Abstract

Compressed sensing is a theory which can reconstruct an image almost perfectly with only a few measurements by finding its sparsest representation. However, the computation time consumed for large images may be a few hours or more. In this work, we both theoretically and experimentally demonstrate a method that combines the advantages of both adaptive computational ghost imaging and compressed sensing, which we call adaptive compressive ghost imaging, whereby both the reconstruction time and measurements required for any image size can be significantly reduced. The technique can be used to improve the performance of all computational ghost imaging protocols, especially when measuring ultra-weak or noisy signals, and can be extended to imaging applications at any wavelength.

© 2014 Optical Society of America

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2013 (4)

2012 (3)

A. Averbuch, S. Dekel, S. Deutsch, “Adaptive compressed image sensing using dictionaries,” SIAM J. Imaging Sci. 5(1), 57–89 (2012).
[CrossRef]

W. L. Gong, S. S. Han, “Experimental investigation of the quality of lensless super-resolution ghost imaging via sparsity constraints,” Phys. Lett. A 376(17), 1519–1522 (2012).
[CrossRef]

N. B. Karahanoglu, H. Erdogan, “A* orthogonal matching pursuit: best-first search for compressed sensing signal recovery,” Digit. Sig. Process. 22(4), 555–568 (2012).
[CrossRef]

2010 (1)

J. Yang, Y. Zhang, W. Yin, “A fast alternating direction method for TVL1-L2 signal reconstruction from partial Fourier data,” IEEE J. Sel. Top. Signal Processing 4(2), 288–297 (2010).
[CrossRef]

2009 (3)

P. Sen, S. Darabi, “Compressive dual photography,” Computer Graphics Forum 28(2), 609–618 (2009).
[CrossRef]

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

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

2008 (5)

M. Fornasier, H. Rauhut, “Iterative thresholding algorithms,” Appl. Comput. Harmon. Anal. 25(2), 187–208 (2008).
[CrossRef]

B. I. Erkmen, J. H. Shapiro, “Unified theory of ghost imaging with Gaussian-state light,” Phys. Rev. A 77(4), 043809 (2008).
[CrossRef]

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

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Proc. Mag. 25(2), 83–91 (2008).
[CrossRef]

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93(12), 121105 (2008).
[CrossRef]

2006 (2)

E. J. Candès, J. Romberg, T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52(2), 489–509 (2006).
[CrossRef]

D. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006).
[CrossRef]

2005 (1)

2004 (1)

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

2000 (1)

S. G. Chang, B. Yu, M. Vetterli, “Adaptive wavelet thresholding for image denoising and compression,” IEEE Trans. Image Process. 9(9), 1532–1546 (2000).
[CrossRef]

1998 (1)

S. S. Chen, D. L. Donoho, M. A. Saunders, “Atomic decomposition by basis pursuit,” SIAM J. Sci. Comput. 20(1), 33–61 (1998).
[CrossRef]

1996 (1)

A. Said, W. Pearlman, “A new, fast, and efficient image codec based on set partitioning in hierarchical trees,” IEEE Trans. Circ. Syst. Video Technol. 6(3), 243–250 (1996).
[CrossRef]

1995 (1)

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, Y. H. Shih, “Observation of two-photon “ghost” interference and diffraction,” Phys. Rev. Lett. 74, 3600–3603 (1995).
[CrossRef] [PubMed]

1993 (1)

J. Shapiro, “Embedded image coding using zerotrees of wavelet coefficients,” IEEE Trans. Signal Proces. 41(12), 3445–3462 (1993).
[CrossRef]

1989 (1)

S. Mallat, “A theory for multiresolution signal decomposition: the wavelet representation,” IEEE Trans. Pattern Anal. 11(7), 674–693 (1989).
[CrossRef]

Aßmann, M.

M. Aßmann, M. Bayer, “Compressive adaptive computational ghost imaging,” Sci. Rep. 3, 1545 (2013).

Averbuch, A.

A. Averbuch, S. Dekel, S. Deutsch, “Adaptive compressed image sensing using dictionaries,” SIAM J. Imaging Sci. 5(1), 57–89 (2012).
[CrossRef]

Bache, M.

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

Baraniuk, R. G.

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93(12), 121105 (2008).
[CrossRef]

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Proc. Mag. 25(2), 83–91 (2008).
[CrossRef]

Bayer, M.

M. Aßmann, M. Bayer, “Compressive adaptive computational ghost imaging,” Sci. Rep. 3, 1545 (2013).

Berinde, R.

R. Berinde, P. Indyk, “Sequential sparse matching pursuit,” in Proc. 47th Annu. Allerton Conf. Commun. Control Comput., (2009), 36–43.

Bobin, J.

V. Studer, J. Bobin, M. Chahid, H. Moussavi, E. J. Candès, M. Dahan, “Compressive fluorescence microscopy for biological and hyperspectral imaging,” in Proceedings of the National Academy of Sciences, (2012), 109(26), E1679–E1687.

Brambilla, E.

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

Bromberg, Y.

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

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

Candès, E. J.

E. J. Candès, J. Romberg, T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52(2), 489–509 (2006).
[CrossRef]

V. Studer, J. Bobin, M. Chahid, H. Moussavi, E. J. Candès, M. Dahan, “Compressive fluorescence microscopy for biological and hyperspectral imaging,” in Proceedings of the National Academy of Sciences, (2012), 109(26), E1679–E1687.

E. J. Candès, “Compressive sampling,” in Proc. Int. Cong. Math, (European Mathematical Society, Madrid, Spain, 2006), 3, pp. 1433–1452.

Castro, R.

J. Haupt, R. Nowak, R. Castro, “Adaptive sensing for sparse signal recovery,” in Proceedings of the 2009 IEEE Digital Signal Processing Workshop and 5th IEEE Signal Processing Education Workshop, (Marco Island, FL, Jan., 2009), 702–707.

Chahid, M.

V. Studer, J. Bobin, M. Chahid, H. Moussavi, E. J. Candès, M. Dahan, “Compressive fluorescence microscopy for biological and hyperspectral imaging,” in Proceedings of the National Academy of Sciences, (2012), 109(26), E1679–E1687.

Chan, W. L.

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93(12), 121105 (2008).
[CrossRef]

Chang, S. G.

S. G. Chang, B. Yu, M. Vetterli, “Adaptive wavelet thresholding for image denoising and compression,” IEEE Trans. Image Process. 9(9), 1532–1546 (2000).
[CrossRef]

Charan, K.

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93(12), 121105 (2008).
[CrossRef]

Chen, S. S.

S. S. Chen, D. L. Donoho, M. A. Saunders, “Atomic decomposition by basis pursuit,” SIAM J. Sci. Comput. 20(1), 33–61 (1998).
[CrossRef]

Chen, X. H.

Dahan, M.

V. Studer, J. Bobin, M. Chahid, H. Moussavi, E. J. Candès, M. Dahan, “Compressive fluorescence microscopy for biological and hyperspectral imaging,” in Proceedings of the National Academy of Sciences, (2012), 109(26), E1679–E1687.

Darabi, S.

P. Sen, S. Darabi, “Compressive dual photography,” Computer Graphics Forum 28(2), 609–618 (2009).
[CrossRef]

Davenport, M. A.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Proc. Mag. 25(2), 83–91 (2008).
[CrossRef]

Dekel, S.

A. Averbuch, S. Dekel, S. Deutsch, “Adaptive compressed image sensing using dictionaries,” SIAM J. Imaging Sci. 5(1), 57–89 (2012).
[CrossRef]

Deutsch, S.

A. Averbuch, S. Dekel, S. Deutsch, “Adaptive compressed image sensing using dictionaries,” SIAM J. Imaging Sci. 5(1), 57–89 (2012).
[CrossRef]

Donoho, D.

D. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006).
[CrossRef]

Donoho, D. L.

S. S. Chen, D. L. Donoho, M. A. Saunders, “Atomic decomposition by basis pursuit,” SIAM J. Sci. Comput. 20(1), 33–61 (1998).
[CrossRef]

Duarte, M. F.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Proc. Mag. 25(2), 83–91 (2008).
[CrossRef]

Erdogan, H.

N. B. Karahanoglu, H. Erdogan, “A* orthogonal matching pursuit: best-first search for compressed sensing signal recovery,” Digit. Sig. Process. 22(4), 555–568 (2012).
[CrossRef]

Erkmen, B. I.

B. I. Erkmen, J. H. Shapiro, “Unified theory of ghost imaging with Gaussian-state light,” Phys. Rev. A 77(4), 043809 (2008).
[CrossRef]

Fan, H.

M. F. Li, Y. R. Zhang, X. F. Liu, X. R. Yao, K. H. Luo, H. Fan, L. A. Wu, “A double-threshold technique for fast time-correspondence imaging,” Appl. Phys. Lett. 103, 211119 (2013).
[CrossRef]

Fornasier, M.

M. Fornasier, H. Rauhut, “Iterative thresholding algorithms,” Appl. Comput. Harmon. Anal. 25(2), 187–208 (2008).
[CrossRef]

Gatti, A.

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

Gong, W. L.

W. L. Gong, S. S. Han, “Experimental investigation of the quality of lensless super-resolution ghost imaging via sparsity constraints,” Phys. Lett. A 376(17), 1519–1522 (2012).
[CrossRef]

Han, S. S.

W. L. Gong, S. S. Han, “Experimental investigation of the quality of lensless super-resolution ghost imaging via sparsity constraints,” Phys. Lett. A 376(17), 1519–1522 (2012).
[CrossRef]

Haupt, J.

J. Haupt, R. Nowak, R. Castro, “Adaptive sensing for sparse signal recovery,” in Proceedings of the 2009 IEEE Digital Signal Processing Workshop and 5th IEEE Signal Processing Education Workshop, (Marco Island, FL, Jan., 2009), 702–707.

Indyk, P.

R. Berinde, P. Indyk, “Sequential sparse matching pursuit,” in Proc. 47th Annu. Allerton Conf. Commun. Control Comput., (2009), 36–43.

Karahanoglu, N. B.

N. B. Karahanoglu, H. Erdogan, “A* orthogonal matching pursuit: best-first search for compressed sensing signal recovery,” Digit. Sig. Process. 22(4), 555–568 (2012).
[CrossRef]

Katz, O.

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

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

Kelly, K. F.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Proc. Mag. 25(2), 83–91 (2008).
[CrossRef]

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93(12), 121105 (2008).
[CrossRef]

Klyshko, D. N.

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, Y. H. Shih, “Observation of two-photon “ghost” interference and diffraction,” Phys. Rev. Lett. 74, 3600–3603 (1995).
[CrossRef] [PubMed]

Laska, J. N.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Proc. Mag. 25(2), 83–91 (2008).
[CrossRef]

Li, C. B.

C. B. Li, “An efficient algorithm for total variation regularization with applications to the single pixel camera and compressive sensing,” Master Thesis, Rice University, (2010).

Li, M. F.

M. F. Li, Y. R. Zhang, X. F. Liu, X. R. Yao, K. H. Luo, H. Fan, L. A. Wu, “A double-threshold technique for fast time-correspondence imaging,” Appl. Phys. Lett. 103, 211119 (2013).
[CrossRef]

Li, S.

Liu, X. F.

W. K. Yu, S. Li, X. R. Yao, X. F. Liu, L. A. Wu, G. J. Zhai, “Protocol based on compressed sensing for high-speed authentication and cryptographic key distribution over a multiparty optical network,” Appl. Opt. 52(33), 7882–7888 (2013).
[CrossRef]

M. F. Li, Y. R. Zhang, X. F. Liu, X. R. Yao, K. H. Luo, H. Fan, L. A. Wu, “A double-threshold technique for fast time-correspondence imaging,” Appl. Phys. Lett. 103, 211119 (2013).
[CrossRef]

Lugiato, L. A.

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

Luo, K. H.

M. F. Li, Y. R. Zhang, X. F. Liu, X. R. Yao, K. H. Luo, H. Fan, L. A. Wu, “A double-threshold technique for fast time-correspondence imaging,” Appl. Phys. Lett. 103, 211119 (2013).
[CrossRef]

Mallat, S.

S. Mallat, “A theory for multiresolution signal decomposition: the wavelet representation,” IEEE Trans. Pattern Anal. 11(7), 674–693 (1989).
[CrossRef]

S. Mallat, A wavelet tour of signal processing, the sparse way (Elsevier, 2009), pp. 340–346.

Mittleman, D. M.

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93(12), 121105 (2008).
[CrossRef]

Moussavi, H.

V. Studer, J. Bobin, M. Chahid, H. Moussavi, E. J. Candès, M. Dahan, “Compressive fluorescence microscopy for biological and hyperspectral imaging,” in Proceedings of the National Academy of Sciences, (2012), 109(26), E1679–E1687.

Nowak, R.

J. Haupt, R. Nowak, R. Castro, “Adaptive sensing for sparse signal recovery,” in Proceedings of the 2009 IEEE Digital Signal Processing Workshop and 5th IEEE Signal Processing Education Workshop, (Marco Island, FL, Jan., 2009), 702–707.

Pearlman, W.

A. Said, W. Pearlman, “A new, fast, and efficient image codec based on set partitioning in hierarchical trees,” IEEE Trans. Circ. Syst. Video Technol. 6(3), 243–250 (1996).
[CrossRef]

Rauhut, H.

M. Fornasier, H. Rauhut, “Iterative thresholding algorithms,” Appl. Comput. Harmon. Anal. 25(2), 187–208 (2008).
[CrossRef]

Romberg, J.

E. J. Candès, J. Romberg, T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52(2), 489–509 (2006).
[CrossRef]

Said, A.

A. Said, W. Pearlman, “A new, fast, and efficient image codec based on set partitioning in hierarchical trees,” IEEE Trans. Circ. Syst. Video Technol. 6(3), 243–250 (1996).
[CrossRef]

Saunders, M. A.

S. S. Chen, D. L. Donoho, M. A. Saunders, “Atomic decomposition by basis pursuit,” SIAM J. Sci. Comput. 20(1), 33–61 (1998).
[CrossRef]

Sen, P.

P. Sen, S. Darabi, “Compressive dual photography,” Computer Graphics Forum 28(2), 609–618 (2009).
[CrossRef]

Sergienko, A. V.

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, Y. H. Shih, “Observation of two-photon “ghost” interference and diffraction,” Phys. Rev. Lett. 74, 3600–3603 (1995).
[CrossRef] [PubMed]

Shapiro, J.

J. Shapiro, “Embedded image coding using zerotrees of wavelet coefficients,” IEEE Trans. Signal Proces. 41(12), 3445–3462 (1993).
[CrossRef]

Shapiro, J. H.

B. I. Erkmen, J. H. Shapiro, “Unified theory of ghost imaging with Gaussian-state light,” Phys. Rev. A 77(4), 043809 (2008).
[CrossRef]

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

Shih, Y. H.

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, Y. H. Shih, “Observation of two-photon “ghost” interference and diffraction,” Phys. Rev. Lett. 74, 3600–3603 (1995).
[CrossRef] [PubMed]

Silberberg, Y.

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

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

Strekalov, D. V.

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, Y. H. Shih, “Observation of two-photon “ghost” interference and diffraction,” Phys. Rev. Lett. 74, 3600–3603 (1995).
[CrossRef] [PubMed]

Studer, V.

V. Studer, J. Bobin, M. Chahid, H. Moussavi, E. J. Candès, M. Dahan, “Compressive fluorescence microscopy for biological and hyperspectral imaging,” in Proceedings of the National Academy of Sciences, (2012), 109(26), E1679–E1687.

Sun, T.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Proc. Mag. 25(2), 83–91 (2008).
[CrossRef]

Takhar, D.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Proc. Mag. 25(2), 83–91 (2008).
[CrossRef]

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