Abstract

This paper describes a generalized framework for single-exposure acquisition of multi-dimensional scene information using integral imaging system based on compressive sensing. In the proposed system, a multi-dimensional scene containing a plurality of information such as 3D coordinates, spectral and polarimetric data is captured by integral imaging optics. The image sensor uses pixel-wise filtering elements arranged randomly. The multi-dimensional original object is reconstructed using an algorithm with a sparsity constraint. The proposed system is demonstrated with simulations and feasible optical experiments based on synthetic aperture integral imaging using multi-dimensional objects including 3D coordinates, spectral, and polarimetric information.

© 2013 Optical Society of America

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References

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2012 (3)

2011 (3)

R. Horisaki and J. Tanida, “Multidimensional TOMBO imaging and its applications,” in Proc. SPIE (2011),  8165, pp. 816516.
[Crossref]

Y. Rivenson and A. Stern, “Conditions for practicing compressive fresnel holography,” Opt. Lett. 36, 3365–3367 (2011).
[Crossref] [PubMed]

M. Cho, M. Daneshpanah, I. Moon, and B. Javidi, “Three-dimensional optical sensing and visualization using integral imaging,” Proc. IEEE 99, 556 –575 (2011).
[Crossref]

2010 (4)

2009 (2)

R. Horstmeyer, G. Euliss, R. Athale, and M. Levoy, “Flexible multimodal camera using a light field architecture,” in “Proc. ICCP09,” (2009), pp. 1–8.

M. DaneshPanah and B. Javidi, “Profilometry and optical slicing by passive three-dimensional imaging,” Opt. Lett. 34, 1105–1107 (2009).
[Crossref] [PubMed]

2008 (1)

E. J. Candes and M. B. Wakin, “An introduction to compressive sampling,” IEEE Sig. Processing Mag. 25, 21–30 (2008).
[Crossref]

2007 (4)

R. Baraniuk, “Compressive sensing,” IEEE Sig. Processing Mag. 24, 118–121 (2007).
[Crossref]

R. Horisaki, S. Irie, Y. Ogura, and J. Tanida, “Three-dimensional information acquisition using a compound imaging system,” Optical Review 14, 347–350 (2007).
[Crossref]

J. M. Bioucas-Dias and M. A. T. Figueiredo, “A new TwIST: Two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE Trans. Image Proc. 16, 2992–3004 (2007).
[Crossref]

T. Sato, T. Araki, Y. Sasaki, T. Tsuru, T. Tadokoro, and S. Kawakami, “Compact ellipsometer employing a static polarimeter module with arrayed polarizer and wave-plate elements,” Appl. Opt. 46, 4963–4967 (2007).
[Crossref] [PubMed]

2006 (5)

J. S. Tyo, D. L. Goldstein, D. B. Chenault, and J. A. Shaw, “Review of passive imaging polarimetry for remote sensing applications,” Appl. Opt. 45, 5453–5469 (2006).
[Crossref] [PubMed]

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

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

F. Okano, J. Arai, K. Mitani, and M. Okui, “Real-time integral imaging based on extremely high resolution video system,” Proc. IEEE 94, 490–501 (2006).
[Crossref]

B. Javidi, S.-H. Hong, and O. Matoba, “Multidimensional optical sensor and imaging system,” Appl. Opt. 45, 2986–2994 (2006).
[Crossref] [PubMed]

2004 (2)

1997 (1)

1993 (1)

M. Okutomi and T. Kanade, “A multiple-baseline stereo,” IEEE Trans. Pattern Anal. Mach. Intell. 15, 353–363 (1993).
[Crossref]

1992 (1)

L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Phys. D 60, 259–268 (1992).
[Crossref]

1988 (1)

1981 (1)

1968 (1)

1908 (1)

G. M. Lippmann, “La photographie integrale,” Comptes-Rendus Academie des Sciences 146, 446–451 (1908).

Alfano, R. R.

Arai, J.

F. Okano, J. Arai, K. Mitani, and M. Okui, “Real-time integral imaging based on extremely high resolution video system,” Proc. IEEE 94, 490–501 (2006).
[Crossref]

Araki, T.

Athale, R.

R. Horstmeyer, G. Euliss, R. Athale, and M. Levoy, “Flexible multimodal camera using a light field architecture,” in “Proc. ICCP09,” (2009), pp. 1–8.

Balber, S.

Baraniuk, R.

R. Baraniuk, “Compressive sensing,” IEEE Sig. Processing Mag. 24, 118–121 (2007).
[Crossref]

Barnard, R.

R. J. Plemmons, S. Prasad, S. Matthews, M. Mirotznik, R. Barnard, B. Gray, V. P. Pauca, T. C. Torgersen, J. van der Gracht, and G. Behrmann, “PERIODIC: Integrated computational array imaging technology,” in “Computational Optical Sensing and Imaging,” (2007), p. CMA1.

Behrmann, G.

R. J. Plemmons, S. Prasad, S. Matthews, M. Mirotznik, R. Barnard, B. Gray, V. P. Pauca, T. C. Torgersen, J. van der Gracht, and G. Behrmann, “PERIODIC: Integrated computational array imaging technology,” in “Computational Optical Sensing and Imaging,” (2007), p. CMA1.

Bioucas-Dias, J. M.

J. M. Bioucas-Dias and M. A. T. Figueiredo, “A new TwIST: Two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE Trans. Image Proc. 16, 2992–3004 (2007).
[Crossref]

Brady, D. J.

Burckhardt, C. B.

Candes, E.

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

Candes, E. J.

E. J. Candes and M. B. Wakin, “An introduction to compressive sampling,” IEEE Sig. Processing Mag. 25, 21–30 (2008).
[Crossref]

Chenault, D. B.

Cho, M.

M. Cho, M. Daneshpanah, I. Moon, and B. Javidi, “Three-dimensional optical sensing and visualization using integral imaging,” Proc. IEEE 99, 556 –575 (2011).
[Crossref]

Choi, K.

Daneshpanah, M.

M. Cho, M. Daneshpanah, I. Moon, and B. Javidi, “Three-dimensional optical sensing and visualization using integral imaging,” Proc. IEEE 99, 556 –575 (2011).
[Crossref]

M. DaneshPanah and B. Javidi, “Profilometry and optical slicing by passive three-dimensional imaging,” Opt. Lett. 34, 1105–1107 (2009).
[Crossref] [PubMed]

Davies, N.

Demos, S. G.

Donoho, D. L.

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

Eismann, M.

Euliss, G.

R. Horstmeyer, G. Euliss, R. Athale, and M. Levoy, “Flexible multimodal camera using a light field architecture,” in “Proc. ICCP09,” (2009), pp. 1–8.

Fatemi, E.

L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Phys. D 60, 259–268 (1992).
[Crossref]

Figueiredo, M. A. T.

J. M. Bioucas-Dias and M. A. T. Figueiredo, “A new TwIST: Two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE Trans. Image Proc. 16, 2992–3004 (2007).
[Crossref]

Goldstein, D. L.

Gray, B.

R. J. Plemmons, S. Prasad, S. Matthews, M. Mirotznik, R. Barnard, B. Gray, V. P. Pauca, T. C. Torgersen, J. van der Gracht, and G. Behrmann, “PERIODIC: Integrated computational array imaging technology,” in “Computational Optical Sensing and Imaging,” (2007), p. CMA1.

Hahn, J.

Hong, S.-H.

Horisaki, R.

Horstmeyer, R.

R. Horstmeyer, G. Euliss, R. Athale, and M. Levoy, “Flexible multimodal camera using a light field architecture,” in “Proc. ICCP09,” (2009), pp. 1–8.

Irie, S.

R. Horisaki, S. Irie, Y. Ogura, and J. Tanida, “Three-dimensional information acquisition using a compound imaging system,” Optical Review 14, 347–350 (2007).
[Crossref]

Jang, J.-S.

Javidi, B.

Kanade, T.

M. Okutomi and T. Kanade, “A multiple-baseline stereo,” IEEE Trans. Pattern Anal. Mach. Intell. 15, 353–363 (1993).
[Crossref]

Kawakami, S.

Kitamura, Y.

Levoy, M.

R. Horstmeyer, G. Euliss, R. Athale, and M. Levoy, “Flexible multimodal camera using a light field architecture,” in “Proc. ICCP09,” (2009), pp. 1–8.

Lim, S.

Lippmann, G. M.

G. M. Lippmann, “La photographie integrale,” Comptes-Rendus Academie des Sciences 146, 446–451 (1908).

Marks, D. L.

Martinez-Corral, M.

Matoba, O.

Matthews, S.

R. J. Plemmons, S. Prasad, S. Matthews, M. Mirotznik, R. Barnard, B. Gray, V. P. Pauca, T. C. Torgersen, J. van der Gracht, and G. Behrmann, “PERIODIC: Integrated computational array imaging technology,” in “Computational Optical Sensing and Imaging,” (2007), p. CMA1.

McCormick, M.

Mirotznik, M.

R. J. Plemmons, S. Prasad, S. Matthews, M. Mirotznik, R. Barnard, B. Gray, V. P. Pauca, T. C. Torgersen, J. van der Gracht, and G. Behrmann, “PERIODIC: Integrated computational array imaging technology,” in “Computational Optical Sensing and Imaging,” (2007), p. CMA1.

Mitani, K.

F. Okano, J. Arai, K. Mitani, and M. Okui, “Real-time integral imaging based on extremely high resolution video system,” Proc. IEEE 94, 490–501 (2006).
[Crossref]

Miyatake, S.

Moon, I.

M. Cho, M. Daneshpanah, I. Moon, and B. Javidi, “Three-dimensional optical sensing and visualization using integral imaging,” Proc. IEEE 99, 556 –575 (2011).
[Crossref]

Ogura, Y.

R. Horisaki, S. Irie, Y. Ogura, and J. Tanida, “Three-dimensional information acquisition using a compound imaging system,” Optical Review 14, 347–350 (2007).
[Crossref]

Okano, F.

F. Okano, J. Arai, K. Mitani, and M. Okui, “Real-time integral imaging based on extremely high resolution video system,” Proc. IEEE 94, 490–501 (2006).
[Crossref]

Okui, M.

F. Okano, J. Arai, K. Mitani, and M. Okui, “Real-time integral imaging based on extremely high resolution video system,” Proc. IEEE 94, 490–501 (2006).
[Crossref]

Okutomi, M.

M. Okutomi and T. Kanade, “A multiple-baseline stereo,” IEEE Trans. Pattern Anal. Mach. Intell. 15, 353–363 (1993).
[Crossref]

Osher, S.

L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Phys. D 60, 259–268 (1992).
[Crossref]

Pauca, V. P.

R. J. Plemmons, S. Prasad, S. Matthews, M. Mirotznik, R. Barnard, B. Gray, V. P. Pauca, T. C. Torgersen, J. van der Gracht, and G. Behrmann, “PERIODIC: Integrated computational array imaging technology,” in “Computational Optical Sensing and Imaging,” (2007), p. CMA1.

Plemmons, R. J.

R. J. Plemmons, S. Prasad, S. Matthews, M. Mirotznik, R. Barnard, B. Gray, V. P. Pauca, T. C. Torgersen, J. van der Gracht, and G. Behrmann, “PERIODIC: Integrated computational array imaging technology,” in “Computational Optical Sensing and Imaging,” (2007), p. CMA1.

Prasad, S.

R. J. Plemmons, S. Prasad, S. Matthews, M. Mirotznik, R. Barnard, B. Gray, V. P. Pauca, T. C. Torgersen, J. van der Gracht, and G. Behrmann, “PERIODIC: Integrated computational array imaging technology,” in “Computational Optical Sensing and Imaging,” (2007), p. CMA1.

Rivenson, Y.

Romberg, J.

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

Rosen, J.

Rot, A.

Rudin, L. I.

L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Phys. D 60, 259–268 (1992).
[Crossref]

Saavedra, G.

Sasaki, Y.

Sato, T.

Schulz, T. J.

Shaw, J. A.

Shogenji, R.

Solomon, J. E.

Stern, A.

Tadokoro, T.

Tanida, J.

Tao, T.

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

Torgersen, T. C.

R. J. Plemmons, S. Prasad, S. Matthews, M. Mirotznik, R. Barnard, B. Gray, V. P. Pauca, T. C. Torgersen, J. van der Gracht, and G. Behrmann, “PERIODIC: Integrated computational array imaging technology,” in “Computational Optical Sensing and Imaging,” (2007), p. CMA1.

Tsuru, T.

Tyo, J. S.

van der Gracht, J.

R. J. Plemmons, S. Prasad, S. Matthews, M. Mirotznik, R. Barnard, B. Gray, V. P. Pauca, T. C. Torgersen, J. van der Gracht, and G. Behrmann, “PERIODIC: Integrated computational array imaging technology,” in “Computational Optical Sensing and Imaging,” (2007), p. CMA1.

Wakin, M. B.

E. J. Candes and M. B. Wakin, “An introduction to compressive sampling,” IEEE Sig. Processing Mag. 25, 21–30 (2008).
[Crossref]

Xiao, X.

Yamada, K.

Yang, L.

Appl. Opt. (7)

Comptes-Rendus Academie des Sciences (1)

G. M. Lippmann, “La photographie integrale,” Comptes-Rendus Academie des Sciences 146, 446–451 (1908).

IEEE Sig. Processing Mag. (2)

R. Baraniuk, “Compressive sensing,” IEEE Sig. Processing Mag. 24, 118–121 (2007).
[Crossref]

E. J. Candes and M. B. Wakin, “An introduction to compressive sampling,” IEEE Sig. Processing Mag. 25, 21–30 (2008).
[Crossref]

IEEE Trans. Image Proc. (1)

J. M. Bioucas-Dias and M. A. T. Figueiredo, “A new TwIST: Two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE Trans. Image Proc. 16, 2992–3004 (2007).
[Crossref]

IEEE Trans. Info. Theory (2)

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

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

IEEE Trans. Pattern Anal. Mach. Intell. (1)

M. Okutomi and T. Kanade, “A multiple-baseline stereo,” IEEE Trans. Pattern Anal. Mach. Intell. 15, 353–363 (1993).
[Crossref]

J. Display Technol. (1)

J. Opt. Soc. Am. (1)

Opt. Express (5)

Opt. Lett. (4)

Optical Review (1)

R. Horisaki, S. Irie, Y. Ogura, and J. Tanida, “Three-dimensional information acquisition using a compound imaging system,” Optical Review 14, 347–350 (2007).
[Crossref]

Phys. D (1)

L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Phys. D 60, 259–268 (1992).
[Crossref]

Proc. ICCP09 (1)

R. Horstmeyer, G. Euliss, R. Athale, and M. Levoy, “Flexible multimodal camera using a light field architecture,” in “Proc. ICCP09,” (2009), pp. 1–8.

Proc. IEEE (2)

F. Okano, J. Arai, K. Mitani, and M. Okui, “Real-time integral imaging based on extremely high resolution video system,” Proc. IEEE 94, 490–501 (2006).
[Crossref]

M. Cho, M. Daneshpanah, I. Moon, and B. Javidi, “Three-dimensional optical sensing and visualization using integral imaging,” Proc. IEEE 99, 556 –575 (2011).
[Crossref]

Proc. SPIE (1)

R. Horisaki and J. Tanida, “Multidimensional TOMBO imaging and its applications,” in Proc. SPIE (2011),  8165, pp. 816516.
[Crossref]

Other (1)

R. J. Plemmons, S. Prasad, S. Matthews, M. Mirotznik, R. Barnard, B. Gray, V. P. Pauca, T. C. Torgersen, J. van der Gracht, and G. Behrmann, “PERIODIC: Integrated computational array imaging technology,” in “Computational Optical Sensing and Imaging,” (2007), p. CMA1.

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Figures (14)

Fig. 1
Fig. 1 Multi-dimensional imaging systems. (a) A conventional sensing approach and (b) a CS approach.

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Fig. 2
Fig. 2 Compressive multi-dimensional integral imaging.

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Fig. 3
Fig. 3 Simulations of sparse samplings. (a) An object image, (b) a regular sparse sampling pattern, and (c) an irregular sparse sampling pattern.

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Fig. 4
Fig. 4 Captured images in the simulations. The total number of captured pixels in all cases are the same. Images by single aperture imaging with (a) regular sparse sampling in Fig. 3(b) and (b) irregular sparse sampling in Fig. 3(c). Images by integral imaging with (c) regular sparse sampling in Fig. 3(b) and (d) irregular sparse sampling in Fig. 3(c).

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Fig. 5
Fig. 5 Reconstructions in the simulations. Reconstructions of single aperture imaging with (a) regular sparse sampling in Fig. 3(b) and (b) irregular sparse sampling in Fig. 3(c). Reconstructions of integral imaging with (c) regular sparse sampling in Fig. 3(b) and (d) irregular sparse sampling in Fig. 3(c).

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Fig. 6
Fig. 6 Relationships between sampling ratios and PSNRs, where SAI is single aperture imaging, II is integral imaging, RSS is regular sparse sampling, and ISS is irregular sparse sampling, respectively.

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Fig. 7
Fig. 7 Entire captured elemental images for spectral integral imaging.

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Fig. 8
Fig. 8 A sample captured elemental image for spectral integral imaging.

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Fig. 9
Fig. 9 The sampled elemental image in Fig. 8 for compressive spectral integral imaging.

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Fig. 10
Fig. 10 Four-dimensional image reconstructions from the compressive spectral integral imaging data. (a) Reconstructed images using back-projection algorithm and (b) reconstructed images using TwIST algorithm. The first plane focuses on the sign and the second plane focuses on the car.

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Fig. 11
Fig. 11 Entire captured elemental images for spectral and polarimetric integral imaging. (a) Intensity elemental images and (b) linearly polarized elemental images.

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Fig. 12
Fig. 12 Sample captured elemental images for spectral and polarimetric integral imaging. (a) Intensity image and (b) linearly polarized image.

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Fig. 13
Fig. 13 The sampled elemental image in Fig. 12 for compressive spectral and polarimetric integral imaging.

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Fig. 14
Fig. 14 Five-dimensional image reconstructions from the compressive spectral and polarimetric integral imaging data. (a) Reconstructed images using back-projection algorithm and (b) Reconstructed images using TwIST algorithm. The first plane focuses on the two plants, the second plane focuses on the truck, and the third plane focuses on the sign. The first row in (a) or (b) is intensity images and the second row in (a) or (b) is linearly polarized images.

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Tables (1)

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Table 1 Applications of the proposed scheme.

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Equations (13)

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𝒢 ( u ) = ∑ C ∫ ℱ C ( u , z ) d z ,
𝒢 K ′ ( u ) = ∑ C 𝒬 C , K ( u ) ∬ 𝒟 ( u − x ) ℱ C ( x − 𝒯 K ( z ) , z ) d x d z ,
g K ′ = H K ′ f
= Q K DT K f ,
Q K = [ Q 1 , K ′ Q 2 , K ′ ⋯ Q N C , K ′ ] ,
D = [ 1 t 0 T … 0 t 0 t 1 t … 0 t ⋮ ⋮ ⋱ ⋮ 0 t 0 t … 1 t ] ,
T K = [ T K ′ O ⋯ O O T K ′ ⋯ O ⋮ ⋮ ⋱ ⋮ O O ⋯ T K ′ ] ,
T K ′ = [ T 1 , K ″ T 2 , K ″ ⋯ T N Z , K ″ ] ,
g = [ g 1 ′ g 2 ′ ⋮ g L X ′ ] = [ H 1 ′ H 2 ′ ⋮ H L X ′ ] f
= Hf ,
f ^ = argmin f ‖ g − Hf ‖ ℓ 2 + τ ℛ ( f ) ,
ℛ ( f ) = ∑ X ∑ Y ∑ Z ∑ C ( f ( X + 1 , Y , Z , C ) − f ( X , Y , Z , C ) ) 2 + ( f ( X , Y + 1 , Z , C ) − f ( X , Y , Z , C ) ) 2 .
PSNR = 20 ⋅ log 10 MAX MSE ,

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