Abstract

Artificial intelligence (AI) techniques such as deep learning (DL) for computational imaging usually require to experimentally collect a large set of labeled data to train a neural network. Here we demonstrate that a practically usable neural network for computational imaging can be trained by using simulation data. We take computational ghost imaging (CGI) as an example to demonstrate this method. We develop a one-step end-to-end neural network, trained with simulation data, to reconstruct two-dimensional images directly from experimentally acquired one-dimensional bucket signals, without the need of the sequence of illumination patterns. This is in particular useful for image transmission through quasi-static scattering media as little care is needed to take to simulate the scattering process when generating the training data. We believe that the concept of training using simulation data can be used in various DL-based solvers for general computational imaging.

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

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References

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2019 (3)

M. Lyu, H. Wang, G. Li, S. Zheng, and G. Situ, “Learning-based lensless imaging through optically thick scattering media,” Adv. Photon. 1(3), 036002 (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]

G. Barbastathis, A. Ozcan, and G. Situ, “On the use of deep learning for computational imaging,” Optica 6(8), 921–943 (2019).
[Crossref]

2018 (8)

2017 (5)

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]

Y. Wang, Y. Liu, J. Suo, G. Situ, C. Qiao, and Q. Dai, “High speed computational ghost imaging via spatial sweeping,” Sci. Rep. 7(1), 45325 (2017).
[Crossref]

M. T. Mccann, K. H. Jin, and M. Unser, “Convolutional neural networks for inverse problems in imaging: A review,” IEEE Sig. Process. Mag. 34(6), 85–95 (2017).
[Crossref]

K. Zhang, W. Zuo, Y. Chen, D. Meng, and L. Zhang, “Beyond a gaussian denoiser: Residual learning of deep CNN for image denoising,” IEEE Trans. Image Process. 26(7), 3142–3155 (2017).
[Crossref]

A. Sinha, J. Lee, S. Li, and G. Barbastathis, “Lensless computational imaging through deep learning,” Optica 4(9), 1117–1125 (2017).
[Crossref]

2016 (7)

G. Wu, T. Nowotny, Y. Zhang, H. Q. Yu, and D. D. Li, “Artificial neural network approaches for fluorescence lifetime imaging techniques,” Opt. Lett. 41(11), 2561–2564 (2016).
[Crossref]

R. Horisaki, R. Takagi, and J. Tanida, “Learning-based imaging through scattering media,” Opt. Express 24(13), 13738–13743 (2016).
[Crossref]

H. Yu, R. Lu, S. Han, H. Xie, G. Du, T. Xiao, and D. Zhu, “Fourier-transform ghost imaging with hard x rays,” Phys. Rev. Lett. 117(11), 113901 (2016).
[Crossref]

D. Pelliccia, A. Rack, M. Scheel, V. Cantelli, and D. M. Paganin, “Experimental X-ray ghost imaging,” Phys. Rev. Lett. 117(11), 113902 (2016).
[Crossref]

L. Bian, J. Suo, G. Situ, Z. Li, J. Fan, F. Chen, and Q. Dai, “Multispectral imaging using a single bucket detector,” Sci. Rep. 6(1), 24752 (2016).
[Crossref]

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. S. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18(8), 083001 (2016).
[Crossref]

W. Gong, C. Zhao, H. Yu, M. Chen, W. Xu, and S. Han, “Three-dimensional ghost imaging lidar via sparsity constraint,” Sci. Rep. 6(1), 26133 (2016).
[Crossref]

2015 (6)

S. Ioffe and C. Szegedy, “Batch normalization: Accelerating deep network training by reducing internal covariate shift,” Proc. ICML 37, 448–456 (2015).

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

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

U. S. Kamilov, I. N. Papadopoulos, M. H. Shoreh, A. Goy, C. Vonesch, M. Unser, and D. Psaltis, “Learning approach to optical tomography,” Optica 2(6), 517–522 (2015).
[Crossref]

W. Wang, X. Hu, J. Liu, S. Zhang, J. Suo, and G. Situ, “Gerchberg-saxton-like ghost imaging,” Opt. Express 23(22), 28416–28422 (2015).
[Crossref]

Y.-K. Xu, W.-T. Liu, E.-F. Zhang, Q. Li, H.-Y. Dai, and P.-X. Chen, “Is ghost imaging intrinsically more powerful against scattering?” Opt. Express 23(26), 32993–33000 (2015).
[Crossref]

2014 (2)

2013 (1)

C. Li, W. Yin, H. Jiang, and Y. Zhang, “An efficient augmented lagrangian method with applications to total variation minimization,” Comput. Optim. Appl. 56(3), 507–530 (2013).
[Crossref]

2012 (4)

A. Krizhevsky, I. Sutskever, and G. E. Hinton, “Imagenet classification with deep convolutional neural networks,” Proc. NIPS 1, 1097–1105 (2012).

C. Zhao, W. Gong, M. Chen, E. Li, H. Wang, W. Xu, and S. Han, “Ghost imaging lidar via sparsity constraints,” Appl. Phys. Lett. 101(14), 141123 (2012).
[Crossref]

J. H. Shapiro and R. W. Boyd, “The physics of ghost imaging,” Quantum Inf. Process. 11(4), 949–993 (2012).
[Crossref]

D. Jin, W. Gong, and S. Han, “The influence of sparsity property of images on ghost imaging with thermal light,” Opt. Lett. 37(6), 1067–1069 (2012).
[Crossref]

2010 (2)

2009 (3)

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

O. Katz, Y. Bromberg, and Y. Silberberg, “Compressive ghost imaging,” Appl. Phys. Lett. 95(13), 131110 (2009).
[Crossref]

B. I. Erkmen and J. H. Shapiro, “Signal-to-noise ratio of gaussian-state ghost imaging,” Phys. Rev. A 79(2), 023833 (2009).
[Crossref]

2008 (1)

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

2006 (1)

G. Scarcelli, V. Berardi, and Y. Shih, “Can two-photon correlation of chaotic light be considered as correlation of intensity fluctuations?” Phys. Rev. Lett. 96(6), 063602 (2006).
[Crossref]

2005 (1)

F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, “High-resolution ghost image and ghost diffraction experiments with thermal light,” Phys. Rev. Lett. 94(18), 183602 (2005).
[Crossref]

2004 (5)

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Correlated imaging, quantum and classical,” Phys. Rev. A 70(1), 013802 (2004).
[Crossref]

R. S. Bennink, S. J. Bentley, R. W. Boyd, and J. C. Howell, “Quantum and classical coincidence imaging,” Phys. Rev. Lett. 92(3), 033601 (2004).
[Crossref]

J. Cheng and S. Han, “Incoherent coincidence imaging and its applicability in x-ray diffraction,” Phys. Rev. Lett. 92(9), 093903 (2004).
[Crossref]

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Ghost imaging with thermal light: Comparing entanglement and classical correlation,” Phys. Rev. Lett. 93(9), 093602 (2004).
[Crossref]

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13(4), 600–612 (2004).
[Crossref]

2002 (1)

R. S. Bennink, S. J. Bentley, and R. W. Boyd, ““two-photon” coincidence imaging with a classical source,” Phys. Rev. Lett. 89(11), 113601 (2002).
[Crossref]

1998 (1)

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

1995 (1)

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52(5), R3429–R3432 (1995).
[Crossref]

1982 (1)

T. S. Ferguson, “An inconsistent maximum likelihood estimate,” J. Am. Stat. Assoc. 77(380), 831 (1982).
[Crossref]

Alfalou, A.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. S. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18(8), 083001 (2016).
[Crossref]

Andrés, P.

Arthur, K.

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

Aspden, R. S.

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

Ba, J.

D. P. Kingma and J. Ba, “Adam: A Method for Stochastic Optimization,” arXiv e-prints 1412.6980 (2014).

Bache, M.

F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, “High-resolution ghost image and ghost diffraction experiments with thermal light,” Phys. Rev. Lett. 94(18), 183602 (2005).
[Crossref]

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Correlated imaging, quantum and classical,” Phys. Rev. A 70(1), 013802 (2004).
[Crossref]

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Ghost imaging with thermal light: Comparing entanglement and classical correlation,” Phys. Rev. Lett. 93(9), 093602 (2004).
[Crossref]

Barbastathis, G.

Barrera, J. F.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. S. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18(8), 083001 (2016).
[Crossref]

Bell, J. E.

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

Bengio, Y.

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

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

Bennink, R. S.

R. S. Bennink, S. J. Bentley, R. W. Boyd, and J. C. Howell, “Quantum and classical coincidence imaging,” Phys. Rev. Lett. 92(3), 033601 (2004).
[Crossref]

R. S. Bennink, S. J. Bentley, and R. W. Boyd, ““two-photon” coincidence imaging with a classical source,” Phys. Rev. Lett. 89(11), 113601 (2002).
[Crossref]

Bentley, S. J.

R. S. Bennink, S. J. Bentley, R. W. Boyd, and J. C. Howell, “Quantum and classical coincidence imaging,” Phys. Rev. Lett. 92(3), 033601 (2004).
[Crossref]

R. S. Bennink, S. J. Bentley, and R. W. Boyd, ““two-photon” coincidence imaging with a classical source,” Phys. Rev. Lett. 89(11), 113601 (2002).
[Crossref]

Berardi, V.

G. Scarcelli, V. Berardi, and Y. Shih, “Can two-photon correlation of chaotic light be considered as correlation of intensity fluctuations?” Phys. Rev. Lett. 96(6), 063602 (2006).
[Crossref]

Bian, L.

L. Bian, J. Suo, G. Situ, Z. Li, J. Fan, F. Chen, and Q. Dai, “Multispectral imaging using a single bucket detector,” Sci. Rep. 6(1), 24752 (2016).
[Crossref]

Bottou, L.

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

Bovik, A. C.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13(4), 600–612 (2004).
[Crossref]

Boyd, R. W.

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

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Optica (6)

Phys. Rev. A (5)

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Correlated imaging, quantum and classical,” Phys. Rev. A 70(1), 013802 (2004).
[Crossref]

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52(5), R3429–R3432 (1995).
[Crossref]

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]

B. I. Erkmen and J. H. Shapiro, “Signal-to-noise ratio of gaussian-state ghost imaging,” Phys. Rev. A 79(2), 023833 (2009).
[Crossref]

Phys. Rev. Lett. (10)

H. Yu, R. Lu, S. Han, H. Xie, G. Du, T. Xiao, and D. Zhu, “Fourier-transform ghost imaging with hard x rays,” Phys. Rev. Lett. 117(11), 113901 (2016).
[Crossref]

D. Pelliccia, A. Rack, M. Scheel, V. Cantelli, and D. M. Paganin, “Experimental X-ray ghost imaging,” Phys. Rev. Lett. 117(11), 113902 (2016).
[Crossref]

F. Ferri, D. Magatti, L. A. Lugiato, and A. Gatti, “Differential ghost imaging,” Phys. Rev. Lett. 104(25), 253603 (2010).
[Crossref]

R. S. Bennink, S. J. Bentley, and R. W. Boyd, ““two-photon” coincidence imaging with a classical source,” Phys. Rev. Lett. 89(11), 113601 (2002).
[Crossref]

J. Cheng and S. Han, “Incoherent coincidence imaging and its applicability in x-ray diffraction,” Phys. Rev. Lett. 92(9), 093903 (2004).
[Crossref]

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Ghost imaging with thermal light: Comparing entanglement and classical correlation,” Phys. Rev. Lett. 93(9), 093602 (2004).
[Crossref]

F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, “High-resolution ghost image and ghost diffraction experiments with thermal light,” Phys. Rev. Lett. 94(18), 183602 (2005).
[Crossref]

R. S. Bennink, S. J. Bentley, R. W. Boyd, and J. C. Howell, “Quantum and classical coincidence imaging,” Phys. Rev. Lett. 92(3), 033601 (2004).
[Crossref]

G. Scarcelli, V. Berardi, and Y. Shih, “Can two-photon correlation of chaotic light be considered as correlation of intensity fluctuations?” Phys. Rev. Lett. 96(6), 063602 (2006).
[Crossref]

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

Proc. ICML (1)

S. Ioffe and C. Szegedy, “Batch normalization: Accelerating deep network training by reducing internal covariate shift,” Proc. ICML 37, 448–456 (2015).

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).
[Crossref]

Proc. NIPS (1)

A. Krizhevsky, I. Sutskever, and G. E. Hinton, “Imagenet classification with deep convolutional neural networks,” Proc. NIPS 1, 1097–1105 (2012).

Quantum Inf. Process. (1)

J. H. Shapiro and R. W. Boyd, “The physics of ghost imaging,” Quantum Inf. Process. 11(4), 949–993 (2012).
[Crossref]

Sci. Rep. (5)

W. Gong, C. Zhao, H. Yu, M. Chen, W. Xu, and S. Han, “Three-dimensional ghost imaging lidar via sparsity constraint,” Sci. Rep. 6(1), 26133 (2016).
[Crossref]

L. Bian, J. Suo, G. Situ, Z. Li, J. Fan, F. Chen, and Q. Dai, “Multispectral imaging using a single bucket detector,” Sci. Rep. 6(1), 24752 (2016).
[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]

Y. Hu, 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]

Y. Wang, Y. Liu, J. Suo, G. Situ, C. Qiao, and Q. Dai, “High speed computational ghost imaging via spatial sweeping,” Sci. Rep. 7(1), 45325 (2017).
[Crossref]

Other (4)

K. He, X. Zhang, S. Ren, and J. Sun, “Deep residual learning for image recognition,” in CVPR770–778 (2016).

D. P. Kingma and J. Ba, “Adam: A Method for Stochastic Optimization,” arXiv e-prints 1412.6980 (2014).

https://github.com/abhi9716/handwritten-MNIST-digit-recognition .

B. I. Erkmen, “Computational ghost imaging for remote sensing applications,” IPN Prog. Rep.42–185 (2011).

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Figures (9)

Fig. 1.
Fig. 1. Schematic illustration of the training pipeline of the proposed end-to-end deep learning ghost imaging. A 2D object function is sequentially multiplied by a real-valued random pattern, which is produced by numerical calculation of free space propagation of a random phase function. The resulting amplitude is then numerically propagated over a distance and reaches the bucket detector. This will end up with a digit which represents the total energy of the light field in this measurement. Running through this calculation process $M$ times with $M$ different random patterns, we will have a sequence of digits with the length of $M$ associated with one object. Then we run the above calculation over again with many different object functions, and obtain associated bucket signals. Then we feed the ground-truth images and their corresponding bucket signals into a Neural Network and optimize its weights and biases. The neural network trained by simulation data produced in this way is used to reconstruct images from experimental acquired data under the illumination of the same set of $M$ random patterns.
Fig. 2.
Fig. 2. Proposed neural network architecture to learn the image restore principle from measured intensities in GI.
Fig. 3.
Fig. 3. Schematic diagram of the optical setup. L1, L2, L3, L4 are lenses with focal length of 80mm, 80mm, 80mm, 40mm. P1, P2 and P3 are linear polarizers. P1 and P3 are vertically polarized, and P2 is horizontally polarized. BS1 and BS2 are both beam splitter. DMD: digital micro-mirror device. SLM: spatial light modulator. Patterns used to modulate the light field were sequentially displayed on the DMD. The object was placed on the SLM.
Fig. 4.
Fig. 4. Comparison of simulation and experiment results from GI, CSGI, DLGI at different $\beta$.
Fig. 5.
Fig. 5. Comparison of experiment results from GI, CSGI, DLGI when $\beta =6.25\%$.
Fig. 6.
Fig. 6. Quantitative evaluation of GI, CSGI, DLGI in experiment. N = $\beta \cdot W \cdot H$ is the sampling times. Each marker represents the mean performance from 100 different test objects at different $\beta$. Each error bar represents the standard deviation. (a) RMSE indicator curve. (b) SSIM indicator curve. (c) SVM prediction accuracy indicator curve.
Fig. 7.
Fig. 7. Comparison of model recovery performance between simulation and experimental data.
Fig. 8.
Fig. 8. Network generalization test results.
Fig. 9.
Fig. 9. Testing results of the proposed DLGI method dealing with scattering media when $\beta =6.25~\%$.

Equations (13)

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S m = I m ( x , y ) T ( x , y ) d x d y .
T ~ ( x , y ) G I = Δ S m Δ I m ,
T ~ ( x , y ) C S = T ( x , y )
arg min Ψ { T ( x , y ) } L 1 ,
I m ( x , y ) T ( x , y ) d x d y = S m , m = 1 , 2 , , M ,
T ~ = R { S m } ,
R ~ l e a r n = arg min R θ , θ Θ j = 1 J L ( T ( x , y ) j , R θ { S m j } ) + φ ( θ )
T ~ ( x , y ) D L = R ~ l e a r n { S m } .
T ~ ( x , y ) G I D L = R ~ l e a r n { T ~ ( x , y ) G I } ,
R ~ l e a r n = arg min R θ , θ Θ j = 1 J L ( T ( x , y ) j , R θ { T ~ ( x , y ) G I j } ) + φ ( θ )
L = 1 J W H j = 1 J u = 1 W v = 1 H ( R θ { S m j } T ( x , y ) ) 2
R M S E = [ 1 W H u = 1 W v = 1 H ( T ~ ( x , y ) T ( x , y ) ) 2 ] 1 2
S S I M = ( 2 u T ~ u T + c 1 ) ( σ T ~ T + c 2 ) ( u T ~ 2 + u T 2 + c 1 ) ( σ T ~ 2 + σ T 2 + c 2 )

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