Abstract

We propose a synchronous implementation of compressive imaging. This method is mathematically equivalent to prevailing sequential methods, but uses a static holographic optical element to create a spatially distributed spot array from which the image can be reconstructed with an instantaneous measurement. We present the holographic design requirements and demonstrate experimentally that the linear algebra of compressed imaging can be implemented with this technique. We believe this technique can be integrated with optical metasurfaces, which will allow the development of new compressive sensing methods.

Published by The Optical Society under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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  1. D. Takhar, J. N. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. F. Kelly, and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” Proc. SPIE 6065, 606509 (2006).
  2. R. Baraniuk, “Compressive sensing,” IEEE Signal Process. Mag. 24(4), 118–121 (2007).
    [Crossref]
  3. M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
    [Crossref]
  4. S. Welsh, M. Edgar, R. Bowman, P. Jonathan, B. Sun, and M. Padgett, “Fast full-color computational imaging with single-pixel detectors,” Opt. Express 21, 23068–23074 (2013).
    [Crossref]
  5. P. Nagesh and B. Li, “Compressive imaging of color images,” in IEEE International Conference on Acoustics, Speech and Signal Processing (IEEE, 2009), pp. 1261–1264.
  6. M. A. Neifeld and J. Ke, “Optical architectures for compressive imaging,” Appl. Opt. 46, 5293–5303 (2007).
    [Crossref]
  7. T. Björklund and E. Magli, “A parallel compressive imaging architecture for one-shot acquisition,” arXiv preprint arXiv:1311.0646 (2013).
  8. A. Stern and B. Javidi, “Random projections imaging with extended space-bandwidth product,” J. Disp. Technol. 3, 315–320 (2007).
    [Crossref]
  9. A. Stern, Y. Rivenson, and B. Javidi, “Single-shot compressive imaging,” Proc. SPIE 6778, 67780J (2008).
  10. M. E. Gehm, R. John, D. J. Brady, R. M. Willett, and T. J. Schulz, “Single-shot compressive spectral imaging with a dual-disperser architecture,” Opt. Express 15, 14013–14027 (2007).
    [Crossref]
  11. C. M. Watts, D. Shrekenhamer, J. Montoya, G. Lipworth, J. Hunt, T. Sleasman, S. Krishna, D. R. Smith, and W. J. Padilla, “Terahertz compressive imaging with metamaterial spatial light modulators,” Nat. Photonics 8, 605–609 (2014).
    [Crossref]
  12. A. Macfaden, S. J. Kindness, and T. D. Wilkinson, “An implementation of one-shot compressive imaging using a diffractive optical element,” in Frontiers in Optics (Optical Society of America, 2015), paper FTh1F.2.
  13. J. Goodman, Introduction to Fourier Optics (McGraw-Hill, 2008).
  14. H. Ohlsson, A. Yang, R. Dong, and S. Sastry, “Compressive phase retrieval from squared output measurements via semidefinite programming,” arXiv preprint arXiv:1111.6323 (2011), pp. 1–27.
  15. D. A. Lorenz, “Constructing test instances for basis pursuit denoising,” IEEE Trans. Signal Process. 61, 1210–1214 (2013).
    [Crossref]
  16. D. A. Lorenz, L1TestPack: a software to generate test instances for l1 minimization problems (2011).
  17. N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13, 139–150 (2014).
    [Crossref]
  18. J. Hunt, T. Driscoll, A. Mrozack, G. Lipworth, M. Reynolds, D. Brady, and D. R. Smith, “Metamaterial apertures for computational imaging,” Science 339, 310–313 (2013).
    [Crossref]
  19. M. Ozaki, J. Kato, and S. Kawata, “Surface-plasmon holography with white-light illumination,” Science 332, 218–220 (2011).
  20. W. T. Chen, K.-Y. Yang, C.-M. Wang, Y.-W. Huang, G. Sun, C. Y. Liao, W.-l. Hsu, H. T. Lin, S. Sun, L. Zhou, A. Q. Liu, and D. P. Tsai, “High-efficiency broadband meta-hologram with polarization controlled dual images,” Nano Lett. 14, 225–230 (2014).
    [Crossref]
  21. Y. August, C. Vachman, Y. Rivenson, and A. Stern, “Compressive hyperspectral imaging by random separable projections in both the spatial and the spectral domains,” Appl. Opt. 52, D46–D54 (2013).
    [Crossref]
  22. A. Majumdar and R. K. Ward, “Compressed sensing of color images,” Signal Process. 90, 3122–3127 (2010).
    [Crossref]
  23. C. Williams, Y. Montelongo, J. O. Tenorio-Pearl, A. Cabrero-Vilatela, S. Hofmann, W. I. Milne, and T. D. Wilkinson, “Engineered pixels using active plasmonic holograms with liquid crystals,” Phys. Status Solidi 9, 125–129 (2015).
  24. http://dx.doi.org/10.17863/CAM.569

2015 (1)

C. Williams, Y. Montelongo, J. O. Tenorio-Pearl, A. Cabrero-Vilatela, S. Hofmann, W. I. Milne, and T. D. Wilkinson, “Engineered pixels using active plasmonic holograms with liquid crystals,” Phys. Status Solidi 9, 125–129 (2015).

2014 (3)

N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13, 139–150 (2014).
[Crossref]

W. T. Chen, K.-Y. Yang, C.-M. Wang, Y.-W. Huang, G. Sun, C. Y. Liao, W.-l. Hsu, H. T. Lin, S. Sun, L. Zhou, A. Q. Liu, and D. P. Tsai, “High-efficiency broadband meta-hologram with polarization controlled dual images,” Nano Lett. 14, 225–230 (2014).
[Crossref]

C. M. Watts, D. Shrekenhamer, J. Montoya, G. Lipworth, J. Hunt, T. Sleasman, S. Krishna, D. R. Smith, and W. J. Padilla, “Terahertz compressive imaging with metamaterial spatial light modulators,” Nat. Photonics 8, 605–609 (2014).
[Crossref]

2013 (4)

D. A. Lorenz, “Constructing test instances for basis pursuit denoising,” IEEE Trans. Signal Process. 61, 1210–1214 (2013).
[Crossref]

S. Welsh, M. Edgar, R. Bowman, P. Jonathan, B. Sun, and M. Padgett, “Fast full-color computational imaging with single-pixel detectors,” Opt. Express 21, 23068–23074 (2013).
[Crossref]

Y. August, C. Vachman, Y. Rivenson, and A. Stern, “Compressive hyperspectral imaging by random separable projections in both the spatial and the spectral domains,” Appl. Opt. 52, D46–D54 (2013).
[Crossref]

J. Hunt, T. Driscoll, A. Mrozack, G. Lipworth, M. Reynolds, D. Brady, and D. R. Smith, “Metamaterial apertures for computational imaging,” Science 339, 310–313 (2013).
[Crossref]

2011 (1)

M. Ozaki, J. Kato, and S. Kawata, “Surface-plasmon holography with white-light illumination,” Science 332, 218–220 (2011).

2010 (1)

A. Majumdar and R. K. Ward, “Compressed sensing of color images,” Signal Process. 90, 3122–3127 (2010).
[Crossref]

2008 (2)

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

A. Stern, Y. Rivenson, and B. Javidi, “Single-shot compressive imaging,” Proc. SPIE 6778, 67780J (2008).

2007 (4)

2006 (1)

D. Takhar, J. N. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. F. Kelly, and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” Proc. SPIE 6065, 606509 (2006).

August, Y.

Baraniuk, R.

R. Baraniuk, “Compressive sensing,” IEEE Signal Process. Mag. 24(4), 118–121 (2007).
[Crossref]

Baraniuk, R. G.

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

D. Takhar, J. N. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. F. Kelly, and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” Proc. SPIE 6065, 606509 (2006).

Baron, D.

D. Takhar, J. N. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. F. Kelly, and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” Proc. SPIE 6065, 606509 (2006).

Björklund, T.

T. Björklund and E. Magli, “A parallel compressive imaging architecture for one-shot acquisition,” arXiv preprint arXiv:1311.0646 (2013).

Bowman, R.

Brady, D.

J. Hunt, T. Driscoll, A. Mrozack, G. Lipworth, M. Reynolds, D. Brady, and D. R. Smith, “Metamaterial apertures for computational imaging,” Science 339, 310–313 (2013).
[Crossref]

Brady, D. J.

Cabrero-Vilatela, A.

C. Williams, Y. Montelongo, J. O. Tenorio-Pearl, A. Cabrero-Vilatela, S. Hofmann, W. I. Milne, and T. D. Wilkinson, “Engineered pixels using active plasmonic holograms with liquid crystals,” Phys. Status Solidi 9, 125–129 (2015).

Capasso, F.

N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13, 139–150 (2014).
[Crossref]

Chen, W. T.

W. T. Chen, K.-Y. Yang, C.-M. Wang, Y.-W. Huang, G. Sun, C. Y. Liao, W.-l. Hsu, H. T. Lin, S. Sun, L. Zhou, A. Q. Liu, and D. P. Tsai, “High-efficiency broadband meta-hologram with polarization controlled dual images,” Nano Lett. 14, 225–230 (2014).
[Crossref]

Davenport, M. A.

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

Dong, R.

H. Ohlsson, A. Yang, R. Dong, and S. Sastry, “Compressive phase retrieval from squared output measurements via semidefinite programming,” arXiv preprint arXiv:1111.6323 (2011), pp. 1–27.

Driscoll, T.

J. Hunt, T. Driscoll, A. Mrozack, G. Lipworth, M. Reynolds, D. Brady, and D. R. Smith, “Metamaterial apertures for computational imaging,” Science 339, 310–313 (2013).
[Crossref]

Duarte, M. F.

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

D. Takhar, J. N. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. F. Kelly, and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” Proc. SPIE 6065, 606509 (2006).

Edgar, M.

Gehm, M. E.

Goodman, J.

J. Goodman, Introduction to Fourier Optics (McGraw-Hill, 2008).

Hofmann, S.

C. Williams, Y. Montelongo, J. O. Tenorio-Pearl, A. Cabrero-Vilatela, S. Hofmann, W. I. Milne, and T. D. Wilkinson, “Engineered pixels using active plasmonic holograms with liquid crystals,” Phys. Status Solidi 9, 125–129 (2015).

Hsu, W.-l.

W. T. Chen, K.-Y. Yang, C.-M. Wang, Y.-W. Huang, G. Sun, C. Y. Liao, W.-l. Hsu, H. T. Lin, S. Sun, L. Zhou, A. Q. Liu, and D. P. Tsai, “High-efficiency broadband meta-hologram with polarization controlled dual images,” Nano Lett. 14, 225–230 (2014).
[Crossref]

Huang, Y.-W.

W. T. Chen, K.-Y. Yang, C.-M. Wang, Y.-W. Huang, G. Sun, C. Y. Liao, W.-l. Hsu, H. T. Lin, S. Sun, L. Zhou, A. Q. Liu, and D. P. Tsai, “High-efficiency broadband meta-hologram with polarization controlled dual images,” Nano Lett. 14, 225–230 (2014).
[Crossref]

Hunt, J.

C. M. Watts, D. Shrekenhamer, J. Montoya, G. Lipworth, J. Hunt, T. Sleasman, S. Krishna, D. R. Smith, and W. J. Padilla, “Terahertz compressive imaging with metamaterial spatial light modulators,” Nat. Photonics 8, 605–609 (2014).
[Crossref]

J. Hunt, T. Driscoll, A. Mrozack, G. Lipworth, M. Reynolds, D. Brady, and D. R. Smith, “Metamaterial apertures for computational imaging,” Science 339, 310–313 (2013).
[Crossref]

Javidi, B.

A. Stern, Y. Rivenson, and B. Javidi, “Single-shot compressive imaging,” Proc. SPIE 6778, 67780J (2008).

A. Stern and B. Javidi, “Random projections imaging with extended space-bandwidth product,” J. Disp. Technol. 3, 315–320 (2007).
[Crossref]

John, R.

Jonathan, P.

Kato, J.

M. Ozaki, J. Kato, and S. Kawata, “Surface-plasmon holography with white-light illumination,” Science 332, 218–220 (2011).

Kawata, S.

M. Ozaki, J. Kato, and S. Kawata, “Surface-plasmon holography with white-light illumination,” Science 332, 218–220 (2011).

Ke, J.

Kelly, K. F.

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

D. Takhar, J. N. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. F. Kelly, and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” Proc. SPIE 6065, 606509 (2006).

Kindness, S. J.

A. Macfaden, S. J. Kindness, and T. D. Wilkinson, “An implementation of one-shot compressive imaging using a diffractive optical element,” in Frontiers in Optics (Optical Society of America, 2015), paper FTh1F.2.

Krishna, S.

C. M. Watts, D. Shrekenhamer, J. Montoya, G. Lipworth, J. Hunt, T. Sleasman, S. Krishna, D. R. Smith, and W. J. Padilla, “Terahertz compressive imaging with metamaterial spatial light modulators,” Nat. Photonics 8, 605–609 (2014).
[Crossref]

Laska, J. N.

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

D. Takhar, J. N. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. F. Kelly, and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” Proc. SPIE 6065, 606509 (2006).

Li, B.

P. Nagesh and B. Li, “Compressive imaging of color images,” in IEEE International Conference on Acoustics, Speech and Signal Processing (IEEE, 2009), pp. 1261–1264.

Liao, C. Y.

W. T. Chen, K.-Y. Yang, C.-M. Wang, Y.-W. Huang, G. Sun, C. Y. Liao, W.-l. Hsu, H. T. Lin, S. Sun, L. Zhou, A. Q. Liu, and D. P. Tsai, “High-efficiency broadband meta-hologram with polarization controlled dual images,” Nano Lett. 14, 225–230 (2014).
[Crossref]

Lin, H. T.

W. T. Chen, K.-Y. Yang, C.-M. Wang, Y.-W. Huang, G. Sun, C. Y. Liao, W.-l. Hsu, H. T. Lin, S. Sun, L. Zhou, A. Q. Liu, and D. P. Tsai, “High-efficiency broadband meta-hologram with polarization controlled dual images,” Nano Lett. 14, 225–230 (2014).
[Crossref]

Lipworth, G.

C. M. Watts, D. Shrekenhamer, J. Montoya, G. Lipworth, J. Hunt, T. Sleasman, S. Krishna, D. R. Smith, and W. J. Padilla, “Terahertz compressive imaging with metamaterial spatial light modulators,” Nat. Photonics 8, 605–609 (2014).
[Crossref]

J. Hunt, T. Driscoll, A. Mrozack, G. Lipworth, M. Reynolds, D. Brady, and D. R. Smith, “Metamaterial apertures for computational imaging,” Science 339, 310–313 (2013).
[Crossref]

Liu, A. Q.

W. T. Chen, K.-Y. Yang, C.-M. Wang, Y.-W. Huang, G. Sun, C. Y. Liao, W.-l. Hsu, H. T. Lin, S. Sun, L. Zhou, A. Q. Liu, and D. P. Tsai, “High-efficiency broadband meta-hologram with polarization controlled dual images,” Nano Lett. 14, 225–230 (2014).
[Crossref]

Lorenz, D. A.

D. A. Lorenz, “Constructing test instances for basis pursuit denoising,” IEEE Trans. Signal Process. 61, 1210–1214 (2013).
[Crossref]

D. A. Lorenz, L1TestPack: a software to generate test instances for l1 minimization problems (2011).

Macfaden, A.

A. Macfaden, S. J. Kindness, and T. D. Wilkinson, “An implementation of one-shot compressive imaging using a diffractive optical element,” in Frontiers in Optics (Optical Society of America, 2015), paper FTh1F.2.

Magli, E.

T. Björklund and E. Magli, “A parallel compressive imaging architecture for one-shot acquisition,” arXiv preprint arXiv:1311.0646 (2013).

Majumdar, A.

A. Majumdar and R. K. Ward, “Compressed sensing of color images,” Signal Process. 90, 3122–3127 (2010).
[Crossref]

Milne, W. I.

C. Williams, Y. Montelongo, J. O. Tenorio-Pearl, A. Cabrero-Vilatela, S. Hofmann, W. I. Milne, and T. D. Wilkinson, “Engineered pixels using active plasmonic holograms with liquid crystals,” Phys. Status Solidi 9, 125–129 (2015).

Montelongo, Y.

C. Williams, Y. Montelongo, J. O. Tenorio-Pearl, A. Cabrero-Vilatela, S. Hofmann, W. I. Milne, and T. D. Wilkinson, “Engineered pixels using active plasmonic holograms with liquid crystals,” Phys. Status Solidi 9, 125–129 (2015).

Montoya, J.

C. M. Watts, D. Shrekenhamer, J. Montoya, G. Lipworth, J. Hunt, T. Sleasman, S. Krishna, D. R. Smith, and W. J. Padilla, “Terahertz compressive imaging with metamaterial spatial light modulators,” Nat. Photonics 8, 605–609 (2014).
[Crossref]

Mrozack, A.

J. Hunt, T. Driscoll, A. Mrozack, G. Lipworth, M. Reynolds, D. Brady, and D. R. Smith, “Metamaterial apertures for computational imaging,” Science 339, 310–313 (2013).
[Crossref]

Nagesh, P.

P. Nagesh and B. Li, “Compressive imaging of color images,” in IEEE International Conference on Acoustics, Speech and Signal Processing (IEEE, 2009), pp. 1261–1264.

Neifeld, M. A.

Ohlsson, H.

H. Ohlsson, A. Yang, R. Dong, and S. Sastry, “Compressive phase retrieval from squared output measurements via semidefinite programming,” arXiv preprint arXiv:1111.6323 (2011), pp. 1–27.

Ozaki, M.

M. Ozaki, J. Kato, and S. Kawata, “Surface-plasmon holography with white-light illumination,” Science 332, 218–220 (2011).

Padgett, M.

Padilla, W. J.

C. M. Watts, D. Shrekenhamer, J. Montoya, G. Lipworth, J. Hunt, T. Sleasman, S. Krishna, D. R. Smith, and W. J. Padilla, “Terahertz compressive imaging with metamaterial spatial light modulators,” Nat. Photonics 8, 605–609 (2014).
[Crossref]

Reynolds, M.

J. Hunt, T. Driscoll, A. Mrozack, G. Lipworth, M. Reynolds, D. Brady, and D. R. Smith, “Metamaterial apertures for computational imaging,” Science 339, 310–313 (2013).
[Crossref]

Rivenson, Y.

Sarvotham, S.

D. Takhar, J. N. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. F. Kelly, and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” Proc. SPIE 6065, 606509 (2006).

Sastry, S.

H. Ohlsson, A. Yang, R. Dong, and S. Sastry, “Compressive phase retrieval from squared output measurements via semidefinite programming,” arXiv preprint arXiv:1111.6323 (2011), pp. 1–27.

Schulz, T. J.

Shrekenhamer, D.

C. M. Watts, D. Shrekenhamer, J. Montoya, G. Lipworth, J. Hunt, T. Sleasman, S. Krishna, D. R. Smith, and W. J. Padilla, “Terahertz compressive imaging with metamaterial spatial light modulators,” Nat. Photonics 8, 605–609 (2014).
[Crossref]

Sleasman, T.

C. M. Watts, D. Shrekenhamer, J. Montoya, G. Lipworth, J. Hunt, T. Sleasman, S. Krishna, D. R. Smith, and W. J. Padilla, “Terahertz compressive imaging with metamaterial spatial light modulators,” Nat. Photonics 8, 605–609 (2014).
[Crossref]

Smith, D. R.

C. M. Watts, D. Shrekenhamer, J. Montoya, G. Lipworth, J. Hunt, T. Sleasman, S. Krishna, D. R. Smith, and W. J. Padilla, “Terahertz compressive imaging with metamaterial spatial light modulators,” Nat. Photonics 8, 605–609 (2014).
[Crossref]

J. Hunt, T. Driscoll, A. Mrozack, G. Lipworth, M. Reynolds, D. Brady, and D. R. Smith, “Metamaterial apertures for computational imaging,” Science 339, 310–313 (2013).
[Crossref]

Stern, A.

Y. August, C. Vachman, Y. Rivenson, and A. Stern, “Compressive hyperspectral imaging by random separable projections in both the spatial and the spectral domains,” Appl. Opt. 52, D46–D54 (2013).
[Crossref]

A. Stern, Y. Rivenson, and B. Javidi, “Single-shot compressive imaging,” Proc. SPIE 6778, 67780J (2008).

A. Stern and B. Javidi, “Random projections imaging with extended space-bandwidth product,” J. Disp. Technol. 3, 315–320 (2007).
[Crossref]

Sun, B.

Sun, G.

W. T. Chen, K.-Y. Yang, C.-M. Wang, Y.-W. Huang, G. Sun, C. Y. Liao, W.-l. Hsu, H. T. Lin, S. Sun, L. Zhou, A. Q. Liu, and D. P. Tsai, “High-efficiency broadband meta-hologram with polarization controlled dual images,” Nano Lett. 14, 225–230 (2014).
[Crossref]

Sun, S.

W. T. Chen, K.-Y. Yang, C.-M. Wang, Y.-W. Huang, G. Sun, C. Y. Liao, W.-l. Hsu, H. T. Lin, S. Sun, L. Zhou, A. Q. Liu, and D. P. Tsai, “High-efficiency broadband meta-hologram with polarization controlled dual images,” Nano Lett. 14, 225–230 (2014).
[Crossref]

Sun, T.

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

D. Takhar, J. N. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. F. Kelly, and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” Proc. SPIE 6065, 606509 (2006).

Tenorio-Pearl, J. O.

C. Williams, Y. Montelongo, J. O. Tenorio-Pearl, A. Cabrero-Vilatela, S. Hofmann, W. I. Milne, and T. D. Wilkinson, “Engineered pixels using active plasmonic holograms with liquid crystals,” Phys. Status Solidi 9, 125–129 (2015).

Tsai, D. P.

W. T. Chen, K.-Y. Yang, C.-M. Wang, Y.-W. Huang, G. Sun, C. Y. Liao, W.-l. Hsu, H. T. Lin, S. Sun, L. Zhou, A. Q. Liu, and D. P. Tsai, “High-efficiency broadband meta-hologram with polarization controlled dual images,” Nano Lett. 14, 225–230 (2014).
[Crossref]

Vachman, C.

Wakin, M. B.

D. Takhar, J. N. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. F. Kelly, and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” Proc. SPIE 6065, 606509 (2006).

Wang, C.-M.

W. T. Chen, K.-Y. Yang, C.-M. Wang, Y.-W. Huang, G. Sun, C. Y. Liao, W.-l. Hsu, H. T. Lin, S. Sun, L. Zhou, A. Q. Liu, and D. P. Tsai, “High-efficiency broadband meta-hologram with polarization controlled dual images,” Nano Lett. 14, 225–230 (2014).
[Crossref]

Ward, R. K.

A. Majumdar and R. K. Ward, “Compressed sensing of color images,” Signal Process. 90, 3122–3127 (2010).
[Crossref]

Watts, C. M.

C. M. Watts, D. Shrekenhamer, J. Montoya, G. Lipworth, J. Hunt, T. Sleasman, S. Krishna, D. R. Smith, and W. J. Padilla, “Terahertz compressive imaging with metamaterial spatial light modulators,” Nat. Photonics 8, 605–609 (2014).
[Crossref]

Welsh, S.

Wilkinson, T. D.

C. Williams, Y. Montelongo, J. O. Tenorio-Pearl, A. Cabrero-Vilatela, S. Hofmann, W. I. Milne, and T. D. Wilkinson, “Engineered pixels using active plasmonic holograms with liquid crystals,” Phys. Status Solidi 9, 125–129 (2015).

A. Macfaden, S. J. Kindness, and T. D. Wilkinson, “An implementation of one-shot compressive imaging using a diffractive optical element,” in Frontiers in Optics (Optical Society of America, 2015), paper FTh1F.2.

Willett, R. M.

Williams, C.

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Figures (5)

Fig. 1.
Fig. 1.

(a) Time-sequential compressive imaging technique that has been extensively implemented. (b) Synchronous approach being proposed, where each image pixel n directs light in known ratios toward an array of detectors m and (c) linear algebra representation showing how an image vector I is mapped onto a shorter measurement vector G by a measurement matrix H.

Fig. 2.
Fig. 2.

Fourier hologram (a) is designed to have a spot array as the replay field (b), computed using the 2D FFT. An array of these sub-holograms can be tiled together (c) to create an imaging system to implement the linear algebra required by compressive sensing.

Fig. 3.
Fig. 3.

Experimental setup (a) used to verify this technique. An example replay field (b) shows how it has been designed to keep the relevant points away from the masked zero order. Use of a dynamic SLM permits direct measurement of the matrix H, shown as an intensity map (c).

Fig. 4.
Fig. 4.

Result of optimizing toward the requirement of Eq. (4) using a number of simulated annealing iterations. The fitness function evaluates the total difference between the two sides of Eq. (4) across all the spots in the replay field, and is normalized against the value after the first round of optimization. Simulated imaging of two target images—one binary and one grayscale—with the hologram at different stages of optimization is shown. The targets are the inset images. A thresholded result is shown for the binary image. The compression ratio is 81%.

Fig. 5.
Fig. 5.

Results for imaging different targets. (a) Both overconstrained and underconstrained linear algebra problems with target images that have 36 pixels. In the overconstrained case, 80 measurements were used, while the underconstrained case used 28 measurements. (b) Target is more sparse in the discrete cosine transform basis, which produced excellent recovery with 28 measurements.

Equations (12)

Equations on this page are rendered with MathJax. Learn more.

(G1GM)=(H11H12H21HM1,NHM,N1HM,N)(I1I2IN),
G=HI=(HD1)(DI)=AS,
g=hi,
spot|A+B|2dS=spot(|A|2+|B|2)dS,
|A|2+|B|2=|A+B|2,
A=aejα,aR,π<απ
B=bejβ,bR,π<βπ.
a2+b2=|aejα+bejβ|2=(aejα+bejβ)(aejα+bejβ)=a2+b2+ab(ej(αβ)+ej(βα))=a2+b2+abej(αβ)+ej(βα).
X=Rλu,
A=(Rλd)2.
M=2πR2(Rλd)2=2πd2λ2.
In=I(x,y,λ,pol)

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