressive time-of-flight imaging,” Opt. Express 25(25), 31096–31110 (2017).
[Crossref]

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.

He, Y.

Y. He, G. Wang, G. Dong, S. Zhu, H. Chen, A. Zhang, and Z. Xu, “Ghost imaging based on deep learning,” Sci. Rep. 8(1), 6469 (2018).
[Crossref]

Higham, C. F.

C. F. Higham, R. Murray-Smith, M. J. Padgett, and M. P. Edgar, “Deep learning for real-time single-pixel video,” Sci. Rep. 8(1), 2369 (2018).
[Crossref]

Hinton, G.

Y. LeCun, Y. Bengio, and G. Hinton, “Deep learning,” Nature 521(7553), 436–444 (2015).
[Crossref]

Hu, S.

Huang, S.

Iliadis, M.

A. Lucas, M. Iliadis, R. Molina, and A. K. Katsaggelos, “Using deep neural networks for inverse problems in imaging: beyond analytical methods,” IEEE Signal Process. Mag. 35(1), 20–36 (2018).
[Crossref]

Irles, E.

Ishimaru, A.

A. Ishimaru, “Wave propagation and scattering in random media and rough surfaces,” Proc. IEEE 79(10), 1359–1366 (1991).
[Crossref]

Ismaelli, A.

Jin, K. H.

H. Gupta, K. H. Jin, H. Q. Nguyen, M. T. McCann, and M. Unser, “Cnn-based projected gradient descent for consistent ct image reconstruction,” IEEE Trans. Med. Imag. 37(6), 1440–1453 (2018).
[Crossref]

Jitrik, O.

M. Zhao, J. Uhlmann, M. Lanzagorta, J. Kanugo, A. Parashar, O. Jitrik, and S. E. Venegas-Andraca, “Passive ghost imaging using caustics modeling,” in Radar Sensor Technology XXI, vol. 10188 (International Society for Optics and Photonics, 2017), p. 101880H.

Kang, C.

M. Zhao, J. Liu, S. Chen, C. Kang, and W. Xu, “Single-pixel imaging with deterministic complex-valued sensing matrices,” J Eur. Opt. Soc-Rapid. 10, 15041 (2015).
[Crossref]

Kanugo, J.

M. Zhao, J. Uhlmann, M. Lanzagorta, J. Kanugo, A. Parashar, O. Jitrik, and S. E. Venegas-Andraca, “Passive ghost imaging using caustics modeling,” in Radar Sensor Technology XXI, vol. 10188 (International Society for Optics and Photonics, 2017), p. 101880H.

Karpel, N.

Y. Y. Schechner and N. Karpel, “Clear underwater vision,” in Proceedings of the 2004 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2004. CVPR 2004., vol. 1 (IEEE, 2004), pp. I.

Kartazayeva, S.

Katsaggelos, A. K.

A. Lucas, M. Iliadis, R. Molina, and A. K. Katsaggelos, “Using deep neural networks for inverse problems in imaging: beyond analytical methods,” IEEE Signal Process. Mag. 35(1), 20–36 (2018).
[Crossref]

Katz, O.

Y. Bromberg, O. Katz, and Y. Silberberg, “Ghost imaging with a single detector,” Phys. Rev. A 79(5), 053840 (2009).
[Crossref]

Kelly, K. F.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
[Crossref]

Kingma, D. P.

D. P. Kingma and J. Ba, “Adam: A method for stochastic optimization,” arXiv preprint arXiv:1412.6980 (2014).

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]

Lancis, J.

Lanzagorta, M.

M. Zhao, J. Uhlmann, M. Lanzagorta, J. Kanugo, A. Parashar, O. Jitrik, and S. E. Venegas-Andraca, “Passive ghost imaging using caustics modeling,” in Radar Sensor Technology XXI, vol. 10188 (International Society for Optics and Photonics, 2017), p. 101880H.

Laska, J. N.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
[Crossref]

Le, M.

LeCun, Y.

Y. LeCun, Y. Bengio, and G. Hinton, “Deep learning,” Nature 521(7553), 436–444 (2015).
[Crossref]

Lee, H.

A. Coates, A. Ng, and H. Lee, “An analysis of single-layer networks in unsupervised feature learning,” in Proceedings of the fourteenth international conference on artificial intelligence and statistics, (2011), pp. 215–223.

Li, F.

H. Wu, M. Zhao, F. Li, Z. Tian, and M. Zhao, “Underwater polarization-based single pixel imaging,” J. Soc. Inf. Disp. 28(2), 157–163 (2020).
[Crossref]

F. Li, H. Chen, A. Pediredla, C. Yeh, K. He, A. Veeraraghavan, and O. Cossairt, “Cs-tof: High-resolution compressive time-of-flight imaging,” Opt. Express 25(25), 31096–31110 (2017).
[Crossref]

Li, G.

M. Lyu, W. Wang, H. Wang, H. Wang, G. Li, N. Chen, and G. Situ, “Deep-learning-based ghost imaging,” Sci. Rep. 7(1), 17865 (2017).
[Crossref]

Li, X.

Li, Y.

Liu, F.

Liu, J.

M. Le, G. Wang, H. Zheng, J. Liu, Y. Zhou, and Z. Xu, “Underwater computational ghost imaging,” Opt. Express 25(19), 22859–22868 (2017).
[Crossref]

M. Zhao, J. Liu, S. Chen, C. Kang, and W. Xu, “Single-pixel imaging with deterministic complex-valued sensing matrices,” J Eur. Opt. Soc-Rapid. 10, 15041 (2015).
[Crossref]

Lucas, A.

A. Lucas, M. Iliadis, R. Molina, and A. K. Katsaggelos, “Using deep neural networks for inverse problems in imaging: beyond analytical methods,” IEEE Signal Process. Mag. 35(1), 20–36 (2018).
[Crossref]

Lugiato, L.

M. Bina, D. Magatti, M. Molteni, A. Gatti, L. Lugiato, and F. Ferri, “Backscattering differential ghost imaging in turbid media,” Phys. Rev. Lett. 110(8), 083901 (2013).
[Crossref]

Lyu, M.

M. Lyu, W. Wang, H. Wang, H. Wang, G. Li, N. Chen, and G. Situ, “Deep-learning-based ghost imaging,” Sci. Rep. 7(1), 17865 (2017).
[Crossref]

Magatti, D.

M. Bina, D. Magatti, M. Molteni, A. Gatti, L. Lugiato, and F. Ferri, “Backscattering differential ghost imaging in turbid media,” Phys. Rev. Lett. 110(8), 083901 (2013).
[Crossref]

Mahon, R.

McCann, M. T.

H. Gupta, K. H. Jin, H. Q. Nguyen, M. T. McCann, and M. Unser, “Cnn-based projected gradient descent for consistent ct image reconstruction,” IEEE Trans. Med. Imag. 37(6), 1440–1453 (2018).
[Crossref]

Metzler, C. A.

C. A. Metzler, P. Schniter, A. Veeraraghavan, and R. G. Baraniuk, “prdeep: Robust phase retrieval with a flexible deep network,” arXiv preprint arXiv:1803.00212 (2018).

Molina, R.

A. Lucas, M. Iliadis, R. Molina, and A. K. Katsaggelos, “Using deep neural networks for inverse problems in imaging: beyond analytical methods,” IEEE Signal Process. Mag. 35(1), 20–36 (2018).
[Crossref]

Molteni, M.

M. Bina, D. Magatti, M. Molteni, A. Gatti, L. Lugiato, and F. Ferri, “Backscattering differential ghost imaging in turbid media,” Phys. Rev. Lett. 110(8), 083901 (2013).
[Crossref]

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).
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N. Ducros, A. L. Mur, and F. Peyrin, “A completion network for reconstruction from compressed acquisition,” in 2020 IEEE 17th International Symposium on Biomedical Imaging (ISBI2020), (2020).

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C. F. Higham, R. Murray-Smith, M. J. Padgett, and M. P. Edgar, “Deep learning for real-time single-pixel video,” Sci. Rep. 8(1), 2369 (2018).
[Crossref]

Muth, J.

Ng, A.

A. Coates, A. Ng, and H. Lee, “An analysis of single-layer networks in unsupervised feature learning,” in Proceedings of the fourteenth international conference on artificial intelligence and statistics, (2011), pp. 215–223.

Nguyen, H. Q.

H. Gupta, K. H. Jin, H. Q. Nguyen, M. T. McCann, and M. Unser, “Cnn-based projected gradient descent for consistent ct image reconstruction,” IEEE Trans. Med. Imag. 37(6), 1440–1453 (2018).
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Padgett, M.

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. Padgett, “3d computational imaging with single-pixel detectors,” Science 340(6134), 844–847 (2013).
[Crossref]

Padgett, M. J.

C. F. Higham, R. Murray-Smith, M. J. Padgett, and M. P. Edgar, “Deep learning for real-time single-pixel video,” Sci. Rep. 8(1), 2369 (2018).
[Crossref]

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M. Zhao, J. Uhlmann, M. Lanzagorta, J. Kanugo, A. Parashar, O. Jitrik, and S. E. Venegas-Andraca, “Passive ghost imaging using caustics modeling,” in Radar Sensor Technology XXI, vol. 10188 (International Society for Optics and Photonics, 2017), p. 101880H.

Pediredla, A.

Peyrin, F.

N. Ducros, A. L. Mur, and F. Peyrin, “A completion network for reconstruction from compressed acquisition,” in 2020 IEEE 17th International Symposium on Biomedical Imaging (ISBI2020), (2020).

Rabinovich, W.

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.

Roggemann, M. C.

Sadar, M.

M. Sadar, “Turbidity instrumentation–an overview of today’s available technology,” in Turbidity and Other Sediment Surrogates Workshop, (Federal Interagency Subcommittee on Sedimentation, Reno, NV, 2002).

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T. Treibitz and Y. Y. Schechner, “Active polarization descattering,” IEEE Trans. Pattern Anal. Mach. Intell. 31(3), 385–399 (2009).
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C. A. Metzler, P. Schniter, A. Veeraraghavan, and R. G. Baraniuk, “prdeep: Robust phase retrieval with a flexible deep network,” arXiv preprint arXiv:1803.00212 (2018).

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Shi, J.

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M. Lyu, W. Wang, H. Wang, H. Wang, G. Li, N. Chen, and G. Situ, “Deep-learning-based ghost imaging,” Sci. Rep. 7(1), 17865 (2017).
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B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. Padgett, “3d computational imaging with single-pixel detectors,” Science 340(6134), 844–847 (2013).
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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.

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M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
[Crossref]

Tajahuerce, E.

Takhar, D.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
[Crossref]

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Tian, Z.

H. Wu, M. Zhao, F. Li, Z. Tian, and M. Zhao, “Underwater polarization-based single pixel imaging,” J. Soc. Inf. Disp. 28(2), 157–163 (2020).
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T. Treibitz and Y. Y. Schechner, “Active polarization descattering,” IEEE Trans. Pattern Anal. Mach. Intell. 31(3), 385–399 (2009).
[Crossref]

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Uhlmann, J.

M. Zhao, J. Uhlmann, M. Lanzagorta, J. Kanugo, A. Parashar, O. Jitrik, and S. E. Venegas-Andraca, “Passive ghost imaging using caustics modeling,” in Radar Sensor Technology XXI, vol. 10188 (International Society for Optics and Photonics, 2017), p. 101880H.

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H. Gupta, K. H. Jin, H. Q. Nguyen, M. T. McCann, and M. Unser, “Cnn-based projected gradient descent for consistent ct image reconstruction,” IEEE Trans. Med. Imag. 37(6), 1440–1453 (2018).
[Crossref]

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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]

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F. Li, H. Chen, A. Pediredla, C. Yeh, K. He, A. Veeraraghavan, and O. Cossairt, “Cs-tof: High-resolution compressive time-of-flight imaging,” Opt. Express 25(25), 31096–31110 (2017).
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C. A. Metzler, P. Schniter, A. Veeraraghavan, and R. G. Baraniuk, “prdeep: Robust phase retrieval with a flexible deep network,” arXiv preprint arXiv:1803.00212 (2018).

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M. Zhao, J. Uhlmann, M. Lanzagorta, J. Kanugo, A. Parashar, O. Jitrik, and S. E. Venegas-Andraca, “Passive ghost imaging using caustics modeling,” in Radar Sensor Technology XXI, vol. 10188 (International Society for Optics and Photonics, 2017), p. 101880H.

Vittert, L. E.

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. Padgett, “3d computational imaging with single-pixel detectors,” Science 340(6134), 844–847 (2013).
[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(7423), 232–234 (2012).
[Crossref]

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Y. He, G. Wang, G. Dong, S. Zhu, H. Chen, A. Zhang, and Z. Xu, “Ghost imaging based on deep learning,” Sci. Rep. 8(1), 6469 (2018).
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M. Le, G. Wang, H. Zheng, J. Liu, Y. Zhou, and Z. Xu, “Underwater computational ghost imaging,” Opt. Express 25(19), 22859–22868 (2017).
[Crossref]

Wang, H.

M. Lyu, W. Wang, H. Wang, H. Wang, G. Li, N. Chen, and G. Situ, “Deep-learning-based ghost imaging,” Sci. Rep. 7(1), 17865 (2017).
[Crossref]

M. Lyu, W. Wang, H. Wang, H. Wang, G. Li, N. Chen, and G. Situ, “Deep-learning-based ghost imaging,” Sci. Rep. 7(1), 17865 (2017).
[Crossref]

Wang, W.

M. Lyu, W. Wang, H. Wang, H. Wang, G. Li, N. Chen, and G. Situ, “Deep-learning-based ghost imaging,” Sci. Rep. 7(1), 17865 (2017).
[Crossref]

Wang, Y.

Wei, Y.

Welsh, S.

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. Padgett, “3d computational imaging with single-pixel detectors,” Science 340(6134), 844–847 (2013).
[Crossref]

Wu, H.

H. Wu, M. Zhao, F. Li, Z. Tian, and M. Zhao, “Underwater polarization-based single pixel imaging,” J. Soc. Inf. Disp. 28(2), 157–163 (2020).
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J. Xie, L. Xu, and E. Chen, “Image denoising and inpainting with deep neural networks,” in Advances in neural information processing systems, (2012), pp. 341–349.

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J. Xie, L. Xu, and E. Chen, “Image denoising and inpainting with deep neural networks,” in Advances in neural information processing systems, (2012), pp. 341–349.

Xu, W.

M. Zhao, J. Liu, S. Chen, C. Kang, and W. Xu, “Single-pixel imaging with deterministic complex-valued sensing matrices,” J Eur. Opt. Soc-Rapid. 10, 15041 (2015).
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Y. He, G. Wang, G. Dong, S. Zhu, H. Chen, A. Zhang, and Z. Xu, “Ghost imaging based on deep learning,” Sci. Rep. 8(1), 6469 (2018).
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M. Le, G. Wang, H. Zheng, J. Liu, Y. Zhou, and Z. Xu, “Underwater computational ghost imaging,” Opt. Express 25(19), 22859–22868 (2017).
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Yang, K.

Yang, Y.

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Zeng, G.

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Y. He, G. Wang, G. Dong, S. Zhu, H. Chen, A. Zhang, and Z. Xu, “Ghost imaging based on deep learning,” Sci. Rep. 8(1), 6469 (2018).
[Crossref]

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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.

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H. Wu, M. Zhao, F. Li, Z. Tian, and M. Zhao, “Underwater polarization-based single pixel imaging,” J. Soc. Inf. Disp. 28(2), 157–163 (2020).
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H. Wu, M. Zhao, F. Li, Z. Tian, and M. Zhao, “Underwater polarization-based single pixel imaging,” J. Soc. Inf. Disp. 28(2), 157–163 (2020).
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M. Zhao, J. Liu, S. Chen, C. Kang, and W. Xu, “Single-pixel imaging with deterministic complex-valued sensing matrices,” J Eur. Opt. Soc-Rapid. 10, 15041 (2015).
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M. Zhao, J. Uhlmann, M. Lanzagorta, J. Kanugo, A. Parashar, O. Jitrik, and S. E. Venegas-Andraca, “Passive ghost imaging using caustics modeling,” in Radar Sensor Technology XXI, vol. 10188 (International Society for Optics and Photonics, 2017), p. 101880H.

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Appl. Opt. (3)

IEEE Signal Process. Mag. (2)

A. Lucas, M. Iliadis, R. Molina, and A. K. Katsaggelos, “Using deep neural networks for inverse problems in imaging: beyond analytical methods,” IEEE Signal Process. Mag. 35(1), 20–36 (2018).
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IEEE Trans. Med. Imag. (1)

H. Gupta, K. H. Jin, H. Q. Nguyen, M. T. McCann, and M. Unser, “Cnn-based projected gradient descent for consistent ct image reconstruction,” IEEE Trans. Med. Imag. 37(6), 1440–1453 (2018).
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IEEE Trans. Pattern Anal. Mach. Intell. (1)

T. Treibitz and Y. Y. Schechner, “Active polarization descattering,” IEEE Trans. Pattern Anal. Mach. Intell. 31(3), 385–399 (2009).
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J Eur. Opt. Soc-Rapid. (1)

M. Zhao, J. Liu, S. Chen, C. Kang, and W. Xu, “Single-pixel imaging with deterministic complex-valued sensing matrices,” J Eur. Opt. Soc-Rapid. 10, 15041 (2015).
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J. Opt. Soc. Am. A (2)

J. Soc. Inf. Disp. (1)

H. Wu, M. Zhao, F. Li, Z. Tian, and M. Zhao, “Underwater polarization-based single pixel imaging,” J. Soc. Inf. Disp. 28(2), 157–163 (2020).
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Y. LeCun, Y. Bengio, and G. Hinton, “Deep learning,” Nature 521(7553), 436–444 (2015).
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Optica (1)

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J. H. Shapiro, “Computational ghost imaging,” Phys. Rev. A 78(6), 061802 (2008).
[Crossref]

Y. Bromberg, O. Katz, and Y. Silberberg, “Ghost imaging with a single detector,” Phys. Rev. A 79(5), 053840 (2009).
[Crossref]

Phys. Rev. Lett. (1)

M. Bina, D. Magatti, M. Molteni, A. Gatti, L. Lugiato, and F. Ferri, “Backscattering differential ghost imaging in turbid media,” Phys. Rev. Lett. 110(8), 083901 (2013).
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[Crossref]

Y. He, G. Wang, G. Dong, S. Zhu, H. Chen, A. Zhang, and Z. Xu, “Ghost imaging based on deep learning,” Sci. Rep. 8(1), 6469 (2018).
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Science (1)

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. Padgett, “3d computational imaging with single-pixel detectors,” Science 340(6134), 844–847 (2013).
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M. Zhao, J. Uhlmann, M. Lanzagorta, J. Kanugo, A. Parashar, O. Jitrik, and S. E. Venegas-Andraca, “Passive ghost imaging using caustics modeling,” in Radar Sensor Technology XXI, vol. 10188 (International Society for Optics and Photonics, 2017), p. 101880H.

Y. Y. Schechner and N. Karpel, “Clear underwater vision,” in Proceedings of the 2004 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2004. CVPR 2004., vol. 1 (IEEE, 2004), pp. I.

J. Xie, L. Xu, and E. Chen, “Image denoising and inpainting with deep neural networks,” in Advances in neural information processing systems, (2012), pp. 341–349.

C. A. Metzler, P. Schniter, A. Veeraraghavan, and R. G. Baraniuk, “prdeep: Robust phase retrieval with a flexible deep network,” arXiv preprint arXiv:1803.00212 (2018).

A. Coates, A. Ng, and H. Lee, “An analysis of single-layer networks in unsupervised feature learning,” in Proceedings of the fourteenth international conference on artificial intelligence and statistics, (2011), pp. 215–223.

N. Ducros, A. L. Mur, and F. Peyrin, “A completion network for reconstruction from compressed acquisition,” in 2020 IEEE 17th International Symposium on Biomedical Imaging (ISBI2020), (2020).

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.

D. P. Kingma and J. Ba, “Adam: A method for stochastic optimization,” arXiv preprint arXiv:1412.6980 (2014).

NVIDIA, “Titanx,” https://www.nvidia.com/en-us/geforce/products/10series/titan-x-pascal/ (2019).

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Figures (9)

Fig. 1.
Fig. 1. (a). We simulate SPD measurements with the first 3000 Hadamard frames (delivering energy from high to low) for averaging of 200 natural images. The red line marks the average intensity and the black line represents the standard deviation. X-axis marks different Hadamard patterns and y-axis represents amplitude. We display an example of Hadamard patterns with high energies in (b) and low energies in (c).
Fig. 2.
Fig. 2. Proposed convolutional Neural network: The input to the neural network is the SPD measurements with the polarization correction. The first layer is a fully connected (FC) layer and a rectified linear unit (ReLU). Following the FC layer, there are multiple convolutional layers (Conv2d) and an eighteen residual layer (ResNet). We lastly use a convolutional layer to generate the output. BN: batch normalization.
Fig. 3.
Fig. 3. Simulated reconstructions using deep learning and compressed sensing in low and high scattering conditions: In a low scattering condition (SNR=25dB), we compare the reconstructions with DL and CS for the sampling rate of 18.3% (a, c) and 2.7% (b, d). In a high scattering condition (SNR=10dB), we also compare the reconstructions with DL and CS for the sampling rate of 18.3% (e, g) and 2.7% (f, h). A quantitative comparison is shown in the table.
Fig. 4.
Fig. 4. Simulated reconstructions using DL: We reconstruct ‘Cameraman’ with DL for different sampling rates (18.3%, 9.5%,2.7% and 1.6%) under different scattering conditions (SNR=25,20,15,and 10dB) as shown in (a). We also quantitatively compare the performance of SSIM (b) and PSNR (c).
Fig. 5.
Fig. 5. Experimental setup: (a) The illumination beam is spatially encoded with a Hadamard pattern displayed on the SLM, and then polarized with a linear polarizer. The reflection is collected with an SPD with another linear polarizer in front. For each Hadamard pattern, we acquire two measurements by rotating the polarizer in front of the SPD. The object is a toy skull with a rough surface (b). We demonstrate the CS reconstruction (c) using the sampling rate of 1 within clear water.
Fig. 6.
Fig. 6. DL and CS reconstructions: The scattering level is from 7FTU, 20FTU, 32FTU, 40FTU. We perform the reconstructions with the sampling rate of 18.3%(a) and 2.7%(b). Upper rows are DL reconstructions, and bottom rows are CS reconstructions. Zoom in for better visualization.
Fig. 7.
Fig. 7. Reconstructions with different Hadamard sequences (or sampling rates) in low and high scattering conditions: We compare the DL reconstructions with different sampling rates of 18.3%, 9.5%, 2.7%, and 1.6% in scattering conditions of 7 FTU (a-d) and 40 FTU (e-h).
Fig. 8.
Fig. 8. Experimental SPD measurements with the first 3000 Hadamard frames: We display the SPD measurements of $I^\parallel$ (a) and $I^\perp$ (b). We perform the polarization correction from the two measurements and achieve the final SPD measurement (c) for the post processing. In each plot, x-axis is the index of the Hadamard pattern, and y-axis represents the amplitude.
Fig. 9.
Fig. 9. Reconstructions with previous and new training: Reconstructions for ‘Lena’ (a) and experimental measurement (b) with the sampling rates of 18.3%: Upper row demonstrates reconstructions with previous training; Bottom row is reconstructions with new training. We also show SSIM (c) and PSNR (d) under different SNRs (scattering conditions) for ‘Lena’.

Equations (18)

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

I m = 0 Δ t 0 N y 0 N x M m ( x , y ) ( S ( x , y , t ) + O ( x , y , t ) ) d x d y d t + n m
I , = I S , + I O ,
I S , = 0 Δ t 0 N y 0 N x M ( x , y ) S , ( x , y , t ) d x d y d t
I O , = 0 Δ t 0 N y 0 N x M ( x , y ) O , ( x , y , t ) d x d y d t
I O = 1 β S β O ( I ( 1 + β S ) I ( 1 β S ) )
σ I O 2 = ( 1 + β S β S β O ) 2 σ I 2 + ( 1 β S β S β O ) 2 σ I 2
I O = A O
O = arg min | | I O A O | | 2 2 + λ | | Φ ( O ) | | 1
L = 1 n i = 1 n ( f ( I O i , Θ ) O i ) 2
β O = ( I O I O ) / ( I O + I O )
β S = ( I S I S ) / ( I S + I S )
I = I O + I S
I = I O + I S
I O = ( 1 + β O ) / ( 1 β O ) I O
I S = ( 1 + β S ) / ( 1 β S ) I S
I = ( 1 + β O ) / ( 1 β O ) I O + ( 1 + β S ) / ( 1 β S ) I S
I O = ( 1 + β S ) ( 1 β O ) I ( 1 β S ) ( 1 β O ) I 2 ( β S β O )
I O = I O + I O = 1 + β O 1 β O I O + I O = 2 1 β O I O = ( 1 + β S ) I ( 1 β S ) I β S β O = 1 β S β O ( I ( 1 + β S ) I ( 1 β S ) )

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