Abstract

The computational ghost imaging with a phase spatial light modulator (SLM) for wave field coding is considered. A transmission-mask amplitude object is reconstructed from multiple intensity observations. Compressive techniques are used in order to gain a successful image reconstruction with a number of observations (measurement experiments), which is smaller than the image size. Maximum likelihood style algorithms are developed, respectively, for Poissonian and approximate Gaussian modeling of random observations. A sparse and overcomplete modeling of the object enables the advanced high accuracy and sharp imaging. Numerical experiments demonstrate that an approximative Gaussian distribution with an invariant variance results in the algorithm that is efficient for Poissonian observations.

© 2012 Optical Society of America

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References

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  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, R3429–R3432 (1995).
    [CrossRef]
  2. A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Correlated imaging, quantum and classical,” Phys. Rev. A 70, 013802 (2004).
    [CrossRef]
  3. Y. Cai and S.-Y. Zhu, “Ghost imaging with incoherent and partially coherent light radiation,” Phys. Rev. E 71, 056607 (2005).
    [CrossRef]
  4. L. Basano and P. Ottonello, “A conceptual experiment on single-beam coincidence detection with pseudothermal light,” Opt. Express 19, 12386–12394 (2009).
  5. B. I. Erkmen and J. H. Shapiro, “Unified theory of ghost imaging with Gaussian-state light,” Phys. Rev. A 77, 043809 (2008).
    [CrossRef]
  6. B. I. Erkmen and J. H. Shapiro, “Ghost imaging: from quantum to classical to computational,” Adv. Opt. Photon. 2, 405–450 (2010).
    [CrossRef]
  7. Y. Shih, “The physics of ghost imaging,” in Advances in Lasers and Electro Optics, N. Costa and A. Cartaxo, eds. (InTech, 2010), pp. 549–594.
  8. J. H. Shapiro, “Computational ghost imaging,” Phys. Rev. A 78, 061802(R) (2008).
  9. Y. Bromberg, O. Katz, and Y. Silberberg, “Ghost imaging with a single detector,” Phys. Rev. A 79, 053840 (2009).
    [CrossRef]
  10. O. Katz, Y. Bromberg, and Y. Silberberg, “Compressive ghost imaging,” Appl. Phys. Lett. 95, 131110 (2009).
    [CrossRef]
  11. L. Jiying, Z. Jubo, L. Chuan, and H. Shisheng, “High-quality quantum-imaging algorithm and experiment based on compressive sensing,” Optics Lett. 35, 1206–1208 (2010).
    [CrossRef]
  12. E. J. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52, 489–509 (2006).
    [CrossRef]
  13. D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52, 1289–1306 (2006).
    [CrossRef]
  14. S. Gazit, A. Szameit, Y. C. Eldar, and M. Segev, “Super-resolution and reconstruction of sparse sub-wavelength images,” Opt. Express 17, 23920–23946 (2009).
    [CrossRef]
  15. R. Willett, R. Marcia, and J. Nichols, “Compressed sensing for practical optical systems: a tutorial,” Opt. Eng. 50, 072601 1–13 (2011).
    [CrossRef]
  16. K. W. C. Chan, M. N. O’Sullivan, and R. W. Boyd, “Optimization of thermal ghost imaging: high-order correlations vs. background subtraction,” Opt. Express 18, 5562–5573 (2010).
    [CrossRef]
  17. A. Danielyan, V. Katkovnik, and K. Egiazarian, “BM3D frames and variational image deblurring,” IEEE Trans. Image Process. 21, 1715–1728 (2012).
    [CrossRef]
  18. V. Katkovnik and J. Astola, “High-accuracy wave field reconstruction: decoupled inverse imaging with sparse modeling of phase and amplitude,” J. Opt. Soc. Am. A 29, 44–54(2012).
    [CrossRef]
  19. K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, “Image denoising by sparse 3D transform-domain collaborative filtering,” IEEE Trans. Image Process. 16, 2080–2095 (2007).
    [CrossRef]
  20. M. Figueiredo and J. Bioucas-Dias, “Restoration of Poissonian images using alternating direction optimization,” IEEE Trans. Image Process. 19, 3133–3145 (2010).
    [CrossRef]
  21. Z. Harmany, R. Marcia, and R. Willett, “This is SPIRAL-TAP: sparse Poisson intensity reconstruction algorithms—theory and practice,” IEEE Trans. Image Process. 21, 1084–1096 (2012).
    [CrossRef]
  22. M. Raginsky, R. Willett, Z. Harmany, and R. Marcia, “Compressed sensing performance bounds under Poisson noise,” IEEE Trans. Signal Process. 58, 3990–4002 (2010).
    [CrossRef]
  23. V. Katkovnik, J. Astola, and K. Egiazarian, “Discrete diffraction transform for propagation, reconstruction, and design of wave field distributions,” Appl. Opt. 47, 3481–3493 (2008).
    [CrossRef]
  24. A. Papoulis, Probability, Random Variables, and Stochastic Processes (McGraw-Hill, 1991).
  25. M. Elad, Sparse and Redundant Representations: From Theory to Applications in Signal and Image Processing (Springer2010).
  26. D. Han, K. Kornelson, D. Larson, and E. Weber, Frames for Undergraduates (Student Mathematical Library, AMS, 2007).
  27. D. P. Bertsekas, Nonlinear Programming, 2nd ed. (Athena Scientific, 1999).
  28. J. W. Goodman, Speckle Phenomena in Optics (Ben Roberts, 2007).

2012

A. Danielyan, V. Katkovnik, and K. Egiazarian, “BM3D frames and variational image deblurring,” IEEE Trans. Image Process. 21, 1715–1728 (2012).
[CrossRef]

Z. Harmany, R. Marcia, and R. Willett, “This is SPIRAL-TAP: sparse Poisson intensity reconstruction algorithms—theory and practice,” IEEE Trans. Image Process. 21, 1084–1096 (2012).
[CrossRef]

V. Katkovnik and J. Astola, “High-accuracy wave field reconstruction: decoupled inverse imaging with sparse modeling of phase and amplitude,” J. Opt. Soc. Am. A 29, 44–54(2012).
[CrossRef]

2011

R. Willett, R. Marcia, and J. Nichols, “Compressed sensing for practical optical systems: a tutorial,” Opt. Eng. 50, 072601 1–13 (2011).
[CrossRef]

2010

M. Raginsky, R. Willett, Z. Harmany, and R. Marcia, “Compressed sensing performance bounds under Poisson noise,” IEEE Trans. Signal Process. 58, 3990–4002 (2010).
[CrossRef]

M. Figueiredo and J. Bioucas-Dias, “Restoration of Poissonian images using alternating direction optimization,” IEEE Trans. Image Process. 19, 3133–3145 (2010).
[CrossRef]

L. Jiying, Z. Jubo, L. Chuan, and H. Shisheng, “High-quality quantum-imaging algorithm and experiment based on compressive sensing,” Optics Lett. 35, 1206–1208 (2010).
[CrossRef]

K. W. C. Chan, M. N. O’Sullivan, and R. W. Boyd, “Optimization of thermal ghost imaging: high-order correlations vs. background subtraction,” Opt. Express 18, 5562–5573 (2010).
[CrossRef]

B. I. Erkmen and J. H. Shapiro, “Ghost imaging: from quantum to classical to computational,” Adv. Opt. Photon. 2, 405–450 (2010).
[CrossRef]

2009

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]

L. Basano and P. Ottonello, “A conceptual experiment on single-beam coincidence detection with pseudothermal light,” Opt. Express 19, 12386–12394 (2009).

S. Gazit, A. Szameit, Y. C. Eldar, and M. Segev, “Super-resolution and reconstruction of sparse sub-wavelength images,” Opt. Express 17, 23920–23946 (2009).
[CrossRef]

2008

V. Katkovnik, J. Astola, and K. Egiazarian, “Discrete diffraction transform for propagation, reconstruction, and design of wave field distributions,” Appl. Opt. 47, 3481–3493 (2008).
[CrossRef]

B. I. Erkmen and J. H. Shapiro, “Unified theory of ghost imaging with Gaussian-state light,” Phys. Rev. A 77, 043809 (2008).
[CrossRef]

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

2007

K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, “Image denoising by sparse 3D transform-domain collaborative filtering,” IEEE Trans. Image Process. 16, 2080–2095 (2007).
[CrossRef]

2006

E. J. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52, 489–509 (2006).
[CrossRef]

D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52, 1289–1306 (2006).
[CrossRef]

2005

Y. Cai and S.-Y. Zhu, “Ghost imaging with incoherent and partially coherent light radiation,” Phys. Rev. E 71, 056607 (2005).
[CrossRef]

2004

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

1995

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, R3429–R3432 (1995).
[CrossRef]

Astola, J.

Bache, M.

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

Basano, L.

L. Basano and P. Ottonello, “A conceptual experiment on single-beam coincidence detection with pseudothermal light,” Opt. Express 19, 12386–12394 (2009).

Bertsekas, D. P.

D. P. Bertsekas, Nonlinear Programming, 2nd ed. (Athena Scientific, 1999).

Bioucas-Dias, J.

M. Figueiredo and J. Bioucas-Dias, “Restoration of Poissonian images using alternating direction optimization,” IEEE Trans. Image Process. 19, 3133–3145 (2010).
[CrossRef]

Boyd, R. W.

Brambilla, E.

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

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]

Cai, Y.

Y. Cai and S.-Y. Zhu, “Ghost imaging with incoherent and partially coherent light radiation,” Phys. Rev. E 71, 056607 (2005).
[CrossRef]

Candès, E. J.

E. J. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52, 489–509 (2006).
[CrossRef]

Chan, K. W. C.

Chuan, L.

L. Jiying, Z. Jubo, L. Chuan, and H. Shisheng, “High-quality quantum-imaging algorithm and experiment based on compressive sensing,” Optics Lett. 35, 1206–1208 (2010).
[CrossRef]

Dabov, K.

K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, “Image denoising by sparse 3D transform-domain collaborative filtering,” IEEE Trans. Image Process. 16, 2080–2095 (2007).
[CrossRef]

Danielyan, A.

A. Danielyan, V. Katkovnik, and K. Egiazarian, “BM3D frames and variational image deblurring,” IEEE Trans. Image Process. 21, 1715–1728 (2012).
[CrossRef]

Donoho, D. L.

D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52, 1289–1306 (2006).
[CrossRef]

Egiazarian, K.

A. Danielyan, V. Katkovnik, and K. Egiazarian, “BM3D frames and variational image deblurring,” IEEE Trans. Image Process. 21, 1715–1728 (2012).
[CrossRef]

V. Katkovnik, J. Astola, and K. Egiazarian, “Discrete diffraction transform for propagation, reconstruction, and design of wave field distributions,” Appl. Opt. 47, 3481–3493 (2008).
[CrossRef]

K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, “Image denoising by sparse 3D transform-domain collaborative filtering,” IEEE Trans. Image Process. 16, 2080–2095 (2007).
[CrossRef]

Elad, M.

M. Elad, Sparse and Redundant Representations: From Theory to Applications in Signal and Image Processing (Springer2010).

Eldar, Y. C.

Erkmen, B. I.

B. I. Erkmen and J. H. Shapiro, “Ghost imaging: from quantum to classical to computational,” Adv. Opt. Photon. 2, 405–450 (2010).
[CrossRef]

B. I. Erkmen and J. H. Shapiro, “Unified theory of ghost imaging with Gaussian-state light,” Phys. Rev. A 77, 043809 (2008).
[CrossRef]

Figueiredo, M.

M. Figueiredo and J. Bioucas-Dias, “Restoration of Poissonian images using alternating direction optimization,” IEEE Trans. Image Process. 19, 3133–3145 (2010).
[CrossRef]

Foi, A.

K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, “Image denoising by sparse 3D transform-domain collaborative filtering,” IEEE Trans. Image Process. 16, 2080–2095 (2007).
[CrossRef]

Gatti, A.

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

Gazit, S.

Goodman, J. W.

J. W. Goodman, Speckle Phenomena in Optics (Ben Roberts, 2007).

Han, D.

D. Han, K. Kornelson, D. Larson, and E. Weber, Frames for Undergraduates (Student Mathematical Library, AMS, 2007).

Harmany, Z.

Z. Harmany, R. Marcia, and R. Willett, “This is SPIRAL-TAP: sparse Poisson intensity reconstruction algorithms—theory and practice,” IEEE Trans. Image Process. 21, 1084–1096 (2012).
[CrossRef]

M. Raginsky, R. Willett, Z. Harmany, and R. Marcia, “Compressed sensing performance bounds under Poisson noise,” IEEE Trans. Signal Process. 58, 3990–4002 (2010).
[CrossRef]

Jiying, L.

L. Jiying, Z. Jubo, L. Chuan, and H. Shisheng, “High-quality quantum-imaging algorithm and experiment based on compressive sensing,” Optics Lett. 35, 1206–1208 (2010).
[CrossRef]

Jubo, Z.

L. Jiying, Z. Jubo, L. Chuan, and H. Shisheng, “High-quality quantum-imaging algorithm and experiment based on compressive sensing,” Optics Lett. 35, 1206–1208 (2010).
[CrossRef]

Katkovnik, V.

V. Katkovnik and J. Astola, “High-accuracy wave field reconstruction: decoupled inverse imaging with sparse modeling of phase and amplitude,” J. Opt. Soc. Am. A 29, 44–54(2012).
[CrossRef]

A. Danielyan, V. Katkovnik, and K. Egiazarian, “BM3D frames and variational image deblurring,” IEEE Trans. Image Process. 21, 1715–1728 (2012).
[CrossRef]

V. Katkovnik, J. Astola, and K. Egiazarian, “Discrete diffraction transform for propagation, reconstruction, and design of wave field distributions,” Appl. Opt. 47, 3481–3493 (2008).
[CrossRef]

K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, “Image denoising by sparse 3D transform-domain collaborative filtering,” IEEE Trans. Image Process. 16, 2080–2095 (2007).
[CrossRef]

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]

Kornelson, K.

D. Han, K. Kornelson, D. Larson, and E. Weber, Frames for Undergraduates (Student Mathematical Library, AMS, 2007).

Larson, D.

D. Han, K. Kornelson, D. Larson, and E. Weber, Frames for Undergraduates (Student Mathematical Library, AMS, 2007).

Lugiato, L. A.

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

Marcia, R.

Z. Harmany, R. Marcia, and R. Willett, “This is SPIRAL-TAP: sparse Poisson intensity reconstruction algorithms—theory and practice,” IEEE Trans. Image Process. 21, 1084–1096 (2012).
[CrossRef]

R. Willett, R. Marcia, and J. Nichols, “Compressed sensing for practical optical systems: a tutorial,” Opt. Eng. 50, 072601 1–13 (2011).
[CrossRef]

M. Raginsky, R. Willett, Z. Harmany, and R. Marcia, “Compressed sensing performance bounds under Poisson noise,” IEEE Trans. Signal Process. 58, 3990–4002 (2010).
[CrossRef]

Nichols, J.

R. Willett, R. Marcia, and J. Nichols, “Compressed sensing for practical optical systems: a tutorial,” Opt. Eng. 50, 072601 1–13 (2011).
[CrossRef]

O’Sullivan, M. N.

Ottonello, P.

L. Basano and P. Ottonello, “A conceptual experiment on single-beam coincidence detection with pseudothermal light,” Opt. Express 19, 12386–12394 (2009).

Papoulis, A.

A. Papoulis, Probability, Random Variables, and Stochastic Processes (McGraw-Hill, 1991).

Pittman, T. B.

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, R3429–R3432 (1995).
[CrossRef]

Raginsky, M.

M. Raginsky, R. Willett, Z. Harmany, and R. Marcia, “Compressed sensing performance bounds under Poisson noise,” IEEE Trans. Signal Process. 58, 3990–4002 (2010).
[CrossRef]

Romberg, J.

E. J. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52, 489–509 (2006).
[CrossRef]

Segev, M.

Sergienko, A. V.

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, R3429–R3432 (1995).
[CrossRef]

Shapiro, J. H.

B. I. Erkmen and J. H. Shapiro, “Ghost imaging: from quantum to classical to computational,” Adv. Opt. Photon. 2, 405–450 (2010).
[CrossRef]

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

B. I. Erkmen and J. H. Shapiro, “Unified theory of ghost imaging with Gaussian-state light,” Phys. Rev. A 77, 043809 (2008).
[CrossRef]

Shih, Y.

Y. Shih, “The physics of ghost imaging,” in Advances in Lasers and Electro Optics, N. Costa and A. Cartaxo, eds. (InTech, 2010), pp. 549–594.

Shih, Y. H.

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, R3429–R3432 (1995).
[CrossRef]

Shisheng, H.

L. Jiying, Z. Jubo, L. Chuan, and H. Shisheng, “High-quality quantum-imaging algorithm and experiment based on compressive sensing,” Optics Lett. 35, 1206–1208 (2010).
[CrossRef]

Silberberg, Y.

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

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

Strekalov, D. V.

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, R3429–R3432 (1995).
[CrossRef]

Szameit, A.

Tao, T.

E. J. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52, 489–509 (2006).
[CrossRef]

Weber, E.

D. Han, K. Kornelson, D. Larson, and E. Weber, Frames for Undergraduates (Student Mathematical Library, AMS, 2007).

Willett, R.

Z. Harmany, R. Marcia, and R. Willett, “This is SPIRAL-TAP: sparse Poisson intensity reconstruction algorithms—theory and practice,” IEEE Trans. Image Process. 21, 1084–1096 (2012).
[CrossRef]

R. Willett, R. Marcia, and J. Nichols, “Compressed sensing for practical optical systems: a tutorial,” Opt. Eng. 50, 072601 1–13 (2011).
[CrossRef]

M. Raginsky, R. Willett, Z. Harmany, and R. Marcia, “Compressed sensing performance bounds under Poisson noise,” IEEE Trans. Signal Process. 58, 3990–4002 (2010).
[CrossRef]

Zhu, S.-Y.

Y. Cai and S.-Y. Zhu, “Ghost imaging with incoherent and partially coherent light radiation,” Phys. Rev. E 71, 056607 (2005).
[CrossRef]

Adv. Opt. Photon.

Appl. Opt.

Appl. Phys. Lett.

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

IEEE Trans. Image Process.

A. Danielyan, V. Katkovnik, and K. Egiazarian, “BM3D frames and variational image deblurring,” IEEE Trans. Image Process. 21, 1715–1728 (2012).
[CrossRef]

K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, “Image denoising by sparse 3D transform-domain collaborative filtering,” IEEE Trans. Image Process. 16, 2080–2095 (2007).
[CrossRef]

M. Figueiredo and J. Bioucas-Dias, “Restoration of Poissonian images using alternating direction optimization,” IEEE Trans. Image Process. 19, 3133–3145 (2010).
[CrossRef]

Z. Harmany, R. Marcia, and R. Willett, “This is SPIRAL-TAP: sparse Poisson intensity reconstruction algorithms—theory and practice,” IEEE Trans. Image Process. 21, 1084–1096 (2012).
[CrossRef]

IEEE Trans. Inf. Theory

E. J. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52, 489–509 (2006).
[CrossRef]

D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52, 1289–1306 (2006).
[CrossRef]

IEEE Trans. Signal Process.

M. Raginsky, R. Willett, Z. Harmany, and R. Marcia, “Compressed sensing performance bounds under Poisson noise,” IEEE Trans. Signal Process. 58, 3990–4002 (2010).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Eng.

R. Willett, R. Marcia, and J. Nichols, “Compressed sensing for practical optical systems: a tutorial,” Opt. Eng. 50, 072601 1–13 (2011).
[CrossRef]

Opt. Express

Optics Lett.

L. Jiying, Z. Jubo, L. Chuan, and H. Shisheng, “High-quality quantum-imaging algorithm and experiment based on compressive sensing,” Optics Lett. 35, 1206–1208 (2010).
[CrossRef]

Phys. Rev. A

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

Y. Bromberg, O. Katz, and Y. Silberberg, “Ghost imaging with a single detector,” Phys. Rev. A 79, 053840 (2009).
[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, R3429–R3432 (1995).
[CrossRef]

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

B. I. Erkmen and J. H. Shapiro, “Unified theory of ghost imaging with Gaussian-state light,” Phys. Rev. A 77, 043809 (2008).
[CrossRef]

Phys. Rev. E

Y. Cai and S.-Y. Zhu, “Ghost imaging with incoherent and partially coherent light radiation,” Phys. Rev. E 71, 056607 (2005).
[CrossRef]

Other

A. Papoulis, Probability, Random Variables, and Stochastic Processes (McGraw-Hill, 1991).

M. Elad, Sparse and Redundant Representations: From Theory to Applications in Signal and Image Processing (Springer2010).

D. Han, K. Kornelson, D. Larson, and E. Weber, Frames for Undergraduates (Student Mathematical Library, AMS, 2007).

D. P. Bertsekas, Nonlinear Programming, 2nd ed. (Athena Scientific, 1999).

J. W. Goodman, Speckle Phenomena in Optics (Ben Roberts, 2007).

Y. Shih, “The physics of ghost imaging,” in Advances in Lasers and Electro Optics, N. Costa and A. Cartaxo, eds. (InTech, 2010), pp. 549–594.

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Figures (7)

Fig. 1.
Fig. 1.

Two-arm SLM GI setup.

Fig. 2.
Fig. 2.

Single-arm computational GI setup.

Fig. 3.
Fig. 3.

TUT test-image, μ=4, d=5df, χ=106. First row from left to right: CS-GIinv reconstruction and true image; second row from left to right: cross-sections of the true image (solid, red in color) and the reconstruction (dash, blue in color), and PSNR versus the number of iterations.

Fig. 4.
Fig. 4.

TUT test-image, μ=8, d=5df, χ=106. First row from left to right: CS-GIinv reconstruction and true image; second row from left to right: cross-sections of the true image (solid, red in color) and the reconstruction (dash, blue in color), and PSNR versus the number of iterations.

Fig. 5.
Fig. 5.

Fragment of cameraman test-image, μ=2, d=df, χ=104. First row: CS-GIinv reconstruction and true image; second row: cross-sections of the true image (solid, red in color) and the reconstruction (dash, blue in color), and PSNR versus the number of iterations.

Fig. 6.
Fig. 6.

Cross-correlation reconstruction of the TUT test-image, d=3df, χ=106: reconstruction and PSNR versus the number of experiments K. In the cross-section, the true image is shown by a solid line (red in color) and the reconstruction by a dashed line (blue in color).

Fig. 7.
Fig. 7.

Cross-correlation reconstruction of the Cameraman test-image, d=df, χ=104: reconstruction and PSNR versus the number of experiments K. In the cross-section, the true image is shown by a solid line (red in color) and the reconstruction by a dashed line (blue in color).

Tables (3)

Tables Icon

Table 1. Object Transparency (TUT Test-Image) Reconstruction (PSNR Values) for Various Distances of the Free-Space Wave Field Propagation d and Compression Ratios μ, χ=102

Tables Icon

Table 2. Object Transparency (TUT Test-Image) Reconstruction (PSNR Values) for Various Distances of the Free-Space Wave Field Propagation d and Compressive Sampling Ratios μ, χ=104

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Table 3. Object Transparency (TUT Test-Image) Reconstruction (PSNR Values) for Various Distances of the Free-Space Wave Field Propagation d and Compressive Sampling Ratios μ, χ=106

Equations (48)

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or=k=1n|uo[k]|2·|ur[k]|2=brTc,r=1,,K.
|u^o[k]|2=1Kr=1K(oro¯)|ur[k]|2.
o˜r=Poisson{brTcχ},
or=Poisson{brTcχ}/χ.
or=brTc+σrεr,r=1,,K,
σr2=brTc/χ,
or=brTc+σεr,r=1,,K,
σ2=bTc/χ,
σ^2=1Kr=1Kor/χ.
c=Ψθ,
θ=Φc.
JG=L({or}1K,c)+τ·Φcp,
σ2=bTc/χ,
c^=argmincJG,orc^=argminc0JG.
L1(c,θ)=L({or}1K,c)+12γ0cΨθ22,σ2=bTc/χ,
L2(c,θ)=τ·θp+12θΦc22.
ct+1=argminc0L1(c,θt),
θt+1=argminθL2(ct+1,θ).
c*=argminc0L1(c,θ*),θ*=argminθL2(c*,θ).
ct+1/2=argmincL1(c,θt),ct+1=P+{ct+1/2},
θt+1=argminθL2(ct+1,θ),
L1(c,θ)=12σ2r=1K(orcTbr)2+12γ0cΨθ22,
1σ2r=1K(orcTbr)br+1γ0(cΨθ)=0.
c=Ψθ+γ0/σ2r=1K(or(cTbr))br
r=1K(1σ2bkTbr+δk,rγ0)xr=r=1K1σ2orbkTbr+1γ0bkTΨθ,k=1,,K.
(1σ2BTB+1γ0IK×K)·x=1σ2BTB·o+1γ0BTΨθ,
c=Ψθ+γ0σ2B(ox).
θ=Thτ(Φc)={Th2τhard(Φc)=Φc1(|Φc|2τ),ifp=0,Thτsoft(Φc)=sign(Φc)max(|Φc|τ,0),ifp=1,
vt+1=ct+1.
Mr[k1,k2]=exp(j2πφr[k1,k2]),1k1N1,1k2N2,
|u^o[k]|2=1Kr=1K(oro¯K)(brb¯K),
b¯K=1Kr=1Kbr,o¯K=1Kr=1Kor.
E{|u^o|2}=DKc,DK=E{1Kr=1K(brb¯K)(brb¯K)T}.
|u^o[k]|2=D^K+·1Kr=1K(oro¯K)(brb¯K),D^K=1Kr=1K(brb¯K)(brb¯K)T.
r=1K1σr2(orcTbr)br+r=1K[1σr2(orcTbr)2+1](12brTcbr)+1γ0(cΨθ)=0.
r=1K1σr2(orcTbr)br+1γ0(cΨθ)=0.
(BTBD+1γ0IK×K)·x=BTBD·o+1γ0BTΨθ,D=diag{1σ12,,1σK2},
c=Ψθ+γ0BD(ox).
L({or}1K,c)=r=1K(o˜rlogb˜rTa+b˜rTa),
L1(c,θ)=r=1K(o˜rlogb˜rTc+b˜rTc)+12γ˜0cΨθ22,
L2(c,θ)=τ·θ0+12θΦc22.
L1(c,θ)/c=r=1K(o˜r1b˜rTcb˜r+b˜r)+1γ˜0(cΨθ)=0.
b˜kTL1(c,θ)/c=r=1K(1o˜r1b˜rTc)b˜kTb˜r+1γ˜0(b˜kTcb˜kTΨθ)=0,k=1,,K.
B˜TB˜(o˜./x˜)1γ˜0x˜=B˜TB˜1K×11γ˜0B˜TΨθ,
c=Ψθ+γ˜0(B˜(o˜./x˜)B˜1K×1).
B˜=Bχ,x˜=xχ,b˜=brχ,o˜=oχ,γ0=γ˜0χ.
BTB(o./x)1γ0x=BTB1K×11γ0BTΨθ,
c=Ψθ+γ0(B·(o./x)B1K×1),

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