Abstract

Deep learning has been extensively applied in many optical imaging problems in recent years. Despite the success, the limitations and drawbacks of deep learning in optical imaging have been seldom investigated. In this work, we show that conventional linear-regression-based methods can outperform the previously proposed deep learning approaches for two black-box optical imaging problems in some extent. Deep learning demonstrates its weakness especially when the number of training samples is small. The advantages and disadvantages of linear-regression-based methods and deep learning are analyzed and compared. Since many optical systems are essentially linear, a deep learning network containing many nonlinearity functions sometimes may not be the most suitable option.

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

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K. Yao, R. Unni, and Y. Zheng, “Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale,” Nanophotonics 8(3), 339–366 (2019).
[Crossref]

S. D. Campbell, D. Sell, R. P. Jenkins, E. B. Whiting, J. A. Fan, and D. H. Werner, “Review of numerical optimization techniques for meta-device design,” Opt. Mater. Express 9(4), 1842–1863 (2019).
[Crossref]

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[Crossref]

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[Crossref]

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[Crossref]

Ç. Işıl, F. S. Oktem, and A. Koç, “Deep iterative reconstruction for phase retrieval,” Appl. Opt. 58(20), 5422–5431 (2019).
[Crossref]

Z. Ren, Z. Xu, and E. Y. Lam, “End-to-end deep learning framework for digital holographic reconstruction,” Adv. Photonics 1(01), 1 (2019).
[Crossref]

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[Crossref]

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[Crossref]

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[Crossref]

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[Crossref]

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[Crossref]

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[Crossref]

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[Crossref]

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[Crossref]

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[Crossref]

F. Wang, H. Wang, H. Wang, G. Li, and G. Situ, “Learning from simulation: An end-to-end deep-learning approach for computational ghost imaging,” Opt. Express 27(18), 25560–25572 (2019).
[Crossref]

M. P. Edgar, G. M. Gibson, and M. J. Padgett, “Principles and prospects for single-pixel imaging,” Nat. Photonics 13(1), 13–20 (2019).
[Crossref]

S. Jiao, J. Feng, Y. Gao, T. Lei, Z. Xie, and X. Yuan, “Optical machine learning with incoherent light and a single-pixel detector,” Opt. Lett. 44(21), 5186–5189 (2019).
[Crossref]

S. Jiao, C. Zhou, Y. Shi, W. Zou, and X. Li, “Review on optical image hiding and watermarking techniques,” Optics,” Opt. Laser Technol. 109, 370–380 (2019).
[Crossref]

Z. Ren, H. K. H. So, and E. Y. Lam, “Fringe Pattern Improvement and Super-Resolution Using Deep Learning in Digital Holography,” IEEE Trans. Ind. Inf. 15(11), 6179–6186 (2019).
[Crossref]

2018 (16)

Z. Niu, J. Shi, L. Sun, Y. Zhu, J. Fan, and G. Zeng, “Photon-limited face image super-resolution based on deep learning,” Opt. Express 26(18), 22773–22782 (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]

L. Bian, J. Suo, Q. Dai, and F. Chen, “Experimental comparison of single-pixel imaging algorithms,” J. Opt. Soc. Am. A 35(1), 78–87 (2018).
[Crossref]

B. Karanov, M. Chagnon, F. Thouin, T. A. Eriksson, H. Bülow, D. Lavery, P. Bayvel, and L. Schmalen, “End-to-end deep learning of optical fiber communications,” J. Lightwave Technol. 36(20), 4843–4855 (2018).
[Crossref]

M. Hutson, “AI researchers allege that machine learning is alchemy,” Science 360(6388), 478 (2018).
[Crossref]

Ç. Işil, M. Yorulmaz, B. Solmaz, A. B. Turhan, C. Yurdakul, S. Ünlü, E. Ozbay, and A. Koç, “Resolution enhancement of wide-field interferometric microscopy by coupled deep autoencoders,” Appl. Opt. 57(10), 2545–2552 (2018).
[Crossref]

T. Nguyen, Y. Xue, Y. Li, L. Tian, and G. Nehmetallah, “Deep learning approach for Fourier ptychography microscopy,” Opt. Express 26(20), 26470–26484 (2018).
[Crossref]

S. Jiang, K. Guo, J. Liao, and G. Zheng, “Solving Fourier ptychographic imaging problems via neural network modeling and TensorFlow Biomed,” Opt. Express 9(7), 3306–3319 (2018).
[Crossref]

T. Shimobaba, Y. Endo, T. Nishitsuji, T. Takahashi, Y. Nagahama, S. Hasegawa, M. Sano, R. Hirayama, T. Kakue, A. Shiraki, and T. Ito, “Computational ghost imaging using deep learning,” Opt. Commun. 413, 147–151 (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]

S. Jiao, Z. Jin, C. Chang, C. Zhou, W. Zou, and X. Li, “Compression of phase-only holograms with JPEG standard and deep learning,” Appl. Sci. 8(8), 1258 (2018).
[Crossref]

Z. Ren, Z. Xu, and E. Y. Lam, “Learning-based nonparametric autofocusing for digital holography,” Optica 5(4), 337–344 (2018).
[Crossref]

G. Zhang, T. Guan, Z. Shen, X. Wang, T. Hu, D. Wang, Y. He, and N. Xie, “Fast phase retrieval in off-axis digital holographic microscopy through deep learning,” Opt. Express 26(15), 19388–19405 (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]

Y. Rivenson, Y. Zhang, H. Günaydın, D. Teng, and A. Ozcan, “Phase recovery and holographic image reconstruction using deep learning in neural networks,” Light: Sci. Appl. 7(2), 17141 (2018).
[Crossref]

H. Wang, M. Lyu, and G. Situ, “eHoloNet: a learning-based end-to-end approach for in-line digital holographic reconstruction,” Opt. Express 26(18), 22603–22614 (2018).
[Crossref]

2017 (2)

2014 (2)

2009 (1)

C. Li, W. Yin, and Y. Zhang, “User’s guide for TVAL3: TV minimization by augmented lagrangian and alternating direction algorithms,” CAAM report 20(46-47), 4 (2009).

2008 (1)

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).
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[Crossref]

Barbastathis, G.

Bayvel, P.

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Y. Lecun, L. Bottou, Y. Bengio, and P. Haffner, “Gradient-based learning applied to document recognition,” Proc. IEEE 86(11), 2278–2324 (1998).
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Chang, C.

S. Jiao, Z. Jin, C. Chang, C. Zhou, W. Zou, and X. Li, “Compression of phase-only holograms with JPEG standard and deep learning,” Appl. Sci. 8(8), 1258 (2018).
[Crossref]

Chen, F.

Chen, Q.

S. Feng, Q. Chen, G. Gu, T. Tao, L. Zhang, Y. Hu, W. Yin, and C. Zuo, “Fringe pattern analysis using deep learning,” Adv. Photonics 1(02), 1 (2019).
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Cheng, Y. F.

Clemente, P.

Dai, Q.

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]

Deb, M.

Di, J.

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]

Durán, V.

Edgar, M. P.

M. P. Edgar, G. M. Gibson, and M. J. Padgett, “Principles and prospects for single-pixel imaging,” Nat. Photonics 13(1), 13–20 (2019).
[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]

Endo, Y.

T. Shimobaba, D. Blinder, M. Makowski, P. Schelkens, Y. Yamamoto, I. Hoshi, T. Nishitsuji, Y. Endo, T. Kakue, and T. Ito, “Dynamic-range compression scheme for digital hologram using a deep neural network,” Opt. Lett. 44(12), 3038–3041 (2019).
[Crossref]

T. Shimobaba, Y. Endo, T. Nishitsuji, T. Takahashi, Y. Nagahama, S. Hasegawa, M. Sano, R. Hirayama, T. Kakue, A. Shiraki, and T. Ito, “Computational ghost imaging using deep learning,” Opt. Commun. 413, 147–151 (2018).
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Gu, G.

S. Feng, Q. Chen, G. Gu, T. Tao, L. Zhang, Y. Hu, W. Yin, and C. Zuo, “Fringe pattern analysis using deep learning,” Adv. Photonics 1(02), 1 (2019).
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Guan, T.

Günaydin, H.

Y. Rivenson, Y. Zhang, H. Günaydın, D. Teng, and A. Ozcan, “Phase recovery and holographic image reconstruction using deep learning in neural networks,” Light: Sci. Appl. 7(2), 17141 (2018).
[Crossref]

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

Guo, C.

S. Liu, C. Guo, and J. T. Sheridan, “A review of optical image encryption techniques,” Opt. Laser Technol. 57, 327–342 (2014).
[Crossref]

Guo, K.

S. Jiang, K. Guo, J. Liao, and G. Zheng, “Solving Fourier ptychographic imaging problems via neural network modeling and TensorFlow Biomed,” Opt. Express 9(7), 3306–3319 (2018).
[Crossref]

Haffner, P.

Y. Lecun, L. Bottou, Y. Bengio, and P. Haffner, “Gradient-based learning applied to document recognition,” Proc. IEEE 86(11), 2278–2324 (1998).
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He, Y.

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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).
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Hinton, G.

A. Krizhevsky and G. Hinton, “Learning multiple layers of features from tiny images”, Technical report, University of Toronto 1(7), pp. 7 (2009).

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T. Shimobaba, Y. Endo, T. Nishitsuji, T. Takahashi, Y. Nagahama, S. Hasegawa, M. Sano, R. Hirayama, T. Kakue, A. Shiraki, and T. Ito, “Computational ghost imaging using deep learning,” Opt. Commun. 413, 147–151 (2018).
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Ito, T.

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Jenkins, R. P.

Jiang, S.

S. Jiang, K. Guo, J. Liao, and G. Zheng, “Solving Fourier ptychographic imaging problems via neural network modeling and TensorFlow Biomed,” Opt. Express 9(7), 3306–3319 (2018).
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S. Jiao, C. Zhou, Y. Shi, W. Zou, and X. Li, “Review on optical image hiding and watermarking techniques,” Optics,” Opt. Laser Technol. 109, 370–380 (2019).
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S. Jiao, Z. Jin, C. Chang, C. Zhou, W. Zou, and X. Li, “Compression of phase-only holograms with JPEG standard and deep learning,” Appl. Sci. 8(8), 1258 (2018).
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Kakue, T.

T. Shimobaba, D. Blinder, M. Makowski, P. Schelkens, Y. Yamamoto, I. Hoshi, T. Nishitsuji, Y. Endo, T. Kakue, and T. Ito, “Dynamic-range compression scheme for digital hologram using a deep neural network,” Opt. Lett. 44(12), 3038–3041 (2019).
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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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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).
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Lam, E. Y.

Z. Ren, Z. Xu, and E. Y. Lam, “End-to-end deep learning framework for digital holographic reconstruction,” Adv. Photonics 1(01), 1 (2019).
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Z. Ren, H. K. H. So, and E. Y. Lam, “Fringe Pattern Improvement and Super-Resolution Using Deep Learning in Digital Holography,” IEEE Trans. Ind. Inf. 15(11), 6179–6186 (2019).
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Z. Ren, Z. Xu, and E. Y. Lam, “Learning-based nonparametric autofocusing for digital holography,” Optica 5(4), 337–344 (2018).
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Lancis, J.

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).
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Li, G.

M. Lyu, H. Wang, G. Li, S. Zheng, and G. Situ, “Learning-based lensless imaging through optically thick scattering media,” Adv. Photonics 1(03), 1 (2019).
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F. Wang, H. Wang, H. Wang, G. Li, and G. Situ, “Learning from simulation: An end-to-end deep-learning approach for computational ghost imaging,” Opt. Express 27(18), 25560–25572 (2019).
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Li, S.

Li, X.

S. Jiao, C. Zhou, Y. Shi, W. Zou, and X. Li, “Review on optical image hiding and watermarking techniques,” Optics,” Opt. Laser Technol. 109, 370–380 (2019).
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S. Jiao, Z. Jin, C. Chang, C. Zhou, W. Zou, and X. Li, “Compression of phase-only holograms with JPEG standard and deep learning,” Appl. Sci. 8(8), 1258 (2018).
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Li, Y.

Liao, J.

S. Jiang, K. Guo, J. Liao, and G. Zheng, “Solving Fourier ptychographic imaging problems via neural network modeling and TensorFlow Biomed,” Opt. Express 9(7), 3306–3319 (2018).
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S. Liu, C. Guo, and J. T. Sheridan, “A review of optical image encryption techniques,” Opt. Laser Technol. 57, 327–342 (2014).
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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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Manifold, B.

Manninen, A.

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).
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T. Shimobaba, Y. Endo, T. Nishitsuji, T. Takahashi, Y. Nagahama, S. Hasegawa, M. Sano, R. Hirayama, T. Kakue, A. Shiraki, and T. Ito, “Computational ghost imaging using deep learning,” Opt. Commun. 413, 147–151 (2018).
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Nehmetallah, G.

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Shi, Y.

S. Jiao, C. Zhou, Y. Shi, W. Zou, and X. Li, “Review on optical image hiding and watermarking techniques,” Optics,” Opt. Laser Technol. 109, 370–380 (2019).
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T. Shimobaba, D. Blinder, M. Makowski, P. Schelkens, Y. Yamamoto, I. Hoshi, T. Nishitsuji, Y. Endo, T. Kakue, and T. Ito, “Dynamic-range compression scheme for digital hologram using a deep neural network,” Opt. Lett. 44(12), 3038–3041 (2019).
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T. Shimobaba, Y. Endo, T. Nishitsuji, T. Takahashi, Y. Nagahama, S. Hasegawa, M. Sano, R. Hirayama, T. Kakue, A. Shiraki, and T. Ito, “Computational ghost imaging using deep learning,” Opt. Commun. 413, 147–151 (2018).
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So, H. K. H.

Z. Ren, H. K. H. So, and E. Y. Lam, “Fringe Pattern Improvement and Super-Resolution Using Deep Learning in Digital Holography,” IEEE Trans. Ind. Inf. 15(11), 6179–6186 (2019).
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Wang, F.

Wang, H.

Wang, K.

Wang, X.

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Whiting, E. B.

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H. Xiao, K. Rasul, and R. Vollgraf, “Fashion-mnist: a novel image dataset for benchmarking machine learning algorithms,” arXiv preprint arXiv:1708.07747 (2017).

Xie, N.

Xie, Z.

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Z. Ren, Z. Xu, and E. Y. Lam, “End-to-end deep learning framework for digital holographic reconstruction,” Adv. Photonics 1(01), 1 (2019).
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Z. Ren, Z. Xu, and E. Y. Lam, “Learning-based nonparametric autofocusing for digital holography,” Optica 5(4), 337–344 (2018).
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Yao, K.

K. Yao, R. Unni, and Y. Zheng, “Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale,” Nanophotonics 8(3), 339–366 (2019).
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S. Feng, Q. Chen, G. Gu, T. Tao, L. Zhang, Y. Hu, W. Yin, and C. Zuo, “Fringe pattern analysis using deep learning,” Adv. Photonics 1(02), 1 (2019).
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Yuan, X.

Yurdakul, C.

Yurt, A.

Zeng, G.

Zhang, C.

Zhang, G.

Zhang, L.

S. Feng, Q. Chen, G. Gu, T. Tao, L. Zhang, Y. Hu, W. Yin, and C. Zuo, “Fringe pattern analysis using deep learning,” Adv. Photonics 1(02), 1 (2019).
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Y. Rivenson, Y. Zhang, H. Günaydın, D. Teng, and A. Ozcan, “Phase recovery and holographic image reconstruction using deep learning in neural networks,” Light: Sci. Appl. 7(2), 17141 (2018).
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C. Li, W. Yin, and Y. Zhang, “User’s guide for TVAL3: TV minimization by augmented lagrangian and alternating direction algorithms,” CAAM report 20(46-47), 4 (2009).

Zhao, J.

Zheng, G.

S. Jiang, K. Guo, J. Liao, and G. Zheng, “Solving Fourier ptychographic imaging problems via neural network modeling and TensorFlow Biomed,” Opt. Express 9(7), 3306–3319 (2018).
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Zheng, S.

M. Lyu, H. Wang, G. Li, S. Zheng, and G. Situ, “Learning-based lensless imaging through optically thick scattering media,” Adv. Photonics 1(03), 1 (2019).
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K. Yao, R. Unni, and Y. Zheng, “Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale,” Nanophotonics 8(3), 339–366 (2019).
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S. Jiao, C. Zhou, Y. Shi, W. Zou, and X. Li, “Review on optical image hiding and watermarking techniques,” Optics,” Opt. Laser Technol. 109, 370–380 (2019).
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S. Jiao, Z. Jin, C. Chang, C. Zhou, W. Zou, and X. Li, “Compression of phase-only holograms with JPEG standard and deep learning,” Appl. Sci. 8(8), 1258 (2018).
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S. Jiao, C. Zhou, Y. Shi, W. Zou, and X. Li, “Review on optical image hiding and watermarking techniques,” Optics,” Opt. Laser Technol. 109, 370–380 (2019).
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Adv. Photonics (3)

M. Lyu, H. Wang, G. Li, S. Zheng, and G. Situ, “Learning-based lensless imaging through optically thick scattering media,” Adv. Photonics 1(03), 1 (2019).
[Crossref]

Z. Ren, Z. Xu, and E. Y. Lam, “End-to-end deep learning framework for digital holographic reconstruction,” Adv. Photonics 1(01), 1 (2019).
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S. Feng, Q. Chen, G. Gu, T. Tao, L. Zhang, Y. Hu, W. Yin, and C. Zuo, “Fringe pattern analysis using deep learning,” Adv. Photonics 1(02), 1 (2019).
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Appl. Opt. (3)

Appl. Sci. (1)

S. Jiao, Z. Jin, C. Chang, C. Zhou, W. Zou, and X. Li, “Compression of phase-only holograms with JPEG standard and deep learning,” Appl. Sci. 8(8), 1258 (2018).
[Crossref]

Biomed. Opt. Express (1)

CAAM report (1)

C. Li, W. Yin, and Y. Zhang, “User’s guide for TVAL3: TV minimization by augmented lagrangian and alternating direction algorithms,” CAAM report 20(46-47), 4 (2009).

IEEE Signal Process. Mag. (2)

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]

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]

IEEE Trans. Ind. Inf. (1)

Z. Ren, H. K. H. So, and E. Y. Lam, “Fringe Pattern Improvement and Super-Resolution Using Deep Learning in Digital Holography,” IEEE Trans. Ind. Inf. 15(11), 6179–6186 (2019).
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J. Lightwave Technol. (1)

J. Opt. Soc. Am. A (1)

Light: Sci. Appl. (1)

Y. Rivenson, Y. Zhang, H. Günaydın, D. Teng, and A. Ozcan, “Phase recovery and holographic image reconstruction using deep learning in neural networks,” Light: Sci. Appl. 7(2), 17141 (2018).
[Crossref]

Nanophotonics (1)

K. Yao, R. Unni, and Y. Zheng, “Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale,” Nanophotonics 8(3), 339–366 (2019).
[Crossref]

Nat. Photonics (1)

M. P. Edgar, G. M. Gibson, and M. J. Padgett, “Principles and prospects for single-pixel imaging,” Nat. Photonics 13(1), 13–20 (2019).
[Crossref]

Opt. Commun. (1)

T. Shimobaba, Y. Endo, T. Nishitsuji, T. Takahashi, Y. Nagahama, S. Hasegawa, M. Sano, R. Hirayama, T. Kakue, A. Shiraki, and T. Ito, “Computational ghost imaging using deep learning,” Opt. Commun. 413, 147–151 (2018).
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Opt. Express (13)

S. Jiang, K. Guo, J. Liao, and G. Zheng, “Solving Fourier ptychographic imaging problems via neural network modeling and TensorFlow Biomed,” Opt. Express 9(7), 3306–3319 (2018).
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H. Wang, M. Lyu, and G. Situ, “eHoloNet: a learning-based end-to-end approach for in-line digital holographic reconstruction,” Opt. Express 26(18), 22603–22614 (2018).
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Z. Niu, J. Shi, L. Sun, Y. Zhu, J. Fan, and G. Zeng, “Photon-limited face image super-resolution based on deep learning,” Opt. Express 26(18), 22773–22782 (2018).
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Opt. Laser Technol. (2)

S. Liu, C. Guo, and J. T. Sheridan, “A review of optical image encryption techniques,” Opt. Laser Technol. 57, 327–342 (2014).
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S. Jiao, C. Zhou, Y. Shi, W. Zou, and X. Li, “Review on optical image hiding and watermarking techniques,” Optics,” Opt. Laser Technol. 109, 370–380 (2019).
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Opt. Lett. (2)

Opt. Mater. Express (1)

Optica (5)

Proc. IEEE (1)

Y. Lecun, L. Bottou, Y. Bengio, and P. Haffner, “Gradient-based learning applied to document recognition,” Proc. IEEE 86(11), 2278–2324 (1998).
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Sci. Rep. (1)

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).
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Science (1)

M. Hutson, “AI researchers allege that machine learning is alchemy,” Science 360(6388), 478 (2018).
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G. A. Seber and A. J. Lee, “Linear regression analysis,” John Wiley & Sons329 (2012).

H. Xiao, K. Rasul, and R. Vollgraf, “Fashion-mnist: a novel image dataset for benchmarking machine learning algorithms,” arXiv preprint arXiv:1708.07747 (2017).

A. Krizhevsky and G. Hinton, “Learning multiple layers of features from tiny images”, Technical report, University of Toronto 1(7), pp. 7 (2009).

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Figures (11)

Fig. 1.
Fig. 1. (a) Linear regression model; (b) A fully connected neural network.
Fig. 2.
Fig. 2. Optical setup of a triple random phase encryption (TRPE) system.
Fig. 3.
Fig. 3. Deep learning network for attacking a TRPE system proposed in the previous work [34] (DecNet).
Fig. 4.
Fig. 4. Optical setup of a single-pixel imaging system.
Fig. 5.
Fig. 5. Deep learning network for blind image reconstruction in SPI proposed in the previous work [35] (Wang’s Net).
Fig. 6.
Fig. 6. Comparison of recovered plaintext image results for a TRPE system with CLR and DecNet (MNIST dataset and Fashion-MNIST dataset).
Fig. 7.
Fig. 7. Comparison of recovered plaintext image results for a TRPE system with CLR and DecNet (CIFAR-100 dataset).
Fig. 8.
Fig. 8. Comparison of reconstructed image results for a SPI system with LRCS and deep learning in the simulation (MNIST dataset).
Fig. 9.
Fig. 9. Comparison of reconstructed image results for a SPI system with LRCS and deep learning in the simulation (CIFAR-100 dataset).
Fig. 10.
Fig. 10. Optical setup of our SPI experiment.
Fig. 11.
Fig. 11. Comparison of reconstructed image results with LRCS and Wang’s Net for a SPI system based on the recorded data in real optical experiments.

Tables (9)

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Table 1. Recovered plaintext image quality with CLR and DecNet (MNIST dataset).

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Table 2. Recovered plaintext image quality with CLR and DecNet (Fashion-MNIST dataset).

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Table 3. Recovered plaintext image quality with CLR and DecNet (CIFAR-100 dataset).

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Table 4. Similarities and differences between CLR and DecNet for attacking a TRPE system.

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Table 5. Blindly reconstructed image quality for SPI with LRCS (MNIST dataset).

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Table 6. Blindly reconstructed image quality for SPI with Wang’s Net (MNIST dataset).

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Table 7. Blindly reconstructed image quality for SPI with LRCS (CIFAR-100 dataset).

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Table 8. Blindly reconstructed image quality for SPI with Wang’s Net (CIFAR-100 dataset).

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Table 9. Similarities and differences between LRCS and Wang’s Net for blind reconstruction in SPI.

Equations (3)

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[ y 1 y 2 y N ] = [ w 11 w 1 M w N 1 w N M ] [ x 1 x 2 x M ]
C = I F T [ F T ( O exp ( i R 1 ) ) exp ( i R 2 ) ] exp ( i R 3 )
O = I F T { F T [ C exp ( i R 3 ) ] exp ( i R 2 ) } exp ( i R 1 )

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