Abstract

Ghost imaging has rapidly developed for about two decades and attracted wide attention from different research fields. However, the practical applications of ghost imaging are still largely limited, by its low reconstruction quality and large required measurements. Inspired by the fact that the natural image patches usually exhibit simple structures, and these structures share common primitives, we propose a patch-primitive driven reconstruction approach to raise the quality of ghost imaging. Specifically, we resort to a statistical learning strategy by representing each image patch with sparse coefficients upon an over-complete dictionary. The dictionary is composed of various primitives learned from a large number of image patches from a natural image database. By introducing a linear mapping between non-overlapping image patches and the whole image, we incorporate the above local prior into the convex optimization framework of compressive ghost imaging. Experiments demonstrate that our method could obtain better reconstruction from the same amount of measurements, and thus reduce the number of requisite measurements for achieving satisfying imaging quality.

© 2015 Optical Society of America

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References

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2014 (6)

E. Li, Z. Bo, M. Chen, W. Gong, and S. Han, “Ghost imaging of a moving target with an unknown constant speed,” Appl. Phys. Lett. 104, 251120 (2014).
[Crossref]

M. Mirhosseini, O. S. Magaña-Loaiza, S. M. H. Rafsanjani, and R. W. Boyd, “Compressive direct measurement of the quantum wave function,” Phys. Rev. Lett. 113, 090402 (2014).
[Crossref] [PubMed]

G. A. Howland, J. Schneeloch, D. J. Lum, and J. C. Howell, “Simultaneous measurement of complementary observables with compressive sensing,” Phys. Rev. Lett. 112, 253602 (2014).
[Crossref] [PubMed]

W. K. Yu, M. F. Li, X. R. Yao, X. F. Liu, L. A. Wu, and G. J. Zhai, “Adaptive compressive ghost imaging based on wavelet trees and sparse representation,” Opt. Express 22, 7133–7144 (2014).
[Crossref] [PubMed]

X. Hu, Y. Deng, X. Lin, J. Suo, Q. Dai, C. Barsi, and R. Raskar, “Robust and accurate transient light transport decomposition via convolutional sparse coding,” Opt. Lett. 39, 3177–3180 (2014).
[Crossref] [PubMed]

W. Wang, Y. P. Wang, J. Li, X. Yang, and Y. Wu, “Iterative ghost imaging,” Opt. Lett. 39, 5150–5153 (2014).
[Crossref] [PubMed]

2013 (4)

W. Chen and X. Chen, “Ghost imaging for three-dimensional optical security,” Appl. Phys. Lett. 103, 221106 (2013).
[Crossref]

M. Aßmann and M. Bayer, “Compressive adaptive computational ghost imaging,” Sci. Rep. 3, 1545 (2013).
[Crossref] [PubMed]

O. S. Magaña-Loaiza, G. A. Howland, M. Malik, J. C. Howell, and R. W. Boyd, “Compressive object tracking using entangled photons,” Appl. Phys. Lett. 102, 231104 (2013).
[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, 844–847 (2013).
[Crossref] [PubMed]

2012 (2)

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, 141123 (2012).
[Crossref]

B. Sun, S. S. Welsh, M. P. Edgar, J. H. Shapiro, and M. J. Padgett, “Normalized ghost imaging,” Opt. Express 20, 16892–16901 (2012).
[Crossref]

2011 (3)

N. Tian, Q. Guo, A. Wang, D. Xu, and L. Fu, “Fluorescence ghost imaging with pseudothermal light,” Opt. Lett. 36, 3302–3304 (2011).
[Crossref] [PubMed]

S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, “Distributed optimization and statistical learning via the alternating direction method of multipliers,” Found. Trends Mach. Learn. 3, 1–122 (2011).
[Crossref]

W. Dong, D. Zhang, G. Shi, and X. Wu, “Image deblurring and super-resolution by adaptive sparse domain selection and adaptive regularization,” IEEE Trans. Image Process. 20, 1838–1857 (2011).
[Crossref] [PubMed]

2010 (5)

W. Gong and S. Han, “Phase-retrieval ghost imaging of complex-valued objects,” Phys. Rev. A 82, 023828 (2010).
[Crossref]

P. Clemente, V. Durán, E. Tajahuerce, and J. Lancis, “Optical encryption based on computational ghost imaging,” Opt. Lett. 35, 2391–2393 (2010).
[Crossref] [PubMed]

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

J. Yang, J. Wright, T. S. Huang, and Y. Ma, “Image super-resolution via sparse representation,” IEEE Trans. Image Process. 19, 2861–2873 (2010).
[Crossref] [PubMed]

P. Zhang, W. Gong, X. Shen, and S. Han, “Correlated imaging through atmospheric turbulence,” Phys. Rev. A 82, 033817 (2010).
[Crossref]

2009 (4)

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

J. Cheng, “Ghost imaging through turbulent atmosphere,” Opt. Express 17, 7916–7921 (2009).
[Crossref] [PubMed]

K. W. C. Chan, M. N. O’Sullivan, and R. W. Boyd, “High-order thermal ghost imaging,” Opt. Lett. 34, 3343–3345 (2009).
[Crossref] [PubMed]

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

2008 (1)

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

2006 (1)

M. Elad and M. Aharon, “Image denoising via sparse and redundant representations over learned dictionaries,” IEEE Trans. Image Process. 15, 3736–3745 (2006).
[Crossref] [PubMed]

2005 (1)

A. Valencia, G. Scarcelli, M. DAngelo, and Y. Shih, “Two-photon imaging with thermal light,” Phys. Rev. Lett. 94, 063601 (2005).
[Crossref] [PubMed]

2004 (1)

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

2002 (1)

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

1999 (1)

1998 (1)

S. S. Chen, D. L. Donoho, and M. A. Saunders, “Atomic decomposition by basis pursuit,” SIAM Sci J. Comput. 20, 33–61 (1998).
[Crossref]

1996 (2)

B. A. Olshausen and D. J. Field, “Natural image statistics and efficient coding,” Network 7, 333–339 (1996).
[Crossref] [PubMed]

B. A. Olshausen and D. J. Field, “Emergence of simple-cell receptive field properties by learning a sparse code for natural images,” Nature 381, 607–609 (1996).
[Crossref] [PubMed]

1995 (1)

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

1992 (1)

E. P. Simoncelli, W. T. Freeman, E. H. Adelson, and D. J. Heeger, “Shiftable multiscale transforms,” IEEE Trans. Inf. Theory 38, 587–607 (1992).
[Crossref]

Adelson, E. H.

E. P. Simoncelli, W. T. Freeman, E. H. Adelson, and D. J. Heeger, “Shiftable multiscale transforms,” IEEE Trans. Inf. Theory 38, 587–607 (1992).
[Crossref]

Aharon, M.

M. Elad and M. Aharon, “Image denoising via sparse and redundant representations over learned dictionaries,” IEEE Trans. Image Process. 15, 3736–3745 (2006).
[Crossref] [PubMed]

Aßmann, M.

M. Aßmann and M. Bayer, “Compressive adaptive computational ghost imaging,” Sci. Rep. 3, 1545 (2013).
[Crossref] [PubMed]

Bache, M.

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

Barsi, C.

Battle, A.

H. Lee, A. Battle, R. Raina, and A. Y. Ng, “Efficient sparse coding algorithms,” in Proceedings of Advances in Neural Information Processing Systems (NIPS, 2006), pp. 801–808.

Bayer, M.

M. Aßmann and M. Bayer, “Compressive adaptive computational ghost imaging,” Sci. Rep. 3, 1545 (2013).
[Crossref] [PubMed]

Bennink, R. S.

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

Bentley, S. J.

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

Bo, Z.

E. Li, Z. Bo, M. Chen, W. Gong, and S. Han, “Ghost imaging of a moving target with an unknown constant speed,” Appl. Phys. Lett. 104, 251120 (2014).
[Crossref]

Boureau, Y. L.

K. Kavukcuoglu, P. Sermanet, Y. L. Boureau, K. Gregor, M. Mathieu, and Y. L. Cun, “Learning convolutional feature hierarchies for visual recognition,” in Proceedings of Advances in Neural Information Processing Systems (NIPS, 2010), pp. 1090–1098.

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, 844–847 (2013).
[Crossref] [PubMed]

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, 844–847 (2013).
[Crossref] [PubMed]

Boyd, R. W.

M. Mirhosseini, O. S. Magaña-Loaiza, S. M. H. Rafsanjani, and R. W. Boyd, “Compressive direct measurement of the quantum wave function,” Phys. Rev. Lett. 113, 090402 (2014).
[Crossref] [PubMed]

O. S. Magaña-Loaiza, G. A. Howland, M. Malik, J. C. Howell, and R. W. Boyd, “Compressive object tracking using entangled photons,” Appl. Phys. Lett. 102, 231104 (2013).
[Crossref]

K. W. C. Chan, M. N. O’Sullivan, and R. W. Boyd, “High-order thermal ghost imaging,” Opt. Lett. 34, 3343–3345 (2009).
[Crossref] [PubMed]

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

Boyd, S.

S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, “Distributed optimization and statistical learning via the alternating direction method of multipliers,” Found. Trends Mach. Learn. 3, 1–122 (2011).
[Crossref]

Brambilla, E.

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

Bromberg, Y.

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

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

Chan, K. W. C.

Chen, M.

E. Li, Z. Bo, M. Chen, W. Gong, and S. Han, “Ghost imaging of a moving target with an unknown constant speed,” Appl. Phys. Lett. 104, 251120 (2014).
[Crossref]

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, 141123 (2012).
[Crossref]

Chen, S. S.

S. S. Chen, D. L. Donoho, and M. A. Saunders, “Atomic decomposition by basis pursuit,” SIAM Sci J. Comput. 20, 33–61 (1998).
[Crossref]

Chen, W.

W. Chen and X. Chen, “Ghost imaging for three-dimensional optical security,” Appl. Phys. Lett. 103, 221106 (2013).
[Crossref]

Chen, X.

W. Chen and X. Chen, “Ghost imaging for three-dimensional optical security,” Appl. Phys. Lett. 103, 221106 (2013).
[Crossref]

Cheng, J.

Chu, E.

S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, “Distributed optimization and statistical learning via the alternating direction method of multipliers,” Found. Trends Mach. Learn. 3, 1–122 (2011).
[Crossref]

Clemente, P.

Cun, Y. L.

K. Kavukcuoglu, P. Sermanet, Y. L. Boureau, K. Gregor, M. Mathieu, and Y. L. Cun, “Learning convolutional feature hierarchies for visual recognition,” in Proceedings of Advances in Neural Information Processing Systems (NIPS, 2010), pp. 1090–1098.

Dai, Q.

DAngelo, M.

A. Valencia, G. Scarcelli, M. DAngelo, and Y. Shih, “Two-photon imaging with thermal light,” Phys. Rev. Lett. 94, 063601 (2005).
[Crossref] [PubMed]

Deng, Y.

Dong, W.

W. Dong, D. Zhang, G. Shi, and X. Wu, “Image deblurring and super-resolution by adaptive sparse domain selection and adaptive regularization,” IEEE Trans. Image Process. 20, 1838–1857 (2011).
[Crossref] [PubMed]

Donoho, D. L.

S. S. Chen, D. L. Donoho, and M. A. Saunders, “Atomic decomposition by basis pursuit,” SIAM Sci J. Comput. 20, 33–61 (1998).
[Crossref]

Durán, V.

Eckstein, J.

S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, “Distributed optimization and statistical learning via the alternating direction method of multipliers,” Found. Trends Mach. Learn. 3, 1–122 (2011).
[Crossref]

Edgar, M. P.

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, 844–847 (2013).
[Crossref] [PubMed]

B. Sun, S. S. Welsh, M. P. Edgar, J. H. Shapiro, and M. J. Padgett, “Normalized ghost imaging,” Opt. Express 20, 16892–16901 (2012).
[Crossref]

Elad, M.

M. Elad and M. Aharon, “Image denoising via sparse and redundant representations over learned dictionaries,” IEEE Trans. Image Process. 15, 3736–3745 (2006).
[Crossref] [PubMed]

Ferri, F.

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

Field, D. J.

B. A. Olshausen and D. J. Field, “Natural image statistics and efficient coding,” Network 7, 333–339 (1996).
[Crossref] [PubMed]

B. A. Olshausen and D. J. Field, “Emergence of simple-cell receptive field properties by learning a sparse code for natural images,” Nature 381, 607–609 (1996).
[Crossref] [PubMed]

Fowlkes, C.

D. Martin, C. Fowlkes, D. Tal, and J. Malik, “A database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecological statistics,” in Proceedings of IEEE International Conference on Computer Vision (IEEE, 2001), pp. 416–423.

Freeman, W. T.

E. P. Simoncelli, W. T. Freeman, E. H. Adelson, and D. J. Heeger, “Shiftable multiscale transforms,” IEEE Trans. Inf. Theory 38, 587–607 (1992).
[Crossref]

Fu, L.

Gatti, A.

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

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

Gong, W.

E. Li, Z. Bo, M. Chen, W. Gong, and S. Han, “Ghost imaging of a moving target with an unknown constant speed,” Appl. Phys. Lett. 104, 251120 (2014).
[Crossref]

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, 141123 (2012).
[Crossref]

W. Gong and S. Han, “Phase-retrieval ghost imaging of complex-valued objects,” Phys. Rev. A 82, 023828 (2010).
[Crossref]

P. Zhang, W. Gong, X. Shen, and S. Han, “Correlated imaging through atmospheric turbulence,” Phys. Rev. A 82, 033817 (2010).
[Crossref]

Gregor, K.

K. Kavukcuoglu, P. Sermanet, Y. L. Boureau, K. Gregor, M. Mathieu, and Y. L. Cun, “Learning convolutional feature hierarchies for visual recognition,” in Proceedings of Advances in Neural Information Processing Systems (NIPS, 2010), pp. 1090–1098.

Guo, Q.

Han, S.

E. Li, Z. Bo, M. Chen, W. Gong, and S. Han, “Ghost imaging of a moving target with an unknown constant speed,” Appl. Phys. Lett. 104, 251120 (2014).
[Crossref]

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, 141123 (2012).
[Crossref]

W. Gong and S. Han, “Phase-retrieval ghost imaging of complex-valued objects,” Phys. Rev. A 82, 023828 (2010).
[Crossref]

P. Zhang, W. Gong, X. Shen, and S. Han, “Correlated imaging through atmospheric turbulence,” Phys. Rev. A 82, 033817 (2010).
[Crossref]

Heeger, D. J.

E. P. Simoncelli, W. T. Freeman, E. H. Adelson, and D. J. Heeger, “Shiftable multiscale transforms,” IEEE Trans. Inf. Theory 38, 587–607 (1992).
[Crossref]

Howell, J. C.

G. A. Howland, J. Schneeloch, D. J. Lum, and J. C. Howell, “Simultaneous measurement of complementary observables with compressive sensing,” Phys. Rev. Lett. 112, 253602 (2014).
[Crossref] [PubMed]

O. S. Magaña-Loaiza, G. A. Howland, M. Malik, J. C. Howell, and R. W. Boyd, “Compressive object tracking using entangled photons,” Appl. Phys. Lett. 102, 231104 (2013).
[Crossref]

Howland, G. A.

G. A. Howland, J. Schneeloch, D. J. Lum, and J. C. Howell, “Simultaneous measurement of complementary observables with compressive sensing,” Phys. Rev. Lett. 112, 253602 (2014).
[Crossref] [PubMed]

O. S. Magaña-Loaiza, G. A. Howland, M. Malik, J. C. Howell, and R. W. Boyd, “Compressive object tracking using entangled photons,” Appl. Phys. Lett. 102, 231104 (2013).
[Crossref]

Hu, X.

Huang, T. S.

J. Yang, J. Wright, T. S. Huang, and Y. Ma, “Image super-resolution via sparse representation,” IEEE Trans. Image Process. 19, 2861–2873 (2010).
[Crossref] [PubMed]

Katz, O.

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

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

Kavukcuoglu, K.

K. Kavukcuoglu, P. Sermanet, Y. L. Boureau, K. Gregor, M. Mathieu, and Y. L. Cun, “Learning convolutional feature hierarchies for visual recognition,” in Proceedings of Advances in Neural Information Processing Systems (NIPS, 2010), pp. 1090–1098.

Lancis, J.

Lee, H.

H. Lee, A. Battle, R. Raina, and A. Y. Ng, “Efficient sparse coding algorithms,” in Proceedings of Advances in Neural Information Processing Systems (NIPS, 2006), pp. 801–808.

Lewicki, M. S.

Li, E.

E. Li, Z. Bo, M. Chen, W. Gong, and S. Han, “Ghost imaging of a moving target with an unknown constant speed,” Appl. Phys. Lett. 104, 251120 (2014).
[Crossref]

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, 141123 (2012).
[Crossref]

Li, J.

Li, M. F.

Lin, X.

Liu, X. F.

Lugiato, L.

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

Lugiato, L. A.

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

Lum, D. J.

G. A. Howland, J. Schneeloch, D. J. Lum, and J. C. Howell, “Simultaneous measurement of complementary observables with compressive sensing,” Phys. Rev. Lett. 112, 253602 (2014).
[Crossref] [PubMed]

Ma, Y.

J. Yang, J. Wright, T. S. Huang, and Y. Ma, “Image super-resolution via sparse representation,” IEEE Trans. Image Process. 19, 2861–2873 (2010).
[Crossref] [PubMed]

Magaña-Loaiza, O. S.

M. Mirhosseini, O. S. Magaña-Loaiza, S. M. H. Rafsanjani, and R. W. Boyd, “Compressive direct measurement of the quantum wave function,” Phys. Rev. Lett. 113, 090402 (2014).
[Crossref] [PubMed]

O. S. Magaña-Loaiza, G. A. Howland, M. Malik, J. C. Howell, and R. W. Boyd, “Compressive object tracking using entangled photons,” Appl. Phys. Lett. 102, 231104 (2013).
[Crossref]

Magatti, D.

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

Malik, J.

D. Martin, C. Fowlkes, D. Tal, and J. Malik, “A database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecological statistics,” in Proceedings of IEEE International Conference on Computer Vision (IEEE, 2001), pp. 416–423.

Malik, M.

O. S. Magaña-Loaiza, G. A. Howland, M. Malik, J. C. Howell, and R. W. Boyd, “Compressive object tracking using entangled photons,” Appl. Phys. Lett. 102, 231104 (2013).
[Crossref]

Martin, D.

D. Martin, C. Fowlkes, D. Tal, and J. Malik, “A database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecological statistics,” in Proceedings of IEEE International Conference on Computer Vision (IEEE, 2001), pp. 416–423.

Mathieu, M.

K. Kavukcuoglu, P. Sermanet, Y. L. Boureau, K. Gregor, M. Mathieu, and Y. L. Cun, “Learning convolutional feature hierarchies for visual recognition,” in Proceedings of Advances in Neural Information Processing Systems (NIPS, 2010), pp. 1090–1098.

Mirhosseini, M.

M. Mirhosseini, O. S. Magaña-Loaiza, S. M. H. Rafsanjani, and R. W. Boyd, “Compressive direct measurement of the quantum wave function,” Phys. Rev. Lett. 113, 090402 (2014).
[Crossref] [PubMed]

Ng, A. Y.

H. Lee, A. Battle, R. Raina, and A. Y. Ng, “Efficient sparse coding algorithms,” in Proceedings of Advances in Neural Information Processing Systems (NIPS, 2006), pp. 801–808.

O’Sullivan, M. N.

Olshausen, B. A.

M. S. Lewicki and B. A. Olshausen, “Probabilistic framework for the adaptation and comparison of image codes,” J. Opt. Soc. Am. A 16, 1587–1601 (1999).
[Crossref]

B. A. Olshausen and D. J. Field, “Emergence of simple-cell receptive field properties by learning a sparse code for natural images,” Nature 381, 607–609 (1996).
[Crossref] [PubMed]

B. A. Olshausen and D. J. Field, “Natural image statistics and efficient coding,” Network 7, 333–339 (1996).
[Crossref] [PubMed]

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, 844–847 (2013).
[Crossref] [PubMed]

Padgett, M. J.

Parikh, N.

S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, “Distributed optimization and statistical learning via the alternating direction method of multipliers,” Found. Trends Mach. Learn. 3, 1–122 (2011).
[Crossref]

Peleato, B.

S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, “Distributed optimization and statistical learning via the alternating direction method of multipliers,” Found. Trends Mach. Learn. 3, 1–122 (2011).
[Crossref]

Pittman, T.

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

Rafsanjani, S. M. H.

M. Mirhosseini, O. S. Magaña-Loaiza, S. M. H. Rafsanjani, and R. W. Boyd, “Compressive direct measurement of the quantum wave function,” Phys. Rev. Lett. 113, 090402 (2014).
[Crossref] [PubMed]

Raina, R.

H. Lee, A. Battle, R. Raina, and A. Y. Ng, “Efficient sparse coding algorithms,” in Proceedings of Advances in Neural Information Processing Systems (NIPS, 2006), pp. 801–808.

Raskar, R.

Saunders, M. A.

S. S. Chen, D. L. Donoho, and M. A. Saunders, “Atomic decomposition by basis pursuit,” SIAM Sci J. Comput. 20, 33–61 (1998).
[Crossref]

Scarcelli, G.

A. Valencia, G. Scarcelli, M. DAngelo, and Y. Shih, “Two-photon imaging with thermal light,” Phys. Rev. Lett. 94, 063601 (2005).
[Crossref] [PubMed]

Schneeloch, J.

G. A. Howland, J. Schneeloch, D. J. Lum, and J. C. Howell, “Simultaneous measurement of complementary observables with compressive sensing,” Phys. Rev. Lett. 112, 253602 (2014).
[Crossref] [PubMed]

Sergienko, A.

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

Sermanet, P.

K. Kavukcuoglu, P. Sermanet, Y. L. Boureau, K. Gregor, M. Mathieu, and Y. L. Cun, “Learning convolutional feature hierarchies for visual recognition,” in Proceedings of Advances in Neural Information Processing Systems (NIPS, 2010), pp. 1090–1098.

Shapiro, J. H.

Shen, X.

P. Zhang, W. Gong, X. Shen, and S. Han, “Correlated imaging through atmospheric turbulence,” Phys. Rev. A 82, 033817 (2010).
[Crossref]

Shi, G.

W. Dong, D. Zhang, G. Shi, and X. Wu, “Image deblurring and super-resolution by adaptive sparse domain selection and adaptive regularization,” IEEE Trans. Image Process. 20, 1838–1857 (2011).
[Crossref] [PubMed]

Shih, Y.

A. Valencia, G. Scarcelli, M. DAngelo, and Y. Shih, “Two-photon imaging with thermal light,” Phys. Rev. Lett. 94, 063601 (2005).
[Crossref] [PubMed]

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

Silberberg, Y.

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

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

Simoncelli, E. P.

E. P. Simoncelli, W. T. Freeman, E. H. Adelson, and D. J. Heeger, “Shiftable multiscale transforms,” IEEE Trans. Inf. Theory 38, 587–607 (1992).
[Crossref]

Strekalov, D.

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

Sun, B.

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, 844–847 (2013).
[Crossref] [PubMed]

B. Sun, S. S. Welsh, M. P. Edgar, J. H. Shapiro, and M. J. Padgett, “Normalized ghost imaging,” Opt. Express 20, 16892–16901 (2012).
[Crossref]

Suo, J.

Tajahuerce, E.

Tal, D.

D. Martin, C. Fowlkes, D. Tal, and J. Malik, “A database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecological statistics,” in Proceedings of IEEE International Conference on Computer Vision (IEEE, 2001), pp. 416–423.

Tian, N.

Valencia, A.

A. Valencia, G. Scarcelli, M. DAngelo, and Y. Shih, “Two-photon imaging with thermal light,” Phys. Rev. Lett. 94, 063601 (2005).
[Crossref] [PubMed]

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, 844–847 (2013).
[Crossref] [PubMed]

Wang, A.

Wang, H.

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, 141123 (2012).
[Crossref]

Wang, W.

Wang, Y. P.

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, 844–847 (2013).
[Crossref] [PubMed]

Welsh, S. S.

Wright, J.

J. Yang, J. Wright, T. S. Huang, and Y. Ma, “Image super-resolution via sparse representation,” IEEE Trans. Image Process. 19, 2861–2873 (2010).
[Crossref] [PubMed]

Wu, L. A.

Wu, X.

W. Dong, D. Zhang, G. Shi, and X. Wu, “Image deblurring and super-resolution by adaptive sparse domain selection and adaptive regularization,” IEEE Trans. Image Process. 20, 1838–1857 (2011).
[Crossref] [PubMed]

Wu, Y.

Xu, D.

Xu, W.

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, 141123 (2012).
[Crossref]

Yang, J.

J. Yang, J. Wright, T. S. Huang, and Y. Ma, “Image super-resolution via sparse representation,” IEEE Trans. Image Process. 19, 2861–2873 (2010).
[Crossref] [PubMed]

Yang, X.

Yao, X. R.

Yu, W. K.

Zhai, G. J.

Zhang, D.

W. Dong, D. Zhang, G. Shi, and X. Wu, “Image deblurring and super-resolution by adaptive sparse domain selection and adaptive regularization,” IEEE Trans. Image Process. 20, 1838–1857 (2011).
[Crossref] [PubMed]

Zhang, P.

P. Zhang, W. Gong, X. Shen, and S. Han, “Correlated imaging through atmospheric turbulence,” Phys. Rev. A 82, 033817 (2010).
[Crossref]

Zhao, C.

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, 141123 (2012).
[Crossref]

Appl. Phys. Lett. (5)

O. S. Magaña-Loaiza, G. A. Howland, M. Malik, J. C. Howell, and R. W. Boyd, “Compressive object tracking using entangled photons,” Appl. Phys. Lett. 102, 231104 (2013).
[Crossref]

E. Li, Z. Bo, M. Chen, W. Gong, and S. Han, “Ghost imaging of a moving target with an unknown constant speed,” Appl. Phys. Lett. 104, 251120 (2014).
[Crossref]

W. Chen and X. Chen, “Ghost imaging for three-dimensional optical security,” Appl. Phys. Lett. 103, 221106 (2013).
[Crossref]

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, 141123 (2012).
[Crossref]

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

Found. Trends Mach. Learn. (1)

S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, “Distributed optimization and statistical learning via the alternating direction method of multipliers,” Found. Trends Mach. Learn. 3, 1–122 (2011).
[Crossref]

IEEE Trans. Image Process. (3)

M. Elad and M. Aharon, “Image denoising via sparse and redundant representations over learned dictionaries,” IEEE Trans. Image Process. 15, 3736–3745 (2006).
[Crossref] [PubMed]

J. Yang, J. Wright, T. S. Huang, and Y. Ma, “Image super-resolution via sparse representation,” IEEE Trans. Image Process. 19, 2861–2873 (2010).
[Crossref] [PubMed]

W. Dong, D. Zhang, G. Shi, and X. Wu, “Image deblurring and super-resolution by adaptive sparse domain selection and adaptive regularization,” IEEE Trans. Image Process. 20, 1838–1857 (2011).
[Crossref] [PubMed]

IEEE Trans. Inf. Theory (1)

E. P. Simoncelli, W. T. Freeman, E. H. Adelson, and D. J. Heeger, “Shiftable multiscale transforms,” IEEE Trans. Inf. Theory 38, 587–607 (1992).
[Crossref]

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

Nature (1)

B. A. Olshausen and D. J. Field, “Emergence of simple-cell receptive field properties by learning a sparse code for natural images,” Nature 381, 607–609 (1996).
[Crossref] [PubMed]

Network (1)

B. A. Olshausen and D. J. Field, “Natural image statistics and efficient coding,” Network 7, 333–339 (1996).
[Crossref] [PubMed]

Opt. Express (3)

Opt. Lett. (5)

Phys. Rev. A (5)

W. Gong and S. Han, “Phase-retrieval ghost imaging of complex-valued objects,” Phys. Rev. A 82, 023828 (2010).
[Crossref]

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

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

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

P. Zhang, W. Gong, X. Shen, and S. Han, “Correlated imaging through atmospheric turbulence,” Phys. Rev. A 82, 033817 (2010).
[Crossref]

Phys. Rev. Lett. (6)

R. S. Bennink, S. J. Bentley, and R. W. Boyd, “Two-photon coincidence imaging with a classical source,” Phys. Rev. Lett. 89, 113601 (2002).
[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, 093602 (2004).
[Crossref] [PubMed]

A. Valencia, G. Scarcelli, M. DAngelo, and Y. Shih, “Two-photon imaging with thermal light,” Phys. Rev. Lett. 94, 063601 (2005).
[Crossref] [PubMed]

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

M. Mirhosseini, O. S. Magaña-Loaiza, S. M. H. Rafsanjani, and R. W. Boyd, “Compressive direct measurement of the quantum wave function,” Phys. Rev. Lett. 113, 090402 (2014).
[Crossref] [PubMed]

G. A. Howland, J. Schneeloch, D. J. Lum, and J. C. Howell, “Simultaneous measurement of complementary observables with compressive sensing,” Phys. Rev. Lett. 112, 253602 (2014).
[Crossref] [PubMed]

Sci. Rep. (1)

M. Aßmann and M. Bayer, “Compressive adaptive computational ghost imaging,” Sci. Rep. 3, 1545 (2013).
[Crossref] [PubMed]

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, 844–847 (2013).
[Crossref] [PubMed]

SIAM Sci J. Comput. (1)

S. S. Chen, D. L. Donoho, and M. A. Saunders, “Atomic decomposition by basis pursuit,” SIAM Sci J. Comput. 20, 33–61 (1998).
[Crossref]

Other (3)

D. Martin, C. Fowlkes, D. Tal, and J. Malik, “A database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecological statistics,” in Proceedings of IEEE International Conference on Computer Vision (IEEE, 2001), pp. 416–423.

K. Kavukcuoglu, P. Sermanet, Y. L. Boureau, K. Gregor, M. Mathieu, and Y. L. Cun, “Learning convolutional feature hierarchies for visual recognition,” in Proceedings of Advances in Neural Information Processing Systems (NIPS, 2010), pp. 1090–1098.

H. Lee, A. Battle, R. Raina, and A. Y. Ng, “Efficient sparse coding algorithms,” in Proceedings of Advances in Neural Information Processing Systems (NIPS, 2006), pp. 801–808.

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Figures (7)

Fig. 1
Fig. 1 Schemetic illustration of our model. The upper part (framed with dashed box) depicts the learning process of patch primitive set. For a given image, each patch pij can be extracted from the image x by Rij, and represented with sparse coefficients sij over the learned over-complete patch primitive set. Inversely, with the patch-to-image mapping { R i j T }, we could reconstruct the whole image using the over-complete patch primitive set and the corresponding sparsity coefficients {sij}.
Fig. 2
Fig. 2 Performance comparison on simulated data. The 1st column displays the ground truth images. The 2nd and the 3rd column is respectively the reconstruction results of TGI and DGI. The 4nd vs. 5rd, and 6th vs. 7th columns compare the reconstruction results of CCGI and PCGI. (a) Images without periodic textures: letters ‘GI’ (SSR=0.08), ‘Leaf’ (SSR=0.10), ‘Eight-triagrams’ (SSR= 0.35), ‘Lena’ (SSR= 0.35), ‘Flower’ (SSR= 0.25). (b) Images with periodic textures: ‘Brickwall’ (SSR= 0.45), ‘Wickerwork’ (SSR= 0.5), ‘Fishscale’ (SSR= 0.45).
Fig. 3
Fig. 3 Quantitative performance comparison with respect to SSRs among six different algorithms referred in Fig. 2. (a) ‘Lena’, (b) ‘Wickerwork’.
Fig. 4
Fig. 4 Comparison of robustness to sensor noise among six algorithms. (a) ‘Lena’, (b) ‘Wickerwork’.
Fig. 5
Fig. 5 The schematic diagram of CGI. Light source: high pressure Mercury lamp (Philips, 200w). DMD: Texas Instrument DLP ® Discovery™4100, .7XGA. Scene: a transmissive film (34mm×34mm). Detector: Thorlabs DET100 Silicon photodiode (integration time: 0.625ns).
Fig. 6
Fig. 6 The reconstructions of ‘GHOST IMAGE’ and ‘Ghost’ from the measurements of different sampling frequencies.
Fig. 7
Fig. 7 The reconstructions from the measurements captured by our prototype. The 1st column displays the PGT, the 2nd and 3rd columns show results of TGI and DGI, and the 4th to 7th column shows the reconstruction by CCGI-TV, PCGI-TV, CCGI-DCT, PCGI-DCT, respectively.

Equations (9)

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

arg min { s u } , { d v } u = 1 U p u v = 1 V s v u d v 2 2 + β u = 1 U s u 1 .
p = Ds ,
R i j x = p i j
x = i j R i j T ( p i j ) .
arg min s i j Ψ x 1 + λ i j s i j 1 s . t . Φ x y 2 2 ε , x = i j R i j T p i j , p i j = D s i j .
arg min s i j Ψ i j R i j T ( D s i j ) 1 + λ i j s i j 1 s . t . Φ i j R i j T ( D s i j ) y 2 2 ε .
arg min s i j Ψ i j R i j T ( D s i j ) 1 + λ i j s i j 1 + μ 2 Φ i j R i j T ( D s i j ) y 2 2 ,
arg min s ˜ Ψ R ˜ T D ˜ s ˜ 1 + λ s ˜ 1 + μ 2 Φ R ˜ T D ˜ s ˜ y | | 2 2 .
arg min s ˜ w 1 + λ s ˜ 1 + μ 2 Φ R ˜ T D ˜ s ˜ y 2 2 s . t . w = Ψ R ˜ T D ˜ s ˜ .

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