Abstract

The separation of morphology components in ghost imaging via sparsity constraint is investigated by adapting the morphology component analysis technique based on the fact that different morphology components can be sparsely expressed in different basis. The successful separation of reconstructed image plays an important role in the ability to identify it, analyze it, enhance it and more. This approach is first studied with numerical simulations and then verified with both table-top and outdoor experimental data. Results show that it can not only separate different morphology components but also improve the quality of the reconstructed image.

© 2014 Optical Society of America

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    [CrossRef]
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  12. P. Zhang, W. Gong, X. Shen, D. Huang, and S. Han, “Improving resolution by the second-order correlation of light fields,” Opt. Lett. 34, 1222–1224 (2009).
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    [CrossRef]
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  31. J. A. Tropp and A. C. Gilbert, “Signal recovery from random measurements via orthogonal matching pursuit,” IEEE Trans. Inf. Theory 53, 4655–4666 (2007).
    [CrossRef]
  32. D. L. Donoho, A. Maleki, and A. Montanari, “Message-passing algorithms for compressed sensing,” Proc. Natl. Acad. Sci. 106, 18914–18919 (2009).
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2012

J. H. Shapiro and R. W. Boyd, “The physics of ghost imaging,” Quantum Inf. Process. 11, 949–993 (2012).
[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, “Experimental investigation of the quality of lensless super-resolution ghost imaging via sparsity constraints,” Phys. Lett. A 376, 1519–1522 (2012).
[CrossRef]

H. Wang and S. Han, “Coherent ghost imaging based on sparsity constraint without phase-sensitive detection,” Europhys. Lett. 98, 24003 (2012).
[CrossRef]

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

H. Wang, S. Han, and M. I. Kolobov, “Quantum limits of super-resolution of optical sparse objects via sparsity constraint,” Opt. Express 20, 23235–23252 (2012).
[CrossRef] [PubMed]

2011

P. Zerom, K. W. C. Chan, J. C. Howell, and R. W. Boyd, “Entangled-photon compressive ghost imaging,” Phys. Rev. A 84, 061804 (2011).
[CrossRef]

2010

X. Qu, X. Cao, D. Guo, C. Hu, and Z. Chen, “Combined sparsifying transforms for compressed sensing MRI,” Electron. Lett. 46, 121–123 (2010).
[CrossRef]

M. J. Fadili, J. L. Starck, J. Bobin, and Y. Moudden, “Image decomposition and separation using sparse representations: An overview,” Proc. IEEE 98, 983–994 (2010).
[CrossRef]

2009

D. L. Donoho, A. Maleki, and A. Montanari, “Message-passing algorithms for compressed sensing,” Proc. Natl. Acad. Sci. 106, 18914–18919 (2009).
[CrossRef] [PubMed]

P. Zhang, W. Gong, X. Shen, D. Huang, and S. Han, “Improving resolution by the second-order correlation of light fields,” Opt. Lett. 34, 1222–1224 (2009).
[CrossRef] [PubMed]

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

P. Zhang, W. Gong, X. Shen, S. Han, and R. Shu, “Homodyne detection in ghost imaging with thermal light,” Phys. Rev. A 80, 033827 (2009).
[CrossRef]

2008

D. Cao, J. Xiong, S. Zhang, L. Lin, L. Gao, and K. Wang, “Enhancing visibility and resolution in Nth-order intensity correlation of thermal light,” Appl. Phys. Lett. 92, 201102 (2008).
[CrossRef]

2007

R. G. Baraniuk, “Compressive sensing [lecture notes],” IEEE Signal Process. Mag. 24, 118–121 (2007).
[CrossRef]

Y. Bai and S. Han, “Ghost imaging with thermal light by third-order correlation,” Phys. Rev. A 76, 043828 (2007).
[CrossRef]

Y. Bai, H. Liu, and S. Han, “Transmission area and correlated imaging,” Opt. Express 15, 6062–6068 (2007).
[CrossRef] [PubMed]

J. Bobin, J. L. Starck, J. M. Fadili, Y. Moudden, and D. L. Donoho, “Morphological component analysis: An adaptive thresholding strategy,” IEEE Trans. Image Process. 16, 2675–2681 (2007).
[CrossRef] [PubMed]

M. A. Figueiredo, R. D. Nowak, and S. J. Wright, “Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems,” IEEE J. Sel. Top. Sign. Proces. 1, 586–597 (2007).
[CrossRef]

J. A. Tropp and A. C. Gilbert, “Signal recovery from random measurements via orthogonal matching pursuit,” IEEE Trans. Inf. Theory 53, 4655–4666 (2007).
[CrossRef]

2006

E. Candes, L. Demanet, D. Donoho, and L. Ying, “Fast discrete curvelet transforms,” Multiscale Model. Simul. 5, 861–899 (2006).
[CrossRef]

A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L. Lugiato, “Coherent imaging with pseudo-thermal incoherent light,” J. Mod. Opt. 53, 739–760 (2006).
[CrossRef]

2005

D. Cao, J. Xiong, and K. Wang, “Geometrical optics in correlated imaging systems,” Phys. Rev. A 71, 013801 (2005).
[CrossRef]

M. D’Angelo and Y. Shih, “Quantum imaging,” Laser Phys. Lett. 2, 567–596 (2005).
[CrossRef]

D. Zhang, Y. H. Zhai, L. A. Wu, and X. H. Chen, “Correlated two-photon imaging with true thermal light,” Opt. Lett. 30, 2354–2356 (2005).
[CrossRef] [PubMed]

2004

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

M. Bache, E. Brambilla, A. Gatti, and L. Lugiato, “Ghost imaging using homodyne detection,” Phys. Rev. A 70, 023823 (2004).
[CrossRef]

2002

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]

2001

D. L. Donoho and X. Huo, “Uncertainty principles and ideal atomic d ecomposition,” IEEE Trans. Inf. Theory 47, 2845–2862 (2001).
[CrossRef]

1995

D. L. Donoho and I. M. Johnstone, “Adapting to unknown smoothness via wavelet shrinkage,” J. Am. Stat. Assoc. 90, 1200–1224 (1995).
[CrossRef]

1974

N. Ahmed, T. Natarajan, and K. R. Rao, “Discrete cosine transform,” IEEE Trans. Comput. 100, 90–93 (1974).
[CrossRef]

Ahmed, N.

N. Ahmed, T. Natarajan, and K. R. Rao, “Discrete cosine transform,” IEEE Trans. Comput. 100, 90–93 (1974).
[CrossRef]

Bache, M.

A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L. Lugiato, “Coherent imaging with pseudo-thermal incoherent light,” J. Mod. Opt. 53, 739–760 (2006).
[CrossRef]

M. Bache, E. Brambilla, A. Gatti, and L. Lugiato, “Ghost imaging using homodyne detection,” Phys. Rev. A 70, 023823 (2004).
[CrossRef]

Bai, Y.

Y. Bai, H. Liu, and S. Han, “Transmission area and correlated imaging,” Opt. Express 15, 6062–6068 (2007).
[CrossRef] [PubMed]

Y. Bai and S. Han, “Ghost imaging with thermal light by third-order correlation,” Phys. Rev. A 76, 043828 (2007).
[CrossRef]

Baraniuk, R. G.

R. G. Baraniuk, “Compressive sensing [lecture notes],” IEEE Signal Process. Mag. 24, 118–121 (2007).
[CrossRef]

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]

Bobin, J.

M. J. Fadili, J. L. Starck, J. Bobin, and Y. Moudden, “Image decomposition and separation using sparse representations: An overview,” Proc. IEEE 98, 983–994 (2010).
[CrossRef]

J. Bobin, J. L. Starck, J. M. Fadili, Y. Moudden, and D. L. Donoho, “Morphological component analysis: An adaptive thresholding strategy,” IEEE Trans. Image Process. 16, 2675–2681 (2007).
[CrossRef] [PubMed]

Boyd, R. W.

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

P. Zerom, K. W. C. Chan, J. C. Howell, and R. W. Boyd, “Entangled-photon compressive ghost imaging,” Phys. Rev. A 84, 061804 (2011).
[CrossRef]

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]

Brambilla, E.

A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L. Lugiato, “Coherent imaging with pseudo-thermal incoherent light,” J. Mod. Opt. 53, 739–760 (2006).
[CrossRef]

M. Bache, E. Brambilla, A. Gatti, and L. Lugiato, “Ghost imaging using homodyne detection,” Phys. Rev. A 70, 023823 (2004).
[CrossRef]

Bromberg, Y.

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

Candes, E.

E. Candes, L. Demanet, D. Donoho, and L. Ying, “Fast discrete curvelet transforms,” Multiscale Model. Simul. 5, 861–899 (2006).
[CrossRef]

Cao, D.

D. Cao, J. Xiong, S. Zhang, L. Lin, L. Gao, and K. Wang, “Enhancing visibility and resolution in Nth-order intensity correlation of thermal light,” Appl. Phys. Lett. 92, 201102 (2008).
[CrossRef]

D. Cao, J. Xiong, and K. Wang, “Geometrical optics in correlated imaging systems,” Phys. Rev. A 71, 013801 (2005).
[CrossRef]

Cao, X.

X. Qu, X. Cao, D. Guo, C. Hu, and Z. Chen, “Combined sparsifying transforms for compressed sensing MRI,” Electron. Lett. 46, 121–123 (2010).
[CrossRef]

Chan, K. W. C.

P. Zerom, K. W. C. Chan, J. C. Howell, and R. W. Boyd, “Entangled-photon compressive ghost imaging,” Phys. Rev. A 84, 061804 (2011).
[CrossRef]

Chen, M.

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, C. Zhao, J. Jiao, E. Li, M. Chen, H. Wang, W. Xu, and S. Han, “Three-dimensional ghost imaging ladar,” arXiv preprint arXiv:1301.5767 (2013).

Chen, S.

S. Chen and D. Donoho, “Basis pursuit,” in “Signals, Systems and Computers, 1994. 1994 Conference Record of the Twenty-Eighth Asilomar Conference on,” (IEEE, 1994), vol. 1, pp. 41–44.

Chen, X. H.

Chen, Z.

X. Qu, X. Cao, D. Guo, C. Hu, and Z. Chen, “Combined sparsifying transforms for compressed sensing MRI,” Electron. Lett. 46, 121–123 (2010).
[CrossRef]

Cheng, J.

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

D’Angelo, M.

M. D’Angelo and Y. Shih, “Quantum imaging,” Laser Phys. Lett. 2, 567–596 (2005).
[CrossRef]

Demanet, L.

E. Candes, L. Demanet, D. Donoho, and L. Ying, “Fast discrete curvelet transforms,” Multiscale Model. Simul. 5, 861–899 (2006).
[CrossRef]

Donoho, D.

E. Candes, L. Demanet, D. Donoho, and L. Ying, “Fast discrete curvelet transforms,” Multiscale Model. Simul. 5, 861–899 (2006).
[CrossRef]

S. Chen and D. Donoho, “Basis pursuit,” in “Signals, Systems and Computers, 1994. 1994 Conference Record of the Twenty-Eighth Asilomar Conference on,” (IEEE, 1994), vol. 1, pp. 41–44.

Donoho, D. L.

D. L. Donoho, A. Maleki, and A. Montanari, “Message-passing algorithms for compressed sensing,” Proc. Natl. Acad. Sci. 106, 18914–18919 (2009).
[CrossRef] [PubMed]

J. Bobin, J. L. Starck, J. M. Fadili, Y. Moudden, and D. L. Donoho, “Morphological component analysis: An adaptive thresholding strategy,” IEEE Trans. Image Process. 16, 2675–2681 (2007).
[CrossRef] [PubMed]

D. L. Donoho and X. Huo, “Uncertainty principles and ideal atomic d ecomposition,” IEEE Trans. Inf. Theory 47, 2845–2862 (2001).
[CrossRef]

D. L. Donoho and I. M. Johnstone, “Adapting to unknown smoothness via wavelet shrinkage,” J. Am. Stat. Assoc. 90, 1200–1224 (1995).
[CrossRef]

Du, J.

Fadili, J. M.

J. Bobin, J. L. Starck, J. M. Fadili, Y. Moudden, and D. L. Donoho, “Morphological component analysis: An adaptive thresholding strategy,” IEEE Trans. Image Process. 16, 2675–2681 (2007).
[CrossRef] [PubMed]

Fadili, M. J.

M. J. Fadili, J. L. Starck, J. Bobin, and Y. Moudden, “Image decomposition and separation using sparse representations: An overview,” Proc. IEEE 98, 983–994 (2010).
[CrossRef]

Ferri, F.

A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L. Lugiato, “Coherent imaging with pseudo-thermal incoherent light,” J. Mod. Opt. 53, 739–760 (2006).
[CrossRef]

Figueiredo, M. A.

M. A. Figueiredo, R. D. Nowak, and S. J. Wright, “Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems,” IEEE J. Sel. Top. Sign. Proces. 1, 586–597 (2007).
[CrossRef]

Gao, L.

D. Cao, J. Xiong, S. Zhang, L. Lin, L. Gao, and K. Wang, “Enhancing visibility and resolution in Nth-order intensity correlation of thermal light,” Appl. Phys. Lett. 92, 201102 (2008).
[CrossRef]

Gatti, A.

A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L. Lugiato, “Coherent imaging with pseudo-thermal incoherent light,” J. Mod. Opt. 53, 739–760 (2006).
[CrossRef]

M. Bache, E. Brambilla, A. Gatti, and L. Lugiato, “Ghost imaging using homodyne detection,” Phys. Rev. A 70, 023823 (2004).
[CrossRef]

Gilbert, A. C.

J. A. Tropp and A. C. Gilbert, “Signal recovery from random measurements via orthogonal matching pursuit,” IEEE Trans. Inf. Theory 53, 4655–4666 (2007).
[CrossRef]

Gong, W.

W. Gong and S. Han, “Experimental investigation of the quality of lensless super-resolution ghost imaging via sparsity constraints,” Phys. Lett. A 376, 1519–1522 (2012).
[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]

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

P. Zhang, W. Gong, X. Shen, S. Han, and R. Shu, “Homodyne detection in ghost imaging with thermal light,” Phys. Rev. A 80, 033827 (2009).
[CrossRef]

P. Zhang, W. Gong, X. Shen, D. Huang, and S. Han, “Improving resolution by the second-order correlation of light fields,” Opt. Lett. 34, 1222–1224 (2009).
[CrossRef] [PubMed]

W. Gong, C. Zhao, J. Jiao, E. Li, M. Chen, H. Wang, W. Xu, and S. Han, “Three-dimensional ghost imaging ladar,” arXiv preprint arXiv:1301.5767 (2013).

Guo, D.

X. Qu, X. Cao, D. Guo, C. Hu, and Z. Chen, “Combined sparsifying transforms for compressed sensing MRI,” Electron. Lett. 46, 121–123 (2010).
[CrossRef]

Han, S.

W. Gong and S. Han, “Experimental investigation of the quality of lensless super-resolution ghost imaging via sparsity constraints,” Phys. Lett. A 376, 1519–1522 (2012).
[CrossRef]

H. Wang and S. Han, “Coherent ghost imaging based on sparsity constraint without phase-sensitive detection,” Europhys. Lett. 98, 24003 (2012).
[CrossRef]

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

H. Wang, S. Han, and M. I. Kolobov, “Quantum limits of super-resolution of optical sparse objects via sparsity constraint,” Opt. Express 20, 23235–23252 (2012).
[CrossRef] [PubMed]

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]

P. Zhang, W. Gong, X. Shen, S. Han, and R. Shu, “Homodyne detection in ghost imaging with thermal light,” Phys. Rev. A 80, 033827 (2009).
[CrossRef]

P. Zhang, W. Gong, X. Shen, D. Huang, and S. Han, “Improving resolution by the second-order correlation of light fields,” Opt. Lett. 34, 1222–1224 (2009).
[CrossRef] [PubMed]

Y. Bai, H. Liu, and S. Han, “Transmission area and correlated imaging,” Opt. Express 15, 6062–6068 (2007).
[CrossRef] [PubMed]

Y. Bai and S. Han, “Ghost imaging with thermal light by third-order correlation,” Phys. Rev. A 76, 043828 (2007).
[CrossRef]

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

W. Gong, C. Zhao, J. Jiao, E. Li, M. Chen, H. Wang, W. Xu, and S. Han, “Three-dimensional ghost imaging ladar,” arXiv preprint arXiv:1301.5767 (2013).

Howell, J. C.

P. Zerom, K. W. C. Chan, J. C. Howell, and R. W. Boyd, “Entangled-photon compressive ghost imaging,” Phys. Rev. A 84, 061804 (2011).
[CrossRef]

Hu, C.

X. Qu, X. Cao, D. Guo, C. Hu, and Z. Chen, “Combined sparsifying transforms for compressed sensing MRI,” Electron. Lett. 46, 121–123 (2010).
[CrossRef]

Huang, D.

Huo, X.

D. L. Donoho and X. Huo, “Uncertainty principles and ideal atomic d ecomposition,” IEEE Trans. Inf. Theory 47, 2845–2862 (2001).
[CrossRef]

Jiao, J.

W. Gong, C. Zhao, J. Jiao, E. Li, M. Chen, H. Wang, W. Xu, and S. Han, “Three-dimensional ghost imaging ladar,” arXiv preprint arXiv:1301.5767 (2013).

Johnstone, I. M.

D. L. Donoho and I. M. Johnstone, “Adapting to unknown smoothness via wavelet shrinkage,” J. Am. Stat. Assoc. 90, 1200–1224 (1995).
[CrossRef]

Katz, O.

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

Kolobov, M. I.

Li, E.

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, C. Zhao, J. Jiao, E. Li, M. Chen, H. Wang, W. Xu, and S. Han, “Three-dimensional ghost imaging ladar,” arXiv preprint arXiv:1301.5767 (2013).

Lin, L.

D. Cao, J. Xiong, S. Zhang, L. Lin, L. Gao, and K. Wang, “Enhancing visibility and resolution in Nth-order intensity correlation of thermal light,” Appl. Phys. Lett. 92, 201102 (2008).
[CrossRef]

Liu, H.

Lugiato, L.

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A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L. Lugiato, “Coherent imaging with pseudo-thermal incoherent light,” J. Mod. Opt. 53, 739–760 (2006).
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D. L. Donoho, A. Maleki, and A. Montanari, “Message-passing algorithms for compressed sensing,” Proc. Natl. Acad. Sci. 106, 18914–18919 (2009).
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Mallat, S.

S. Mallat, A Wavelet Tour of Signal Processing (Access Online via Elsevier, 1999).

Montanari, A.

D. L. Donoho, A. Maleki, and A. Montanari, “Message-passing algorithms for compressed sensing,” Proc. Natl. Acad. Sci. 106, 18914–18919 (2009).
[CrossRef] [PubMed]

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M. J. Fadili, J. L. Starck, J. Bobin, and Y. Moudden, “Image decomposition and separation using sparse representations: An overview,” Proc. IEEE 98, 983–994 (2010).
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J. Bobin, J. L. Starck, J. M. Fadili, Y. Moudden, and D. L. Donoho, “Morphological component analysis: An adaptive thresholding strategy,” IEEE Trans. Image Process. 16, 2675–2681 (2007).
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N. Ahmed, T. Natarajan, and K. R. Rao, “Discrete cosine transform,” IEEE Trans. Comput. 100, 90–93 (1974).
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M. A. Figueiredo, R. D. Nowak, and S. J. Wright, “Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems,” IEEE J. Sel. Top. Sign. Proces. 1, 586–597 (2007).
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N. Ahmed, T. Natarajan, and K. R. Rao, “Discrete cosine transform,” IEEE Trans. Comput. 100, 90–93 (1974).
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J. H. Shapiro and R. W. Boyd, “The physics of ghost imaging,” Quantum Inf. Process. 11, 949–993 (2012).
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P. Zhang, W. Gong, X. Shen, S. Han, and R. Shu, “Homodyne detection in ghost imaging with thermal light,” Phys. Rev. A 80, 033827 (2009).
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M. D’Angelo and Y. Shih, “Quantum imaging,” Laser Phys. Lett. 2, 567–596 (2005).
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P. Zhang, W. Gong, X. Shen, S. Han, and R. Shu, “Homodyne detection in ghost imaging with thermal light,” Phys. Rev. A 80, 033827 (2009).
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O. Katz, Y. Bromberg, and Y. Silberberg, “Compressive ghost imaging,” Appl. Phys. Lett. 95, 131110 (2009).
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M. J. Fadili, J. L. Starck, J. Bobin, and Y. Moudden, “Image decomposition and separation using sparse representations: An overview,” Proc. IEEE 98, 983–994 (2010).
[CrossRef]

J. Bobin, J. L. Starck, J. M. Fadili, Y. Moudden, and D. L. Donoho, “Morphological component analysis: An adaptive thresholding strategy,” IEEE Trans. Image Process. 16, 2675–2681 (2007).
[CrossRef] [PubMed]

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J. A. Tropp and A. C. Gilbert, “Signal recovery from random measurements via orthogonal matching pursuit,” IEEE Trans. Inf. Theory 53, 4655–4666 (2007).
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H. Wang and S. Han, “Coherent ghost imaging based on sparsity constraint without phase-sensitive detection,” Europhys. Lett. 98, 24003 (2012).
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D. Cao, J. Xiong, S. Zhang, L. Lin, L. Gao, and K. Wang, “Enhancing visibility and resolution in Nth-order intensity correlation of thermal light,” Appl. Phys. Lett. 92, 201102 (2008).
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M. A. Figueiredo, R. D. Nowak, and S. J. Wright, “Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems,” IEEE J. Sel. Top. Sign. Proces. 1, 586–597 (2007).
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D. Cao, J. Xiong, S. Zhang, L. Lin, L. Gao, and K. Wang, “Enhancing visibility and resolution in Nth-order intensity correlation of thermal light,” Appl. Phys. Lett. 92, 201102 (2008).
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D. Cao, J. Xiong, and K. Wang, “Geometrical optics in correlated imaging systems,” Phys. Rev. A 71, 013801 (2005).
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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).
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W. Gong, C. Zhao, J. Jiao, E. Li, M. Chen, H. Wang, W. Xu, and S. Han, “Three-dimensional ghost imaging ladar,” arXiv preprint arXiv:1301.5767 (2013).

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E. Candes, L. Demanet, D. Donoho, and L. Ying, “Fast discrete curvelet transforms,” Multiscale Model. Simul. 5, 861–899 (2006).
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P. Zerom, K. W. C. Chan, J. C. Howell, and R. W. Boyd, “Entangled-photon compressive ghost imaging,” Phys. Rev. A 84, 061804 (2011).
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Zhang, D.

Zhang, P.

P. Zhang, W. Gong, X. Shen, D. Huang, and S. Han, “Improving resolution by the second-order correlation of light fields,” Opt. Lett. 34, 1222–1224 (2009).
[CrossRef] [PubMed]

P. Zhang, W. Gong, X. Shen, S. Han, and R. Shu, “Homodyne detection in ghost imaging with thermal light,” Phys. Rev. A 80, 033827 (2009).
[CrossRef]

Zhang, S.

D. Cao, J. Xiong, S. Zhang, L. Lin, L. Gao, and K. Wang, “Enhancing visibility and resolution in Nth-order intensity correlation of thermal light,” Appl. Phys. Lett. 92, 201102 (2008).
[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]

W. Gong, C. Zhao, J. Jiao, E. Li, M. Chen, H. Wang, W. Xu, and S. Han, “Three-dimensional ghost imaging ladar,” arXiv preprint arXiv:1301.5767 (2013).

Appl. Phys. Lett.

D. Cao, J. Xiong, S. Zhang, L. Lin, L. Gao, and K. Wang, “Enhancing visibility and resolution in Nth-order intensity correlation of thermal light,” Appl. Phys. Lett. 92, 201102 (2008).
[CrossRef]

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

Electron. Lett.

X. Qu, X. Cao, D. Guo, C. Hu, and Z. Chen, “Combined sparsifying transforms for compressed sensing MRI,” Electron. Lett. 46, 121–123 (2010).
[CrossRef]

Europhys. Lett.

H. Wang and S. Han, “Coherent ghost imaging based on sparsity constraint without phase-sensitive detection,” Europhys. Lett. 98, 24003 (2012).
[CrossRef]

IEEE J. Sel. Top. Sign. Proces.

M. A. Figueiredo, R. D. Nowak, and S. J. Wright, “Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems,” IEEE J. Sel. Top. Sign. Proces. 1, 586–597 (2007).
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IEEE Trans. Image Process.

J. Bobin, J. L. Starck, J. M. Fadili, Y. Moudden, and D. L. Donoho, “Morphological component analysis: An adaptive thresholding strategy,” IEEE Trans. Image Process. 16, 2675–2681 (2007).
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IEEE Trans. Inf. Theory

D. L. Donoho and X. Huo, “Uncertainty principles and ideal atomic d ecomposition,” IEEE Trans. Inf. Theory 47, 2845–2862 (2001).
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A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L. Lugiato, “Coherent imaging with pseudo-thermal incoherent light,” J. Mod. Opt. 53, 739–760 (2006).
[CrossRef]

Laser Phys. Lett.

M. D’Angelo and Y. Shih, “Quantum imaging,” Laser Phys. Lett. 2, 567–596 (2005).
[CrossRef]

Multiscale Model. Simul.

E. Candes, L. Demanet, D. Donoho, and L. Ying, “Fast discrete curvelet transforms,” Multiscale Model. Simul. 5, 861–899 (2006).
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Opt. Express

Opt. Lett.

Phys. Lett. A

W. Gong and S. Han, “Experimental investigation of the quality of lensless super-resolution ghost imaging via sparsity constraints,” Phys. Lett. A 376, 1519–1522 (2012).
[CrossRef]

Phys. Rev. A

P. Zhang, W. Gong, X. Shen, S. Han, and R. Shu, “Homodyne detection in ghost imaging with thermal light,” Phys. Rev. A 80, 033827 (2009).
[CrossRef]

M. Bache, E. Brambilla, A. Gatti, and L. Lugiato, “Ghost imaging using homodyne detection,” Phys. Rev. A 70, 023823 (2004).
[CrossRef]

D. Cao, J. Xiong, and K. Wang, “Geometrical optics in correlated imaging systems,” Phys. Rev. A 71, 013801 (2005).
[CrossRef]

P. Zerom, K. W. C. Chan, J. C. Howell, and R. W. Boyd, “Entangled-photon compressive ghost imaging,” Phys. Rev. A 84, 061804 (2011).
[CrossRef]

Y. Bai and S. Han, “Ghost imaging with thermal light by third-order correlation,” Phys. Rev. A 76, 043828 (2007).
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Proc. IEEE

M. J. Fadili, J. L. Starck, J. Bobin, and Y. Moudden, “Image decomposition and separation using sparse representations: An overview,” Proc. IEEE 98, 983–994 (2010).
[CrossRef]

Proc. Natl. Acad. Sci.

D. L. Donoho, A. Maleki, and A. Montanari, “Message-passing algorithms for compressed sensing,” Proc. Natl. Acad. Sci. 106, 18914–18919 (2009).
[CrossRef] [PubMed]

Quantum Inf. Process.

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

Other

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S. Chen and D. Donoho, “Basis pursuit,” in “Signals, Systems and Computers, 1994. 1994 Conference Record of the Twenty-Eighth Asilomar Conference on,” (IEEE, 1994), vol. 1, pp. 41–44.

W. Gong, C. Zhao, J. Jiao, E. Li, M. Chen, H. Wang, W. Xu, and S. Han, “Three-dimensional ghost imaging ladar,” arXiv preprint arXiv:1301.5767 (2013).

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Figures (6)

Fig. 1
Fig. 1

The experimental setup of ghost imaging via sparsity constraint(GISC).

Fig. 2
Fig. 2

The object and simulation results. (a) the object of 64 × 64 pixels used in the simulation; (b–e) simulation results with SNR=16dB,19dB,22dB,25dB respectively. The first row shows the GPSR reconstruction results, the third row the separated “point” component, the fourth row the separated “line” component and the second row the combination of the two separated components.

Fig. 3
Fig. 3

The RMSE values of the reconstructed images using MCA in GISC and GISC without MCA. (a)The RMSE values of results from data with different SNR. (b)The RMSE values of the results reconstructed from different numbers of sampling.

Fig. 4
Fig. 4

The experimental results of ghost imaging via sparse constraint. (a) the target object; (b–f) experimental results with K = 800, 1200, 1600, 2000 respectively. The first row shows the GPSR reconstructed results, the third row the “point” component, the forth row the “line” component and the second row the combination of the two separated components.

Fig. 5
Fig. 5

The RMSE with different number of samplings in the experiment. The blue line is the RMSE of GISC and the red one is the RMSE of sum of the separated components when MCA is used in GISC.

Fig. 6
Fig. 6

The results of a natural scene. (a) the original scene captured with a telescope; (b) the result of GISC; (c) the “point” component; (d) the “line” component; (e) the combination of the two components. The first to third row of (b–e) is just three of these different slices and last row is the sum of all slices.

Equations (2)

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

Y = A X + ε = A Ψ θ + ε ,
X = Ψ 1 θ 1 + Ψ 2 θ 2 ; which minimizes : 1 2 Y AX 2 2 + τ ( θ 1 1 + θ 2 1 ) .

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