Abstract

A structured image reconstruction method has been proposed to obtain high quality images in three-dimensional ghost imaging lidar. By considering the spatial structure relationship between recovered images of scene slices at different longitudinal distances, orthogonality constraint has been incorporated to reconstruct the three-dimensional scenes in remote sensing. Numerical simulations have been performed to demonstrate that scene slices with various sparse ratios can be recovered more accurately by applying orthogonality constraint, and the enhancement is significant especially for ghost imaging with less measurements. A simulated three-dimensional city scene has been successfully reconstructed by using structured image reconstruction in three-dimensional ghost imaging lidar.

© 2015 Optical Society of America

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References

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    [Crossref]

2015 (1)

2014 (3)

2013 (4)

M. Bina, D. Magatti, M. Molteni, A. Gatti, L. A. Lugiato, and F. Ferri, “Backscattering differential ghost imaging in turbid media,” Phys. Rev. Lett. 110(8), 083901 (2013).
[Crossref] [PubMed]

N. D. Hardy and J. H. Shapiro, “Computational ghost imaging versus imaging laser radar for three-dimensional imaging,” Phys. Rev. A 87(2), 023820 (2013).
[Crossref]

D. Shi, C. Fan, P. Zhang, H. Shen, J. Zhang, C. Qiao, and Y. Wang, “Two-wavelength ghost imaging through atmospheric turbulence,” Opt. Express 21(2), 2050–2064 (2013).
[Crossref] [PubMed]

W. Gong, Z. Bo, E. Li, and S. Han, “Experimental investigation of the quality of ghost imaging via sparsity constraints,” Appl. Opt. 52(15), 3510–3515 (2013).
[Crossref] [PubMed]

2012 (8)

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

M. E. Davies and Y. C. Eldar, “Rank awareness in joint sparse recovery,” IEEE Trans. Inf. Theory 58(2), 1135–1146 (2012).
[Crossref]

B. I. Erkmen, “Computational ghost imaging for remote sensing,” J. Opt. Soc. Am. A 29(5), 782–789 (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(21), 23235–23252 (2012).
[Crossref] [PubMed]

H. Wang and S. Han, “Coherent ghost imaging based on sparsity constraint without phase-sensitive detection,” Europhys. Lett. 98(2), 24003 (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(17), 1519–1522 (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(6), 1067–1069 (2012).
[Crossref] [PubMed]

W. Gong and S. Han, “Multiple-input ghost imaging via sparsity constraints,” J. Opt. Soc. Am. A 29(8), 1571–1579 (2012).
[Crossref] [PubMed]

2011 (4)

E. Meyers, K. S. Deacon, and Y. Shih, “Turbulence free ghost imaging,” Appl. Phys. Lett. 98(11), 111115 (2011).
[Crossref]

P. Zerom, K. W. C. Chan, J. C. Howell, and R. W. Boyd, “Entangled-photon compressive ghost imaging,” Phys. Rev. A 84(6), 061804 (2011).
[Crossref]

A. Kirmani, A. Colaço, F. N. C. Wong, and V. K. Goyal, “Exploiting sparsity in time-of-flight range acquisition using a single time-resolved sensor,” Opt. Express 19(22), 21485–21507 (2011).
[Crossref] [PubMed]

M. F. Duarte and Y. C. Eldar, “Structured compressed sensing: from theory to applications,” IEEE Trans. Signal Process. 59(9), 4053–4085 (2011).
[Crossref]

2010 (2)

R. G. Baraniuk, V. Cevher, M. F. Duarte, and C. Hegde, “Model-based compressive sensing,” IEEE Trans. Inf. Theory 56(4), 1982–2001 (2010).
[Crossref]

P. Zhang, W. Gong, X. Shen, and S. Han, “Correlated imaging through atmospheric turbulence,” Phys. Rev. A 82(3), 033817 (2010).
[Crossref]

2009 (5)

J. Cheng, “Ghost imaging through turbulent atmosphere,” Opt. Express 17(10), 7916–7921 (2009).
[Crossref] [PubMed]

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

S. Gazit, A. Szameit, Y. C. Eldar, and M. Segev, “Super-resolution and reconstruction of sparse sub-wavelength images,” Opt. Express 17(26), 23920–23946 (2009).
[Crossref] [PubMed]

A. Beck and M. Teboulle, “A fast iterative shrinkage-thresholding algorithm for linear inverse problems,” SIAM J. Imaging Sci. 2(1), 183–202 (2009).
[Crossref]

Y. C. Eldar and M. Mishali, “Robust recovery of signals from a structured union of subspaces,” IEEE Trans. Inf. Theory 55(11), 5302–5316 (2009).
[Crossref]

2007 (1)

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(11), 2675–2681 (2007).
[Crossref] [PubMed]

2006 (2)

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

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

2005 (1)

S. F. Cotter, B. D. Rao, K. Engan, and K. Kreutz-Delgado, “Sparse solutions to linear inverse problems with multiple measurement vectors,” IEEE Trans. Signal Process. 53(7), 2477–2488 (2005).
[Crossref]

2004 (1)

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

Baraniuk, R. G.

R. G. Baraniuk, V. Cevher, M. F. Duarte, and C. Hegde, “Model-based compressive sensing,” IEEE Trans. Inf. Theory 56(4), 1982–2001 (2010).
[Crossref]

Beck, A.

A. Beck and M. Teboulle, “A fast iterative shrinkage-thresholding algorithm for linear inverse problems,” SIAM J. Imaging Sci. 2(1), 183–202 (2009).
[Crossref]

Bina, M.

M. Bina, D. Magatti, M. Molteni, A. Gatti, L. A. Lugiato, and F. Ferri, “Backscattering differential ghost imaging in turbid media,” Phys. Rev. Lett. 110(8), 083901 (2013).
[Crossref] [PubMed]

Bo, Z.

Bobin, J.

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(11), 2675–2681 (2007).
[Crossref] [PubMed]

Boyd, R. W.

P. Zerom, K. W. C. Chan, J. C. Howell, and R. W. Boyd, “Entangled-photon compressive ghost imaging,” Phys. Rev. A 84(6), 061804 (2011).
[Crossref]

Bromberg, Y.

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

Candes, E. J.

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

Cevher, V.

R. G. Baraniuk, V. Cevher, M. F. Duarte, and C. Hegde, “Model-based compressive sensing,” IEEE Trans. Inf. Theory 56(4), 1982–2001 (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(6), 061804 (2011).
[Crossref]

Chen, M.

M. Chen, E. Li, and S. Han, “Application of multi-correlation-scale measurement matrices in ghost imaging via sparsity constraints,” Appl. Opt. 53(13), 2924–2928 (2014).
[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(14), 141123 (2012).
[Crossref]

Cheng, J.

J. Cheng, “Ghost imaging through turbulent atmosphere,” Opt. Express 17(10), 7916–7921 (2009).
[Crossref] [PubMed]

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

Colaço, A.

Cotter, S. F.

S. F. Cotter, B. D. Rao, K. Engan, and K. Kreutz-Delgado, “Sparse solutions to linear inverse problems with multiple measurement vectors,” IEEE Trans. Signal Process. 53(7), 2477–2488 (2005).
[Crossref]

Davies, M. E.

M. E. Davies and Y. C. Eldar, “Rank awareness in joint sparse recovery,” IEEE Trans. Inf. Theory 58(2), 1135–1146 (2012).
[Crossref]

Deacon, K. S.

E. Meyers, K. S. Deacon, and Y. Shih, “Turbulence free ghost imaging,” Appl. Phys. Lett. 98(11), 111115 (2011).
[Crossref]

Donoho, D. L.

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(11), 2675–2681 (2007).
[Crossref] [PubMed]

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

Du, J.

Duarte, M. F.

M. F. Duarte and Y. C. Eldar, “Structured compressed sensing: from theory to applications,” IEEE Trans. Signal Process. 59(9), 4053–4085 (2011).
[Crossref]

R. G. Baraniuk, V. Cevher, M. F. Duarte, and C. Hegde, “Model-based compressive sensing,” IEEE Trans. Inf. Theory 56(4), 1982–2001 (2010).
[Crossref]

Eldar, Y. C.

M. E. Davies and Y. C. Eldar, “Rank awareness in joint sparse recovery,” IEEE Trans. Inf. Theory 58(2), 1135–1146 (2012).
[Crossref]

M. F. Duarte and Y. C. Eldar, “Structured compressed sensing: from theory to applications,” IEEE Trans. Signal Process. 59(9), 4053–4085 (2011).
[Crossref]

Y. C. Eldar and M. Mishali, “Robust recovery of signals from a structured union of subspaces,” IEEE Trans. Inf. Theory 55(11), 5302–5316 (2009).
[Crossref]

S. Gazit, A. Szameit, Y. C. Eldar, and M. Segev, “Super-resolution and reconstruction of sparse sub-wavelength images,” Opt. Express 17(26), 23920–23946 (2009).
[Crossref] [PubMed]

Engan, K.

S. F. Cotter, B. D. Rao, K. Engan, and K. Kreutz-Delgado, “Sparse solutions to linear inverse problems with multiple measurement vectors,” IEEE Trans. Signal Process. 53(7), 2477–2488 (2005).
[Crossref]

Erkmen, B. I.

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(11), 2675–2681 (2007).
[Crossref] [PubMed]

Fan, C.

Ferri, F.

M. Bina, D. Magatti, M. Molteni, A. Gatti, L. A. Lugiato, and F. Ferri, “Backscattering differential ghost imaging in turbid media,” Phys. Rev. Lett. 110(8), 083901 (2013).
[Crossref] [PubMed]

Gatti, A.

M. Bina, D. Magatti, M. Molteni, A. Gatti, L. A. Lugiato, and F. Ferri, “Backscattering differential ghost imaging in turbid media,” Phys. Rev. Lett. 110(8), 083901 (2013).
[Crossref] [PubMed]

Gazit, S.

Gong, W.

X. Xu, E. Li, H. Yu, W. Gong, and S. Han, “Morphology separation in ghost imaging via sparsity constraint,” Opt. Express 22(12), 14375–14381 (2014).
[Crossref] [PubMed]

W. Gong, Z. Bo, E. Li, and S. Han, “Experimental investigation of the quality of ghost imaging via sparsity constraints,” Appl. Opt. 52(15), 3510–3515 (2013).
[Crossref] [PubMed]

W. Gong and S. Han, “Multiple-input ghost imaging via sparsity constraints,” J. Opt. Soc. Am. A 29(8), 1571–1579 (2012).
[Crossref] [PubMed]

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

W. Gong and 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]

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

P. Zhang, W. Gong, X. Shen, and S. Han, “Correlated imaging through atmospheric turbulence,” Phys. Rev. A 82(3), 033817 (2010).
[Crossref]

Goyal, V. K.

Han, S.

X. Xu, E. Li, H. Yu, W. Gong, and S. Han, “Morphology separation in ghost imaging via sparsity constraint,” Opt. Express 22(12), 14375–14381 (2014).
[Crossref] [PubMed]

M. Chen, E. Li, and S. Han, “Application of multi-correlation-scale measurement matrices in ghost imaging via sparsity constraints,” Appl. Opt. 53(13), 2924–2928 (2014).
[Crossref] [PubMed]

W. Gong, Z. Bo, E. Li, and S. Han, “Experimental investigation of the quality of ghost imaging via sparsity constraints,” Appl. Opt. 52(15), 3510–3515 (2013).
[Crossref] [PubMed]

W. Gong and S. Han, “Multiple-input ghost imaging via sparsity constraints,” J. Opt. Soc. Am. A 29(8), 1571–1579 (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(21), 23235–23252 (2012).
[Crossref] [PubMed]

J. Du, W. Gong, and S. Han, “The influence of sparsity property of images on ghost imaging with thermal light,” Opt. Lett. 37(6), 1067–1069 (2012).
[Crossref] [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(14), 141123 (2012).
[Crossref]

H. Wang and S. Han, “Coherent ghost imaging based on sparsity constraint without phase-sensitive detection,” Europhys. Lett. 98(2), 24003 (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(17), 1519–1522 (2012).
[Crossref]

P. Zhang, W. Gong, X. Shen, and S. Han, “Correlated imaging through atmospheric turbulence,” Phys. Rev. A 82(3), 033817 (2010).
[Crossref]

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

Hardy, N. D.

N. D. Hardy and J. H. Shapiro, “Computational ghost imaging versus imaging laser radar for three-dimensional imaging,” Phys. Rev. A 87(2), 023820 (2013).
[Crossref]

Hegde, C.

R. G. Baraniuk, V. Cevher, M. F. Duarte, and C. Hegde, “Model-based compressive sensing,” IEEE Trans. Inf. Theory 56(4), 1982–2001 (2010).
[Crossref]

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(6), 061804 (2011).
[Crossref]

Katz, O.

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

Kirmani, A.

Kolobov, M. I.

Kreutz-Delgado, K.

S. F. Cotter, B. D. Rao, K. Engan, and K. Kreutz-Delgado, “Sparse solutions to linear inverse problems with multiple measurement vectors,” IEEE Trans. Signal Process. 53(7), 2477–2488 (2005).
[Crossref]

Li, E.

Li, L.-Z.

Li, M. F.

Liu, X. F.

Liu, X.-F.

Lugiato, L. A.

M. Bina, D. Magatti, M. Molteni, A. Gatti, L. A. Lugiato, and F. Ferri, “Backscattering differential ghost imaging in turbid media,” Phys. Rev. Lett. 110(8), 083901 (2013).
[Crossref] [PubMed]

Magatti, D.

M. Bina, D. Magatti, M. Molteni, A. Gatti, L. A. Lugiato, and F. Ferri, “Backscattering differential ghost imaging in turbid media,” Phys. Rev. Lett. 110(8), 083901 (2013).
[Crossref] [PubMed]

Meyers, E.

E. Meyers, K. S. Deacon, and Y. Shih, “Turbulence free ghost imaging,” Appl. Phys. Lett. 98(11), 111115 (2011).
[Crossref]

Mishali, M.

Y. C. Eldar and M. Mishali, “Robust recovery of signals from a structured union of subspaces,” IEEE Trans. Inf. Theory 55(11), 5302–5316 (2009).
[Crossref]

Molteni, M.

M. Bina, D. Magatti, M. Molteni, A. Gatti, L. A. Lugiato, and F. Ferri, “Backscattering differential ghost imaging in turbid media,” Phys. Rev. Lett. 110(8), 083901 (2013).
[Crossref] [PubMed]

Moudden, Y.

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(11), 2675–2681 (2007).
[Crossref] [PubMed]

Qiao, C.

Rao, B. D.

S. F. Cotter, B. D. Rao, K. Engan, and K. Kreutz-Delgado, “Sparse solutions to linear inverse problems with multiple measurement vectors,” IEEE Trans. Signal Process. 53(7), 2477–2488 (2005).
[Crossref]

Romberg, J.

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

Segev, M.

Shapiro, J. H.

N. D. Hardy and J. H. Shapiro, “Computational ghost imaging versus imaging laser radar for three-dimensional imaging,” Phys. Rev. A 87(2), 023820 (2013).
[Crossref]

Shen, H.

Shen, X.

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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(11), 2675–2681 (2007).
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E. J. Candes, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52(2), 489–509 (2006).
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Teboulle, M.

A. Beck and M. Teboulle, “A fast iterative shrinkage-thresholding algorithm for linear inverse problems,” SIAM J. Imaging Sci. 2(1), 183–202 (2009).
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H. Wang and S. Han, “Coherent ghost imaging based on sparsity constraint without phase-sensitive detection,” Europhys. Lett. 98(2), 24003 (2012).
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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(14), 141123 (2012).
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H. Wang, S. Han, and M. I. Kolobov, “Quantum limits of super-resolution of optical sparse objects via sparsity constraint,” Opt. Express 20(21), 23235–23252 (2012).
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Appl. Opt. (3)

Appl. Phys. Lett. (3)

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

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

E. Meyers, K. S. Deacon, and Y. Shih, “Turbulence free ghost imaging,” Appl. Phys. Lett. 98(11), 111115 (2011).
[Crossref]

Europhys. Lett. (1)

H. Wang and S. Han, “Coherent ghost imaging based on sparsity constraint without phase-sensitive detection,” Europhys. Lett. 98(2), 24003 (2012).
[Crossref]

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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(11), 2675–2681 (2007).
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M. F. Duarte and Y. C. Eldar, “Structured compressed sensing: from theory to applications,” IEEE Trans. Signal Process. 59(9), 4053–4085 (2011).
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W. Gong and S. Han, “Experimental investigation of the quality of lensless super-resolution ghost imaging via sparsity constraints,” Phys. Lett. A 376(17), 1519–1522 (2012).
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N. D. Hardy and J. H. Shapiro, “Computational ghost imaging versus imaging laser radar for three-dimensional imaging,” Phys. Rev. A 87(2), 023820 (2013).
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P. Zhang, W. Gong, X. Shen, and S. Han, “Correlated imaging through atmospheric turbulence,” Phys. Rev. A 82(3), 033817 (2010).
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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(6), 061804 (2011).
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Phys. Rev. Lett. (2)

M. Bina, D. Magatti, M. Molteni, A. Gatti, L. A. Lugiato, and F. Ferri, “Backscattering differential ghost imaging in turbid media,” Phys. Rev. Lett. 110(8), 083901 (2013).
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J. Cheng and S. Han, “Incoherent coincidence imaging and its applicability in x-ray diffraction,” Phys. Rev. Lett. 92(9), 093903 (2004).
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SIAM J. Imaging Sci. (1)

A. Beck and M. Teboulle, “A fast iterative shrinkage-thresholding algorithm for linear inverse problems,” SIAM J. Imaging Sci. 2(1), 183–202 (2009).
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Other (2)

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).

W. Gong and S. Han, “Super-resolution ghost imaging via compressive sampling reconstruction,” arXiv preprint arXiv: 0910.4823v1 (2009).

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Figures (7)

Fig. 1
Fig. 1 Schematics for 3D GISC. GG is a rotating ground glass, and BS is a beam splitter.
Fig. 2
Fig. 2 Illustration for the orthogonality constraint in 3D GISC.
Fig. 3
Fig. 3 Simulation results of image reconstruction in 3D GISC. (a) is the four scene slices with sparse ratios 0.086, 0.173, 0.259, and 0.346 from left to right, (b)-(d) are the reconstructed results without structure considering, (e)-(g) are the results of structured reconstruction using orthogonality constraint. (b)(e), (c)(f), and (d)(g) are the results of 1000, 500, 200 measurements, respectively.
Fig. 4
Fig. 4 Coherence between any two different recovered images of the four scene slices. (a) is the average coherence curves, (b) is the max coherence curves.
Fig. 5
Fig. 5 MSE of the recovered images of the four scene slices. (a)-(c) are the MSE curves of iteration number, measurement number, and SNR, respectively. The red, blue, black and green lines are the results of slices with sparse ratios 0.086, 0.173, 0.259, and 0.346, respectively.
Fig. 6
Fig. 6 Reconstructed results of a simulated city scene in 3D GISC. (a) and (b) are the original 3D scene and some of its characteristic slices, (c) and (d) are the results of structured reconstruction, (c) is the simulated aerial photography results of 3D GISC lidar, (d) is the reconstructed 3D scene, (e) and (f) are the slice results of structured reconstruction and standard reconstruction.
Fig. 7
Fig. 7 MSE3D of the reconstructed three-dimensional city scene. (a) is the MSE3D curves of measurement number, (b) is the MSE3D curves of slice amount.

Equations (13)

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X ^ =[ x ^ 1 ,, x ^ i ,, x ^ K ]=argmin 1 2 y i A x i 2 2 + τ i θ i 1 ,1iK.
μ( x i , x j )= < x i , x j > < x i , x i > < x j , x j > ,ji.
μ(X)=maxμ( x i , x j )=max < x i , x j > < x i , x i > < x j , x j > ,1jiK.
Y=AXs.t.μ(X)=0.
Y =AXH+Es.t.μ(X)=0.
H=[ h 0 0 0 h 0 0 0 h ].
μ ( X )= 2 K ( K 1) i j < x i , x j > < x i , x i > < x j , x j > ,1j<i K .
Y =A X +Es.t. μ ( X )δ.
X ^ =[ x ^ 1 ,, x ^ i ,, x ^ K ]=argmin 1 2 y i A x i 2 2 + τ i θ i 1 + τ c μ ( X ),1i K .
X ^ =[ x ^ p ,, x ^ i ,, x ^ q ]=argmin 1 2 y i A x i 2 2 + τ i θ i 1 + τ c μ ( X ),piq.
f( X )= 1 2 y i A x i 2 2 + τ c μ ( X ),g( X )= τ i θ i 1 ,piq.
P( X )= (| x i | τ i L ) + sgn( x i ),piq.
X k =P( Z k 1 L f( Z k )), t k+1 = 1+ 1+4 t k 2 2 , Z k+1 = X k + t k 1 t k+1 ( X k X k1 ).

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