Abstract

Compressed sensing has been discussed separately in spatial and temporal domains. Compressive holography has been introduced as a method that allows 3D tomographic reconstruction at different depths from a single 2D image. Coded exposure is a temporal compressed sensing method for high speed video acquisition. In this work, we combine compressive holography and coded exposure techniques and extend the discussion to 4D reconstruction in space and time from one coded captured image. In our prototype, digital in-line holography was used for imaging macroscopic, fast moving objects. The pixel-wise temporal modulation was implemented by a digital micromirror device. In this paper we demonstrate 10× temporal super resolution with multiple depths recovery from a single image. Two examples are presented for the purpose of recording subtle vibrations and tracking small particles within 5 ms.

© 2017 Optical Society of America

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References

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2016 (2)

J. Song, C. L. Swisher, H. Im, S. Jeong, D. Pathania, Y. Iwamoto, M. Pivovarov, R. Weissleder, and H. Lee, “Sparsity-based pixel super resolution for lens-free digital in-line holography,” Sci. Rep. 6, 24681 (2016).

R. Egami, R. Horisaki, L. Tian, and J. Tanida, “Relaxation of mask design for single-shot phase imaging with a coded aperture,” Appl. Opt. 55(8), 1830–1837 (2016).
[Crossref] [PubMed]

2015 (3)

2014 (5)

X. Yu, J. Hong, C. Liu, and M. K. Kim, “Review of digital holographic microscopy for three-dimensional profiling and tracking,” Opt. Eng. 53(11), 112306 (2014).
[Crossref]

X. Yu, J. Hong, C. Liu, and M. K. Kim, “Review of digital holographic microscopy for three dimensional profiling and tracking,” Opt. Eng. 53, 112306 (2014).
[Crossref]

D. Liu, J. Gu, Y. Hitomi, M. Gupta, T. Mitsunaga, and S. K. Nayar, “Efficient space-time sampling with pixel-wise coded exposure for high-speed imaging,” IEEE Trans. Pattern Anal. Machine Intelligence 36(2), 248–260 (2014).
[Crossref]

Y. Liu, L. Tian, C. Hsieh, and G. Barbastathis, “Compressive holographic two-dimensional localization with 1/302 subpixel accuracy,” Opt. Express 22, 9774–9782 (2014).
[Crossref] [PubMed]

R. Horisaki, Y. Ogura, M. Aino, and J. Tanida, “Single-shot phase imaging with a coded aperture,” Opt. Lett. 39(22), 6466–6469 (2014).
[Crossref] [PubMed]

2013 (1)

2012 (2)

Y. Liu, L. Tian, J. W. Lee, H. Y. Huang, M. S. Triantafyllou, and G. Barbastathis, “Scanning-free compressive holography for object localization with subpixel accuracy,” Opt. Lett. 37(16), 3357–3359 (2012).
[Crossref]

T. Su, L. Xue, and A. Ozcan, “High-throughput lensfree 3D tracking of human sperms reveals rare statistics of helical trajectories,” Proc. Natl. Acad. Sci. U. S. A. 109(40), 16018–16022 (2012).
[Crossref] [PubMed]

2011 (3)

2010 (6)

2009 (2)

2008 (2)

M. Lustig, D. L. Donoho, J. M. Santos, and J. M. Pauly, “Compressed sensing MRI,” IEEE Signal Processing Magazine 25(2), 72–82 (2008).
[Crossref]

N. Salah, G. Godard, D. Lebrun, P. Paranthoën, D. Allano, and S. Coëtmellec, “Application of multiple exposure digital in-line holography to particle tracking in a Bénard–von Kármán vortex flow,” Meas. Sci. Technol. 19(7), 074001 (2008).
[Crossref]

2007 (2)

2006 (5)

R. Raskar, A. Agrawal, and J. Tumblin, “Coded exposure photography: motion deblurring using fluttered shutter,” ACM Trans. Graphics (TOG) 25(3), 795–804 (2006).
[Crossref]

E. Candès and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inform. Theory 52(12) 489–509 (2006).
[Crossref]

E. Candès and T. Tao, “Near-optimal signal recovery from random projections: Universal encoding strategies?” IEEE Trans. Inform. Theory 52(12) 5406–5425 (2006).
[Crossref]

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

J. Garcia-Sucerquia, W. Xu, S. K. Jericho, P. Klages, M. H. Jericho, and H. J. Kreuzer, “Digital in-line holographic microscopy,” Appl. Opt. 45(5), 836–850 (2006).
[Crossref] [PubMed]

2003 (1)

2001 (2)

W. Xu, M. H. Jericho, I. A. Meinertzhagen, and H. J. Kreuzer, “Digital in-line holography for biological applications,” Proc. Natl. Acad. Sci. 98(20), 11301–11305 (2001).
[Crossref] [PubMed]

L. Xu, X. Peng, J. Miao, and A. K. Asundi, “Studies of digital microscopic holography with applications to microstructure testing,” Appl. Opt. 40(28), 5046–5051 (2001).
[Crossref]

2000 (1)

B. J. Nilsson and T. E. Carlsson, “Simultaneous measurement of shape and deformation using digital light-in-flight recording by holography,” Opt. Eng. 39, 244–253 (2000).
[Crossref]

1997 (1)

M. J. Saxton and K. Jacobson, “Single-particle tracking: applications to membrane dynamics,” Ann. Rev. Biophys. Biomolecular Structure 26(1), 373–399 (1997).
[Crossref]

1948 (1)

D. Gabor, “A new microscopic principle,” Nature 161(4098), 777–778 (1948).
[Crossref] [PubMed]

Agrawal, A.

R. Raskar, A. Agrawal, and J. Tumblin, “Coded exposure photography: motion deblurring using fluttered shutter,” ACM Trans. Graphics (TOG) 25(3), 795–804 (2006).
[Crossref]

M. Gupta, A. Agrawal, A. Veeraraghavan, and S. G. Narasimhan, “Flexible voxels for motion-aware videography,” in European Conference on Computer Vision (2010), pp. 100–114.

Aino, M.

Allano, D.

N. Salah, G. Godard, D. Lebrun, P. Paranthoën, D. Allano, and S. Coëtmellec, “Application of multiple exposure digital in-line holography to particle tracking in a Bénard–von Kármán vortex flow,” Meas. Sci. Technol. 19(7), 074001 (2008).
[Crossref]

Angelini, E.

Asundi, A. K.

Atlan, M.

Barbastathis, G.

Bioucas-Dias, J. M.

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

Brady, D.

Brady, D. J.

Bub, G.

G. Bub, M. Tecza, M. Helmes, P. Lee, and P. Kohl, “Temporal pixel multiplexing for simultaneous high-speed, high-resolution imaging,” Nat. Methods 7, 209–211 (2010).
[Crossref] [PubMed]

Candès, E.

E. Candès and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inform. Theory 52(12) 489–509 (2006).
[Crossref]

E. Candès and T. Tao, “Near-optimal signal recovery from random projections: Universal encoding strategies?” IEEE Trans. Inform. Theory 52(12) 5406–5425 (2006).
[Crossref]

Carin, L.

Carlsson, T. E.

B. J. Nilsson and T. E. Carlsson, “Simultaneous measurement of shape and deformation using digital light-in-flight recording by holography,” Opt. Eng. 39, 244–253 (2000).
[Crossref]

Castro, A.

Chellappa, R.

D. Reddy, A. Veeraraghavan, and R. Chellappa, “P2C2: Programmable pixel compressive camera for high speed imaging,” in IEEE Conference on Computer Vision and Pattern Recognition (CVPR, 2011), pp. 329–336.

Chen, W.

Chen, Y.

Cheong, F. C.

Choi, K.

Coëtmellec, S.

N. Salah, G. Godard, D. Lebrun, P. Paranthoën, D. Allano, and S. Coëtmellec, “Application of multiple exposure digital in-line holography to particle tracking in a Bénard–von Kármán vortex flow,” Meas. Sci. Technol. 19(7), 074001 (2008).
[Crossref]

Coppola, G.

Cossairt, O.

Cull, C. F.

Di Caprio, G.

Dixon, L.

Domínguez-Caballero, J. A.

Donoho, D. L.

M. Lustig, D. L. Donoho, J. M. Santos, and J. M. Pauly, “Compressed sensing MRI,” IEEE Signal Processing Magazine 25(2), 72–82 (2008).
[Crossref]

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

Egami, R.

Ferraro, P.

Figueiredo, M. A.

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

Frauel, Y.

Gabor, D.

D. Gabor, “A new microscopic principle,” Nature 161(4098), 777–778 (1948).
[Crossref] [PubMed]

Gan, L.

L. Gan, “Block compressed sensing of natural images,” in International Conference on Digital Signal Processing (2007), pp. 403–406.

Gao, Y.

Garcia-Sucerquia, J.

Ge, B.

Godard, G.

N. Salah, G. Godard, D. Lebrun, P. Paranthoën, D. Allano, and S. Coëtmellec, “Application of multiple exposure digital in-line holography to particle tracking in a Bénard–von Kármán vortex flow,” Meas. Sci. Technol. 19(7), 074001 (2008).
[Crossref]

Grier, D. G.

Gu, J.

D. Liu, J. Gu, Y. Hitomi, M. Gupta, T. Mitsunaga, and S. K. Nayar, “Efficient space-time sampling with pixel-wise coded exposure for high-speed imaging,” IEEE Trans. Pattern Anal. Machine Intelligence 36(2), 248–260 (2014).
[Crossref]

Gupta, M.

D. Liu, J. Gu, Y. Hitomi, M. Gupta, T. Mitsunaga, and S. K. Nayar, “Efficient space-time sampling with pixel-wise coded exposure for high-speed imaging,” IEEE Trans. Pattern Anal. Machine Intelligence 36(2), 248–260 (2014).
[Crossref]

M. Gupta, A. Agrawal, A. Veeraraghavan, and S. G. Narasimhan, “Flexible voxels for motion-aware videography,” in European Conference on Computer Vision (2010), pp. 100–114.

Hahn, J.

Helmes, M.

G. Bub, M. Tecza, M. Helmes, P. Lee, and P. Kohl, “Temporal pixel multiplexing for simultaneous high-speed, high-resolution imaging,” Nat. Methods 7, 209–211 (2010).
[Crossref] [PubMed]

Hitomi, Y.

D. Liu, J. Gu, Y. Hitomi, M. Gupta, T. Mitsunaga, and S. K. Nayar, “Efficient space-time sampling with pixel-wise coded exposure for high-speed imaging,” IEEE Trans. Pattern Anal. Machine Intelligence 36(2), 248–260 (2014).
[Crossref]

Hong, J.

X. Yu, J. Hong, C. Liu, and M. K. Kim, “Review of digital holographic microscopy for three-dimensional profiling and tracking,” Opt. Eng. 53(11), 112306 (2014).
[Crossref]

X. Yu, J. Hong, C. Liu, and M. K. Kim, “Review of digital holographic microscopy for three dimensional profiling and tracking,” Opt. Eng. 53, 112306 (2014).
[Crossref]

Horisaki, R.

Hsieh, C.

Huang, H. Y.

Im, H.

J. Song, C. L. Swisher, H. Im, S. Jeong, D. Pathania, Y. Iwamoto, M. Pivovarov, R. Weissleder, and H. Lee, “Sparsity-based pixel super resolution for lens-free digital in-line holography,” Sci. Rep. 6, 24681 (2016).

Iwamoto, Y.

J. Song, C. L. Swisher, H. Im, S. Jeong, D. Pathania, Y. Iwamoto, M. Pivovarov, R. Weissleder, and H. Lee, “Sparsity-based pixel super resolution for lens-free digital in-line holography,” Sci. Rep. 6, 24681 (2016).

Jacobson, K.

M. J. Saxton and K. Jacobson, “Single-particle tracking: applications to membrane dynamics,” Ann. Rev. Biophys. Biomolecular Structure 26(1), 373–399 (1997).
[Crossref]

Javidi, B.

Jeong, S.

J. Song, C. L. Swisher, H. Im, S. Jeong, D. Pathania, Y. Iwamoto, M. Pivovarov, R. Weissleder, and H. Lee, “Sparsity-based pixel super resolution for lens-free digital in-line holography,” Sci. Rep. 6, 24681 (2016).

Jericho, M. H.

Jericho, S. K.

Katsaggelos, A. K.

Katz, J.

J. Katz and J. Sheng, “Applications of holography in fluid mechanics and particle dynamics,” Ann. Rev. Fluid Mech. 42, 531–555 (2010).
[Crossref]

Kim, M. K.

X. Yu, J. Hong, C. Liu, and M. K. Kim, “Review of digital holographic microscopy for three dimensional profiling and tracking,” Opt. Eng. 53, 112306 (2014).
[Crossref]

X. Yu, J. Hong, C. Liu, and M. K. Kim, “Review of digital holographic microscopy for three-dimensional profiling and tracking,” Opt. Eng. 53(11), 112306 (2014).
[Crossref]

M. K. Kim, Digital Holographic Microscopy (Springer, 2011).
[Crossref]

Kittle, D.

Klages, P.

Kohl, P.

G. Bub, M. Tecza, M. Helmes, P. Lee, and P. Kohl, “Temporal pixel multiplexing for simultaneous high-speed, high-resolution imaging,” Nat. Methods 7, 209–211 (2010).
[Crossref] [PubMed]

Koller, R.

Kreuzer, H. J.

Lebrun, D.

N. Salah, G. Godard, D. Lebrun, P. Paranthoën, D. Allano, and S. Coëtmellec, “Application of multiple exposure digital in-line holography to particle tracking in a Bénard–von Kármán vortex flow,” Meas. Sci. Technol. 19(7), 074001 (2008).
[Crossref]

Lee, H.

J. Song, C. L. Swisher, H. Im, S. Jeong, D. Pathania, Y. Iwamoto, M. Pivovarov, R. Weissleder, and H. Lee, “Sparsity-based pixel super resolution for lens-free digital in-line holography,” Sci. Rep. 6, 24681 (2016).

Lee, H. P.

Lee, J. W.

Lee, P.

G. Bub, M. Tecza, M. Helmes, P. Lee, and P. Kohl, “Temporal pixel multiplexing for simultaneous high-speed, high-resolution imaging,” Nat. Methods 7, 209–211 (2010).
[Crossref] [PubMed]

Liao, X.

Lim, S.

Liu, C.

X. Yu, J. Hong, C. Liu, and M. K. Kim, “Review of digital holographic microscopy for three-dimensional profiling and tracking,” Opt. Eng. 53(11), 112306 (2014).
[Crossref]

X. Yu, J. Hong, C. Liu, and M. K. Kim, “Review of digital holographic microscopy for three dimensional profiling and tracking,” Opt. Eng. 53, 112306 (2014).
[Crossref]

Liu, D.

D. Liu, J. Gu, Y. Hitomi, M. Gupta, T. Mitsunaga, and S. K. Nayar, “Efficient space-time sampling with pixel-wise coded exposure for high-speed imaging,” IEEE Trans. Pattern Anal. Machine Intelligence 36(2), 248–260 (2014).
[Crossref]

Liu, Y.

Llull, P.

Loomis, N.

Lü, Q.

Lustig, M.

M. Lustig, D. L. Donoho, J. M. Santos, and J. M. Pauly, “Compressed sensing MRI,” IEEE Signal Processing Magazine 25(2), 72–82 (2008).
[Crossref]

Mait, J. N.

Marim, M. M.

Marks, D.

Marks, D. L.

Matsuda, N.

Mattheiss, M.

McDonald, J. B.

McElhinney, C. P.

Meinertzhagen, I. A.

W. Xu, M. H. Jericho, H. J. Kreuzer, and I. A. Meinertzhagen, “Tracking particles in four dimensions with in-line holographic microscopy,” Opt. Lett. 28(3), 164–166 (2003).
[Crossref] [PubMed]

W. Xu, M. H. Jericho, I. A. Meinertzhagen, and H. J. Kreuzer, “Digital in-line holography for biological applications,” Proc. Natl. Acad. Sci. 98(20), 11301–11305 (2001).
[Crossref] [PubMed]

Memmolo, P.

Miao, J.

Miccio, L.

Mitsunaga, T.

D. Liu, J. Gu, Y. Hitomi, M. Gupta, T. Mitsunaga, and S. K. Nayar, “Efficient space-time sampling with pixel-wise coded exposure for high-speed imaging,” IEEE Trans. Pattern Anal. Machine Intelligence 36(2), 248–260 (2014).
[Crossref]

Narasimhan, S. G.

M. Gupta, A. Agrawal, A. Veeraraghavan, and S. G. Narasimhan, “Flexible voxels for motion-aware videography,” in European Conference on Computer Vision (2010), pp. 100–114.

Naughton, T. J.

Nayar, S. K.

D. Liu, J. Gu, Y. Hitomi, M. Gupta, T. Mitsunaga, and S. K. Nayar, “Efficient space-time sampling with pixel-wise coded exposure for high-speed imaging,” IEEE Trans. Pattern Anal. Machine Intelligence 36(2), 248–260 (2014).
[Crossref]

Netti, P. A.

Niederberger, T.

Nilsson, B. J.

B. J. Nilsson and T. E. Carlsson, “Simultaneous measurement of shape and deformation using digital light-in-flight recording by holography,” Opt. Eng. 39, 244–253 (2000).
[Crossref]

Ogura, Y.

Olivo-Martin, J.-C.

Ozcan, A.

T. Su, L. Xue, and A. Ozcan, “High-throughput lensfree 3D tracking of human sperms reveals rare statistics of helical trajectories,” Proc. Natl. Acad. Sci. U. S. A. 109(40), 16018–16022 (2012).
[Crossref] [PubMed]

Paranthoën, P.

N. Salah, G. Godard, D. Lebrun, P. Paranthoën, D. Allano, and S. Coëtmellec, “Application of multiple exposure digital in-line holography to particle tracking in a Bénard–von Kármán vortex flow,” Meas. Sci. Technol. 19(7), 074001 (2008).
[Crossref]

Pathania, D.

J. Song, C. L. Swisher, H. Im, S. Jeong, D. Pathania, Y. Iwamoto, M. Pivovarov, R. Weissleder, and H. Lee, “Sparsity-based pixel super resolution for lens-free digital in-line holography,” Sci. Rep. 6, 24681 (2016).

Paturzo, M.

Pauly, J. M.

M. Lustig, D. L. Donoho, J. M. Santos, and J. M. Pauly, “Compressed sensing MRI,” IEEE Signal Processing Magazine 25(2), 72–82 (2008).
[Crossref]

Peng, X.

Pivovarov, M.

J. Song, C. L. Swisher, H. Im, S. Jeong, D. Pathania, Y. Iwamoto, M. Pivovarov, R. Weissleder, and H. Lee, “Sparsity-based pixel super resolution for lens-free digital in-line holography,” Sci. Rep. 6, 24681 (2016).

Raskar, R.

R. Raskar, A. Agrawal, and J. Tumblin, “Coded exposure photography: motion deblurring using fluttered shutter,” ACM Trans. Graphics (TOG) 25(3), 795–804 (2006).
[Crossref]

Reddy, D.

D. Reddy, A. Veeraraghavan, and R. Chellappa, “P2C2: Programmable pixel compressive camera for high speed imaging,” in IEEE Conference on Computer Vision and Pattern Recognition (CVPR, 2011), pp. 329–336.

Rehman, S.

Rivenson, Y.

Y. Rivenson, A. Stern, and B. Javidi, “Compressive Fresnel holography,” J. Disp. Technol. 6(10), 506–509 (2010).
[Crossref]

Salah, N.

N. Salah, G. Godard, D. Lebrun, P. Paranthoën, D. Allano, and S. Coëtmellec, “Application of multiple exposure digital in-line holography to particle tracking in a Bénard–von Kármán vortex flow,” Meas. Sci. Technol. 19(7), 074001 (2008).
[Crossref]

Santos, J. M.

M. Lustig, D. L. Donoho, J. M. Santos, and J. M. Pauly, “Compressed sensing MRI,” IEEE Signal Processing Magazine 25(2), 72–82 (2008).
[Crossref]

Sapiro, G.

Saxton, M. J.

M. J. Saxton and K. Jacobson, “Single-particle tracking: applications to membrane dynamics,” Ann. Rev. Biophys. Biomolecular Structure 26(1), 373–399 (1997).
[Crossref]

Schmid, L.

Schuster, G.

Sheng, J.

J. Katz and J. Sheng, “Applications of holography in fluid mechanics and particle dynamics,” Ann. Rev. Fluid Mech. 42, 531–555 (2010).
[Crossref]

Song, J.

J. Song, C. L. Swisher, H. Im, S. Jeong, D. Pathania, Y. Iwamoto, M. Pivovarov, R. Weissleder, and H. Lee, “Sparsity-based pixel super resolution for lens-free digital in-line holography,” Sci. Rep. 6, 24681 (2016).

Spinoulas, L.

Stern, A.

Y. Rivenson, A. Stern, and B. Javidi, “Compressive Fresnel holography,” J. Disp. Technol. 6(10), 506–509 (2010).
[Crossref]

Su, T.

T. Su, L. Xue, and A. Ozcan, “High-throughput lensfree 3D tracking of human sperms reveals rare statistics of helical trajectories,” Proc. Natl. Acad. Sci. U. S. A. 109(40), 16018–16022 (2012).
[Crossref] [PubMed]

Swisher, C. L.

J. Song, C. L. Swisher, H. Im, S. Jeong, D. Pathania, Y. Iwamoto, M. Pivovarov, R. Weissleder, and H. Lee, “Sparsity-based pixel super resolution for lens-free digital in-line holography,” Sci. Rep. 6, 24681 (2016).

Tanida, J.

Tao, T.

E. Candès and T. Tao, “Near-optimal signal recovery from random projections: Universal encoding strategies?” IEEE Trans. Inform. Theory 52(12) 5406–5425 (2006).
[Crossref]

E. Candès and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inform. Theory 52(12) 489–509 (2006).
[Crossref]

Tecza, M.

G. Bub, M. Tecza, M. Helmes, P. Lee, and P. Kohl, “Temporal pixel multiplexing for simultaneous high-speed, high-resolution imaging,” Nat. Methods 7, 209–211 (2010).
[Crossref] [PubMed]

Tian, L.

Triantafyllou, M. S.

Tumblin, J.

R. Raskar, A. Agrawal, and J. Tumblin, “Coded exposure photography: motion deblurring using fluttered shutter,” ACM Trans. Graphics (TOG) 25(3), 795–804 (2006).
[Crossref]

Veeraraghavan, A.

D. Reddy, A. Veeraraghavan, and R. Chellappa, “P2C2: Programmable pixel compressive camera for high speed imaging,” in IEEE Conference on Computer Vision and Pattern Recognition (CVPR, 2011), pp. 329–336.

M. Gupta, A. Agrawal, A. Veeraraghavan, and S. G. Narasimhan, “Flexible voxels for motion-aware videography,” in European Conference on Computer Vision (2010), pp. 100–114.

Weissleder, R.

J. Song, C. L. Swisher, H. Im, S. Jeong, D. Pathania, Y. Iwamoto, M. Pivovarov, R. Weissleder, and H. Lee, “Sparsity-based pixel super resolution for lens-free digital in-line holography,” Sci. Rep. 6, 24681 (2016).

Wikner, D. A.

Xu, L.

Xu, W.

Xue, L.

T. Su, L. Xue, and A. Ozcan, “High-throughput lensfree 3D tracking of human sperms reveals rare statistics of helical trajectories,” Proc. Natl. Acad. Sci. U. S. A. 109(40), 16018–16022 (2012).
[Crossref] [PubMed]

Yang, J.

Yu, X.

X. Yu, J. Hong, C. Liu, and M. K. Kim, “Review of digital holographic microscopy for three dimensional profiling and tracking,” Opt. Eng. 53, 112306 (2014).
[Crossref]

X. Yu, J. Hong, C. Liu, and M. K. Kim, “Review of digital holographic microscopy for three-dimensional profiling and tracking,” Opt. Eng. 53(11), 112306 (2014).
[Crossref]

Yuan, R.

Yuan, X.

Zhang, Y.

Zhang, Z.

ACM Trans. Graphics (TOG) (1)

R. Raskar, A. Agrawal, and J. Tumblin, “Coded exposure photography: motion deblurring using fluttered shutter,” ACM Trans. Graphics (TOG) 25(3), 795–804 (2006).
[Crossref]

Adv. Opt. Photon. (1)

Ann. Rev. Biophys. Biomolecular Structure (1)

M. J. Saxton and K. Jacobson, “Single-particle tracking: applications to membrane dynamics,” Ann. Rev. Biophys. Biomolecular Structure 26(1), 373–399 (1997).
[Crossref]

Ann. Rev. Fluid Mech. (1)

J. Katz and J. Sheng, “Applications of holography in fluid mechanics and particle dynamics,” Ann. Rev. Fluid Mech. 42, 531–555 (2010).
[Crossref]

Appl. Opt. (7)

IEEE Signal Processing Magazine (1)

M. Lustig, D. L. Donoho, J. M. Santos, and J. M. Pauly, “Compressed sensing MRI,” IEEE Signal Processing Magazine 25(2), 72–82 (2008).
[Crossref]

IEEE Trans. Image Process. (1)

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

IEEE Trans. Inform. Theory (3)

E. Candès and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inform. Theory 52(12) 489–509 (2006).
[Crossref]

E. Candès and T. Tao, “Near-optimal signal recovery from random projections: Universal encoding strategies?” IEEE Trans. Inform. Theory 52(12) 5406–5425 (2006).
[Crossref]

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

IEEE Trans. Pattern Anal. Machine Intelligence (1)

D. Liu, J. Gu, Y. Hitomi, M. Gupta, T. Mitsunaga, and S. K. Nayar, “Efficient space-time sampling with pixel-wise coded exposure for high-speed imaging,” IEEE Trans. Pattern Anal. Machine Intelligence 36(2), 248–260 (2014).
[Crossref]

J. Disp. Technol. (1)

Y. Rivenson, A. Stern, and B. Javidi, “Compressive Fresnel holography,” J. Disp. Technol. 6(10), 506–509 (2010).
[Crossref]

Meas. Sci. Technol. (1)

N. Salah, G. Godard, D. Lebrun, P. Paranthoën, D. Allano, and S. Coëtmellec, “Application of multiple exposure digital in-line holography to particle tracking in a Bénard–von Kármán vortex flow,” Meas. Sci. Technol. 19(7), 074001 (2008).
[Crossref]

Nat. Methods (1)

G. Bub, M. Tecza, M. Helmes, P. Lee, and P. Kohl, “Temporal pixel multiplexing for simultaneous high-speed, high-resolution imaging,” Nat. Methods 7, 209–211 (2010).
[Crossref] [PubMed]

Nature (1)

D. Gabor, “A new microscopic principle,” Nature 161(4098), 777–778 (1948).
[Crossref] [PubMed]

Opt. Eng. (3)

B. J. Nilsson and T. E. Carlsson, “Simultaneous measurement of shape and deformation using digital light-in-flight recording by holography,” Opt. Eng. 39, 244–253 (2000).
[Crossref]

X. Yu, J. Hong, C. Liu, and M. K. Kim, “Review of digital holographic microscopy for three dimensional profiling and tracking,” Opt. Eng. 53, 112306 (2014).
[Crossref]

X. Yu, J. Hong, C. Liu, and M. K. Kim, “Review of digital holographic microscopy for three-dimensional profiling and tracking,” Opt. Eng. 53(11), 112306 (2014).
[Crossref]

Opt. Express (7)

Opt. Lett. (5)

Proc. Natl. Acad. Sci. (1)

W. Xu, M. H. Jericho, I. A. Meinertzhagen, and H. J. Kreuzer, “Digital in-line holography for biological applications,” Proc. Natl. Acad. Sci. 98(20), 11301–11305 (2001).
[Crossref] [PubMed]

Proc. Natl. Acad. Sci. U. S. A. (1)

T. Su, L. Xue, and A. Ozcan, “High-throughput lensfree 3D tracking of human sperms reveals rare statistics of helical trajectories,” Proc. Natl. Acad. Sci. U. S. A. 109(40), 16018–16022 (2012).
[Crossref] [PubMed]

Sci. Rep. (1)

J. Song, C. L. Swisher, H. Im, S. Jeong, D. Pathania, Y. Iwamoto, M. Pivovarov, R. Weissleder, and H. Lee, “Sparsity-based pixel super resolution for lens-free digital in-line holography,” Sci. Rep. 6, 24681 (2016).

Other (5)

M. Gupta, A. Agrawal, A. Veeraraghavan, and S. G. Narasimhan, “Flexible voxels for motion-aware videography,” in European Conference on Computer Vision (2010), pp. 100–114.

D. Reddy, A. Veeraraghavan, and R. Chellappa, “P2C2: Programmable pixel compressive camera for high speed imaging,” in IEEE Conference on Computer Vision and Pattern Recognition (CVPR, 2011), pp. 329–336.

L. Gan, “Block compressed sensing of natural images,” in International Conference on Digital Signal Processing (2007), pp. 403–406.

M. K. Kim, Digital Holographic Microscopy (Springer, 2011).
[Crossref]

“DLP LightCrafterTM 4500,” http://www.ti.com/lsds/ti/dlp/advanced-light-control/microarray-greater-than-1million-lightcrafter4500.page . Accessed: 2016-06-01.

Supplementary Material (4)

NameDescription
» Visualization 1: MOV (30525 KB)      Tomographic reconstruction, full resolution
» Visualization 2: MOV (30525 KB)      Tomographic reconstruction, 10% hologram
» Visualization 3: AVI (210 KB)      4D reconstruction example, at d1
» Visualization 4: AVI (171 KB)      4D reconstruction example, at d2

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Figures (6)

Fig. 1
Fig. 1

4D holographic model. E0(x, y, t; z0): projection of a 4D field at z0, the n-th depth plane has a distance of dn to z0; M(x, y, t): temporal coded mask located at z1; G(x, y, Δt): captured image with an integral over Δt. The sensor is located at z2.

Fig. 2
Fig. 2

Schematic of the experimental setup. (PG: Pulse Generator; DL: Diode Laser; CL: Collimating Lens; DMD: Digital Micromirror Device; OL: Objective Lens. A trigger signal generated from the DMD is sent to the camera for exposure. The minimum time between successive DMD mask patterns is PT = 500μs with a pattern exposure Pd = 250μs. The camera is triggered every N patterns. (N is equal to T in previous context.)

Fig. 3
Fig. 3

Subsampling holograms (background subtracted). (a)hologram of two static furs 7.1 cm and 10.1 cm away from sensor. (b) DMD mask, 10%, uniformly random (background divided). (c) subsampled hologram. (d) Comparison of reconstructions from both back-propagation (BP) method and compressed sensing (CS) method using the full hologram. (e) Comparison for BP and CS using 10% subsampled hologram. (f) Normalized variance vs. distance on z direction. Blue series: BP; red series: CS; full curve: 100% hologram; dashed curve: 10% hologram. (See Visualization 1 and Visualization 2.)

Fig. 4
Fig. 4

Performance simulations. (a) Scenario: two Peranema with different sizes moving at different planes (dz), a single image is simulated at the sensor plane; (b) Space-time performance. Horizontal axis indicates different spacing between the two objects. “100%”: full resolution; “50%”: 50% of the pixels are randomly sampled at each time frame, which corresponds to a temporal increase of 2; “20%”: temporal increase of 5; “10%”: temporal increase of 10. Lines represent CS results and dashed lines represent BP results. PSNR in dB. (c) Reconstruction results at depth d1. Marked as red circle in (b).

Fig. 5
Fig. 5

Reconstruction results from a single image (moving hairs). 10 frames of video and two depth frames are reconstructed from a single captured hologram. Due to space constraints, 3 video frames (3rd, 6th, 9th) and two depths (d1 = 73mm, d2 = 111mm) are presented (see Visualization 3 and Visualization 4).

Fig. 6
Fig. 6

Reconstruction results from a single image (dropping glitters). (a) Glitters; (b) captured image; (c) normalized image; (d) reconstruction map. 2 depths and 4 out of 10 frames are shown; (e) normalized variance plot from 2 particles at d1 and d2; (f) 4D particle tracking; (g) velocity plotting with time range from 500μs to 4000μs.

Tables (1)

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Table 1 Analysis of all the variables appearing in Eq. (8).

Equations (10)

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E ( x , y ; z ) = i k 2 π Σ 0 E 0 ( x 0 , y 0 ) exp ( i k r ) r d x 0 d y 0 , i k 2 π z Σ 0 E 0 ( x 0 , y 0 ) exp { i k [ ( x x 0 ) 2 + ( y y 0 ) 2 + z 2 ] 1 2 } d x 0 d y 0 ,
E ( x , y ; z ) = H * E 0 ,
H ( x , y ; z ) = i k 2 π z exp [ i k ( x 2 + y 2 + z 2 ) 1 2 ] .
E 0 ( x , y , t ; z 0 ) = n = 1 N d H d n * O ( x , y , z 0 d n , t ) + R ,
G ( x , y , Δ t ) = t = t 0 t 0 + Δ t I ( x , y , t ; z 2 ) d t = t = t 0 t 0 + Δ t | H z 2 z 1 * { M ( x , y , t ) [ H z 1 z 0 * E 0 ( x , y , t ; z 0 ) ] } | 2 d t ,
G ( x , y , Δ t ) = i = 0 T 1 t = t i t i + 1 | H z 2 z 1 * { M ( x , y , t ) [ H z 1 z 0 * E 0 ( x , y , t ; z 0 ) ] } | 2 d t = τ i = 0 T 1 | H z 2 z 1 * { M ( x , y , t i ) [ H z 1 z 0 * E 0 ( x , y , t i ; z 0 ) ] } | 2 = τ i = 0 T 1 | H z 2 z 1 * { M ( x , y , t i ) [ H z 1 z 0 * ( n = 1 N d H d n * O ( x , y , z 0 d n , t i ) + R ) ] } | 2 = τ i = 0 T 1 | O c , i + R c , i | 2 ,
I = { O c R c * + O c * R c } + O c 2 + R c 2 = 2 Re { O c R c * } + E E ,
g = 2 S T Re { H T , z 21 { M T [ H T , z 10 ( H T , d n o ) ] } } + e + n = A ( o ) + e + n ,
o ^ = argmin o 1 2 g A ( o ) 2 2 + λ Φ ( o )
Φ ( o ) = o TV = t = 0 T 1 n = 1 N d x = 1 N M x y = 1 N M y | ( O ) x , y , n , t | ,

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