Abstract

Single pixel imaging can be the preferred method over traditional 2D-array imaging in spectral ranges where conventional cameras are not available. However, when it comes to real-time video imaging, single pixel imaging cannot compete with the framerates of conventional cameras, especially when high-resolution images are desired. Here we evaluate the performance of an imaging approach using two detectors simultaneously. First, we present theoretical results on how low SNR affects final image quality followed by experimentally determined results. Obtained video framerates were doubled compared to state of the art systems, resulting in a framerate from 22 Hz for a 32×32 resolution to 0.75 Hz for a 128×128 resolution image. Additionally, the two detector imaging technique enables the acquisition of images with a resolution of 256×256 in less than 3 s.

© 2016 Optical Society of America

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  22. S. S. Welsh, M. P. Edgar, R. Bowman, P. Jonathan, B. Sun, and M. J. Padgett, “Fast full-color computational imaging with single-pixel detectors,” Opt. Express 21, 23068–23074 (2013).
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  31. K. Shibuya, K. Nakae, Y. Mizutani, and T. Iwata, “Comparison of reconstructed images between ghost imaging and Hadamard transform imaging,” Opt. Rev. 22, 897–902 (2015).
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  32. K. Guo, S. Jiang, and G. Zheng, “Multilayer fluorescence imaging on a single-pixel detector,” Biomed. Opt. Express 7, 2425–2431 (2016).
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  33. N. Huynh, E. Zhang, M. Betcke, S. Arridge, P. Beard, and B. Cox, “Single-pixel optical camera for video rate ultrasonic imaging,” Optica 3, 26–29 (2016).
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  35. B. Lochocki, A. Gambín, S. Manzanera, E. Irles, E. Tajahuerce, J. Lancis, and P. Artal, “Single pixel camera ophthalmoscope,” Optica 3, 1056–1059 (2016).
    [Crossref]

2016 (8)

F. Soldevila, P. Clemente, E. Tajahuerce, N. Uribe-Patarroyo, P. Andrés, and J. Lancis, “Computational imaging with a balanced detector,” Sci. Rep. 6, 29181 (2016).
[Crossref]

W. K. Yu, X. R. Yao, X. F. Liu, R. M. Lan, L. A. Wu, G. J. Zhai, and Q. Zhao, “Compressive microscopic imaging with “positive-negative” light modulation,” Opt. Commun. 371, 105–111 (2016).
[Crossref]

M. J. Sun, M. P. Edgar, G. M. Gibson, B. Sun, N. Radwell, R. Lamb, and M. J. Padgett, “Single-pixel 3D imaging with time-based depth resolution,” Nat. Commun. 7, 1–10 (2016).

N. Huynh, E. Zhang, M. Betcke, S. Arridge, P. Beard, and B. Cox, “Single-pixel optical camera for video rate ultrasonic imaging,” Optica 3, 26–29 (2016).
[Crossref]

J. P. Dumas, M. A. Lodhi, W. U. Bajwa, and M. C. Pierce, “Computational imaging with a highly parallel image-plane-coded architecture: challenges and solutions,” Opt. Express 24, 6145–6155 (2016).
[Crossref]

M. J. Sun, M. P. Edgar, D. B. Phillips, G. M. Gibson, and M. J. Padgett, “Improving the signal-to-noise ratio of single-pixel imaging using digital microscanning,” Opt. Express 24, 10476–10485 (2016).
[Crossref]

K. Guo, S. Jiang, and G. Zheng, “Multilayer fluorescence imaging on a single-pixel detector,” Biomed. Opt. Express 7, 2425–2431 (2016).
[Crossref]

B. Lochocki, A. Gambín, S. Manzanera, E. Irles, E. Tajahuerce, J. Lancis, and P. Artal, “Single pixel camera ophthalmoscope,” Optica 3, 1056–1059 (2016).
[Crossref]

2015 (4)

K. Nitta, S. Hayashi, and O. Matoba, “Divided Hadamard pattern illumination for fewer times measurements,” Work. Inf. Opt. 20152, 1–3 (2015).

K. Shibuya, K. Nakae, Y. Mizutani, and T. Iwata, “Comparison of reconstructed images between ghost imaging and Hadamard transform imaging,” Opt. Rev. 22, 897–902 (2015).
[Crossref]

Z. Zhang, X. Ma, and J. Zhong, “Single-pixel imaging by means of Fourier spectrum acquisition,” Nat. Commun. 6, 1–6 (2015).

M. P. Edgar, G. M. Gibson, R. W. Bowman, B. Sun, N. Radwell, K. J. Mitchell, S. S. Welsh, and M. J. Padgett, “Simultaneous real-time visible and infrared video with single-pixel detectors,” Sci. Rep. 5, 10669 (2015).
[Crossref]

2014 (4)

2013 (2)

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

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, “3D computational imaging with single-pixel detectors,” Science 340, 844–847 (2013).
[Crossref]

2012 (1)

2011 (1)

R. M. Willett, R. F. Marcia, and J. M. Nichols, “Compressed sensing for practical optical imaging systems: a tutorial,” Opt. Eng. 50, 72601–72613 (2011).
[Crossref]

2010 (1)

F. Ferri, D. Magatti, L. A. Lugiato, and A. Gatti, “Differential ghost imaging,” Phys. Rev. Lett. 104, 1–4 (2010).
[Crossref]

2009 (1)

2008 (1)

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]

2007 (1)

E. Candès and J. Romberg, “Sparsity and incoherence in compressive sampling,” Inverse Probl. 23, 969–985 (2007).
[Crossref]

2001 (1)

R. Coifman, F. Geshwind, and Y. Meyer, “Noiselets,” Appl. Comput. Harmon. Anal. 10, 27–44 (2001).
[Crossref]

1985 (1)

C. F. Chen and W. K. Leung, “Algorithms for converting sequence-, dyadic-, and Hadamard-ordered Walsh functions,” Math. Comput. Simul. 27, 471–478 (1985).
[Crossref]

1969 (1)

W. K. Pratt, J. Kane, and H. C. Andrews, “Hadamard transform image coding,” Proc. IEEE 57, 58–68 (1969).
[Crossref]

Amirparviz, B.

X. Miao and B. Amirparviz, “Single pixel camera,” U.S. patentUS20150042834 A1 (12February2015).

Andrés, P.

F. Soldevila, P. Clemente, E. Tajahuerce, N. Uribe-Patarroyo, P. Andrés, and J. Lancis, “Computational imaging with a balanced detector,” Sci. Rep. 6, 29181 (2016).
[Crossref]

E. Tajahuerce, V. Durán, P. Clemente, E. Irles, F. Soldevila, P. Andrés, and J. Lancis, “Image transmission through dynamic scattering media by single-pixel photodetection,” Opt. Express 22, 16945–16955 (2014).
[Crossref]

Andrews, H. C.

W. K. Pratt, J. Kane, and H. C. Andrews, “Hadamard transform image coding,” Proc. IEEE 57, 58–68 (1969).
[Crossref]

Arridge, S.

Artal, P.

Bajwa, W. U.

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]

M. B. Wakin, J. N. Laska, M. F. Duarte, D. Baron, S. Sarvotham, D. Takhar, K. F. Kelly, and R. G. Baraniuk, “An architecture for compressive imaging,” in International Conference on Image Processing (IEEE, 2006), pp. 1273–1276.

R. G. Baraniuk, K. F. Kelly, R. F. Bridge, S. Chatterjee, and L. McMackin, “Dual-port measurements of light reflected from micromirror array,” U.S. patent8717466 B2 (4September, 2014).

Baron, D.

M. B. Wakin, J. N. Laska, M. F. Duarte, D. Baron, S. Sarvotham, D. Takhar, K. F. Kelly, and R. G. Baraniuk, “An architecture for compressive imaging,” in International Conference on Image Processing (IEEE, 2006), pp. 1273–1276.

Beard, P.

Betcke, M.

Bowman, A.

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, “3D computational imaging with single-pixel detectors,” Science 340, 844–847 (2013).
[Crossref]

Bowman, R.

Bowman, R. W.

M. P. Edgar, G. M. Gibson, R. W. Bowman, B. Sun, N. Radwell, K. J. Mitchell, S. S. Welsh, and M. J. Padgett, “Simultaneous real-time visible and infrared video with single-pixel detectors,” Sci. Rep. 5, 10669 (2015).
[Crossref]

Bridge, R. F.

R. G. Baraniuk, K. F. Kelly, R. F. Bridge, S. Chatterjee, and L. McMackin, “Dual-port measurements of light reflected from micromirror array,” U.S. patent8717466 B2 (4September, 2014).

Burling-Claridge, G. R.

Candès, E.

E. Candès and J. Romberg, “Sparsity and incoherence in compressive sampling,” Inverse Probl. 23, 969–985 (2007).
[Crossref]

Chatterjee, S.

R. G. Baraniuk, K. F. Kelly, R. F. Bridge, S. Chatterjee, and L. McMackin, “Dual-port measurements of light reflected from micromirror array,” U.S. patent8717466 B2 (4September, 2014).

Chen, C. F.

C. F. Chen and W. K. Leung, “Algorithms for converting sequence-, dyadic-, and Hadamard-ordered Walsh functions,” Math. Comput. Simul. 27, 471–478 (1985).
[Crossref]

Clemente, P.

Coifman, R.

R. Coifman, F. Geshwind, and Y. Meyer, “Noiselets,” Appl. Comput. Harmon. Anal. 10, 27–44 (2001).
[Crossref]

Cox, B.

Cree, M. J.

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]

Dawson, R.

S. J. Olivas, Y. Rachlin, L. Gu, B. Gardiner, R. Dawson, J. P. Laine, and J. Ford, Single Pixel Compressive Imaging of Laboratory and Natural Light Scenes (2013).

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]

M. B. Wakin, J. N. Laska, M. F. Duarte, D. Baron, S. Sarvotham, D. Takhar, K. F. Kelly, and R. G. Baraniuk, “An architecture for compressive imaging,” in International Conference on Image Processing (IEEE, 2006), pp. 1273–1276.

Dumas, J. P.

Durán, V.

Edgar, M. P.

M. J. Sun, M. P. Edgar, G. M. Gibson, B. Sun, N. Radwell, R. Lamb, and M. J. Padgett, “Single-pixel 3D imaging with time-based depth resolution,” Nat. Commun. 7, 1–10 (2016).

M. J. Sun, M. P. Edgar, D. B. Phillips, G. M. Gibson, and M. J. Padgett, “Improving the signal-to-noise ratio of single-pixel imaging using digital microscanning,” Opt. Express 24, 10476–10485 (2016).
[Crossref]

M. P. Edgar, G. M. Gibson, R. W. Bowman, B. Sun, N. Radwell, K. J. Mitchell, S. S. Welsh, and M. J. Padgett, “Simultaneous real-time visible and infrared video with single-pixel detectors,” Sci. Rep. 5, 10669 (2015).
[Crossref]

N. Radwell, K. J. Mitchell, G. M. Gibson, M. P. Edgar, R. Bowman, and M. J. Padgett, “Single-pixel infrared and visible microscope,” Optica 1, 285–289 (2014).
[Crossref]

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

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, “3D computational imaging with single-pixel detectors,” Science 340, 844–847 (2013).
[Crossref]

B. Sun, S. S. Welsh, M. P. Edgar, J. H. Shapiro, and M. J. Padgett, “Normalized ghost imaging,” Opt. Express 20, 16892–16901 (2012).
[Crossref]

Ferri, F.

F. Ferri, D. Magatti, L. A. Lugiato, and A. Gatti, “Differential ghost imaging,” Phys. Rev. Lett. 104, 1–4 (2010).
[Crossref]

Ford, J.

S. J. Olivas, Y. Rachlin, L. Gu, B. Gardiner, R. Dawson, J. P. Laine, and J. Ford, Single Pixel Compressive Imaging of Laboratory and Natural Light Scenes (2013).

Gambín, A.

Gardiner, B.

S. J. Olivas, Y. Rachlin, L. Gu, B. Gardiner, R. Dawson, J. P. Laine, and J. Ford, Single Pixel Compressive Imaging of Laboratory and Natural Light Scenes (2013).

Gatti, A.

F. Ferri, D. Magatti, L. A. Lugiato, and A. Gatti, “Differential ghost imaging,” Phys. Rev. Lett. 104, 1–4 (2010).
[Crossref]

Geshwind, F.

R. Coifman, F. Geshwind, and Y. Meyer, “Noiselets,” Appl. Comput. Harmon. Anal. 10, 27–44 (2001).
[Crossref]

Gibson, G. M.

M. J. Sun, M. P. Edgar, G. M. Gibson, B. Sun, N. Radwell, R. Lamb, and M. J. Padgett, “Single-pixel 3D imaging with time-based depth resolution,” Nat. Commun. 7, 1–10 (2016).

M. J. Sun, M. P. Edgar, D. B. Phillips, G. M. Gibson, and M. J. Padgett, “Improving the signal-to-noise ratio of single-pixel imaging using digital microscanning,” Opt. Express 24, 10476–10485 (2016).
[Crossref]

M. P. Edgar, G. M. Gibson, R. W. Bowman, B. Sun, N. Radwell, K. J. Mitchell, S. S. Welsh, and M. J. Padgett, “Simultaneous real-time visible and infrared video with single-pixel detectors,” Sci. Rep. 5, 10669 (2015).
[Crossref]

N. Radwell, K. J. Mitchell, G. M. Gibson, M. P. Edgar, R. Bowman, and M. J. Padgett, “Single-pixel infrared and visible microscope,” Optica 1, 285–289 (2014).
[Crossref]

R. I. Stantchev, B. Sun, S. M. Hornett, P. A. Hobson, G. M. Gibson, M. J. Padgett, and E. Hendry, “Non-invasive, near-field terahertz imaging of hidden objects using a single pixel detector,” arXiv (2015).

Gu, L.

S. J. Olivas, Y. Rachlin, L. Gu, B. Gardiner, R. Dawson, J. P. Laine, and J. Ford, Single Pixel Compressive Imaging of Laboratory and Natural Light Scenes (2013).

Guo, K.

Gupta, M.

J. Wang, M. Gupta, and A. C. Sankaranarayanan, “LiSens—A scalable architecture for video compressive sensing,” arXiv (2015).

Hayashi, S.

K. Nitta, S. Hayashi, and O. Matoba, “Divided Hadamard pattern illumination for fewer times measurements,” Work. Inf. Opt. 20152, 1–3 (2015).

Hendry, E.

R. I. Stantchev, B. Sun, S. M. Hornett, P. A. Hobson, G. M. Gibson, M. J. Padgett, and E. Hendry, “Non-invasive, near-field terahertz imaging of hidden objects using a single pixel detector,” arXiv (2015).

Hobson, P. A.

R. I. Stantchev, B. Sun, S. M. Hornett, P. A. Hobson, G. M. Gibson, M. J. Padgett, and E. Hendry, “Non-invasive, near-field terahertz imaging of hidden objects using a single pixel detector,” arXiv (2015).

Hornett, S. M.

R. I. Stantchev, B. Sun, S. M. Hornett, P. A. Hobson, G. M. Gibson, M. J. Padgett, and E. Hendry, “Non-invasive, near-field terahertz imaging of hidden objects using a single pixel detector,” arXiv (2015).

Huynh, N.

Irles, E.

Iwata, T.

K. Shibuya, K. Nakae, Y. Mizutani, and T. Iwata, “Comparison of reconstructed images between ghost imaging and Hadamard transform imaging,” Opt. Rev. 22, 897–902 (2015).
[Crossref]

Jiang, S.

Jonathan, P.

Kane, J.

W. K. Pratt, J. Kane, and H. C. Andrews, “Hadamard transform image coding,” Proc. IEEE 57, 58–68 (1969).
[Crossref]

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]

M. B. Wakin, J. N. Laska, M. F. Duarte, D. Baron, S. Sarvotham, D. Takhar, K. F. Kelly, and R. G. Baraniuk, “An architecture for compressive imaging,” in International Conference on Image Processing (IEEE, 2006), pp. 1273–1276.

R. G. Baraniuk, K. F. Kelly, R. F. Bridge, S. Chatterjee, and L. McMackin, “Dual-port measurements of light reflected from micromirror array,” U.S. patent8717466 B2 (4September, 2014).

Künnemeyer, R.

Laine, J. P.

S. J. Olivas, Y. Rachlin, L. Gu, B. Gardiner, R. Dawson, J. P. Laine, and J. Ford, Single Pixel Compressive Imaging of Laboratory and Natural Light Scenes (2013).

Lamb, R.

M. J. Sun, M. P. Edgar, G. M. Gibson, B. Sun, N. Radwell, R. Lamb, and M. J. Padgett, “Single-pixel 3D imaging with time-based depth resolution,” Nat. Commun. 7, 1–10 (2016).

Lan, R. M.

W. K. Yu, X. R. Yao, X. F. Liu, R. M. Lan, L. A. Wu, G. J. Zhai, and Q. Zhao, “Compressive microscopic imaging with “positive-negative” light modulation,” Opt. Commun. 371, 105–111 (2016).
[Crossref]

Lancis, J.

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]

M. B. Wakin, J. N. Laska, M. F. Duarte, D. Baron, S. Sarvotham, D. Takhar, K. F. Kelly, and R. G. Baraniuk, “An architecture for compressive imaging,” in International Conference on Image Processing (IEEE, 2006), pp. 1273–1276.

Leung, W. K.

C. F. Chen and W. K. Leung, “Algorithms for converting sequence-, dyadic-, and Hadamard-ordered Walsh functions,” Math. Comput. Simul. 27, 471–478 (1985).
[Crossref]

Liu, X. F.

W. K. Yu, X. R. Yao, X. F. Liu, R. M. Lan, L. A. Wu, G. J. Zhai, and Q. Zhao, “Compressive microscopic imaging with “positive-negative” light modulation,” Opt. Commun. 371, 105–111 (2016).
[Crossref]

W. K. Yu, X. F. Liu, X. R. Yao, C. Wang, Y. Zhai, and G. J. Zhai, “Complementary compressive imaging for the telescopic system,” Sci. Rep. 4, 5834 (2014).

Liu, Y.

H. Yu, Y. Liu, Y. Peng, W. Xu, and M. Zhang, “A portable single-pixel camera based on coarse-to-fine coding light,” in IEEE International Conference on Imaging Systems and Techniques (IST) (2015), pp. 1–5.

Lochocki, B.

Lodhi, M. A.

Lugiato, L. A.

F. Ferri, D. Magatti, L. A. Lugiato, and A. Gatti, “Differential ghost imaging,” Phys. Rev. Lett. 104, 1–4 (2010).
[Crossref]

Ma, X.

Z. Zhang, X. Ma, and J. Zhong, “Single-pixel imaging by means of Fourier spectrum acquisition,” Nat. Commun. 6, 1–6 (2015).

Magatti, D.

F. Ferri, D. Magatti, L. A. Lugiato, and A. Gatti, “Differential ghost imaging,” Phys. Rev. Lett. 104, 1–4 (2010).
[Crossref]

Manzanera, S.

Marcia, R. F.

R. M. Willett, R. F. Marcia, and J. M. Nichols, “Compressed sensing for practical optical imaging systems: a tutorial,” Opt. Eng. 50, 72601–72613 (2011).
[Crossref]

Matoba, O.

K. Nitta, S. Hayashi, and O. Matoba, “Divided Hadamard pattern illumination for fewer times measurements,” Work. Inf. Opt. 20152, 1–3 (2015).

McMackin, L.

R. G. Baraniuk, K. F. Kelly, R. F. Bridge, S. Chatterjee, and L. McMackin, “Dual-port measurements of light reflected from micromirror array,” U.S. patent8717466 B2 (4September, 2014).

Meyer, Y.

R. Coifman, F. Geshwind, and Y. Meyer, “Noiselets,” Appl. Comput. Harmon. Anal. 10, 27–44 (2001).
[Crossref]

Miao, X.

X. Miao and B. Amirparviz, “Single pixel camera,” U.S. patentUS20150042834 A1 (12February2015).

Mitchell, K. J.

M. P. Edgar, G. M. Gibson, R. W. Bowman, B. Sun, N. Radwell, K. J. Mitchell, S. S. Welsh, and M. J. Padgett, “Simultaneous real-time visible and infrared video with single-pixel detectors,” Sci. Rep. 5, 10669 (2015).
[Crossref]

N. Radwell, K. J. Mitchell, G. M. Gibson, M. P. Edgar, R. Bowman, and M. J. Padgett, “Single-pixel infrared and visible microscope,” Optica 1, 285–289 (2014).
[Crossref]

Mizutani, Y.

K. Shibuya, K. Nakae, Y. Mizutani, and T. Iwata, “Comparison of reconstructed images between ghost imaging and Hadamard transform imaging,” Opt. Rev. 22, 897–902 (2015).
[Crossref]

Nakae, K.

K. Shibuya, K. Nakae, Y. Mizutani, and T. Iwata, “Comparison of reconstructed images between ghost imaging and Hadamard transform imaging,” Opt. Rev. 22, 897–902 (2015).
[Crossref]

Nichols, J. M.

R. M. Willett, R. F. Marcia, and J. M. Nichols, “Compressed sensing for practical optical imaging systems: a tutorial,” Opt. Eng. 50, 72601–72613 (2011).
[Crossref]

Nitta, K.

K. Nitta, S. Hayashi, and O. Matoba, “Divided Hadamard pattern illumination for fewer times measurements,” Work. Inf. Opt. 20152, 1–3 (2015).

Olivas, S. J.

S. J. Olivas, Y. Rachlin, L. Gu, B. Gardiner, R. Dawson, J. P. Laine, and J. Ford, Single Pixel Compressive Imaging of Laboratory and Natural Light Scenes (2013).

Padgett, M. J.

M. J. Sun, M. P. Edgar, G. M. Gibson, B. Sun, N. Radwell, R. Lamb, and M. J. Padgett, “Single-pixel 3D imaging with time-based depth resolution,” Nat. Commun. 7, 1–10 (2016).

M. J. Sun, M. P. Edgar, D. B. Phillips, G. M. Gibson, and M. J. Padgett, “Improving the signal-to-noise ratio of single-pixel imaging using digital microscanning,” Opt. Express 24, 10476–10485 (2016).
[Crossref]

M. P. Edgar, G. M. Gibson, R. W. Bowman, B. Sun, N. Radwell, K. J. Mitchell, S. S. Welsh, and M. J. Padgett, “Simultaneous real-time visible and infrared video with single-pixel detectors,” Sci. Rep. 5, 10669 (2015).
[Crossref]

N. Radwell, K. J. Mitchell, G. M. Gibson, M. P. Edgar, R. Bowman, and M. J. Padgett, “Single-pixel infrared and visible microscope,” Optica 1, 285–289 (2014).
[Crossref]

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

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, “3D computational imaging with single-pixel detectors,” Science 340, 844–847 (2013).
[Crossref]

B. Sun, S. S. Welsh, M. P. Edgar, J. H. Shapiro, and M. J. Padgett, “Normalized ghost imaging,” Opt. Express 20, 16892–16901 (2012).
[Crossref]

R. I. Stantchev, B. Sun, S. M. Hornett, P. A. Hobson, G. M. Gibson, M. J. Padgett, and E. Hendry, “Non-invasive, near-field terahertz imaging of hidden objects using a single pixel detector,” arXiv (2015).

Peng, Y.

H. Yu, Y. Liu, Y. Peng, W. Xu, and M. Zhang, “A portable single-pixel camera based on coarse-to-fine coding light,” in IEEE International Conference on Imaging Systems and Techniques (IST) (2015), pp. 1–5.

Phillips, D. B.

Pierce, M. C.

Pratt, W. K.

W. K. Pratt, J. Kane, and H. C. Andrews, “Hadamard transform image coding,” Proc. IEEE 57, 58–68 (1969).
[Crossref]

Rachlin, Y.

S. J. Olivas, Y. Rachlin, L. Gu, B. Gardiner, R. Dawson, J. P. Laine, and J. Ford, Single Pixel Compressive Imaging of Laboratory and Natural Light Scenes (2013).

Radwell, N.

M. J. Sun, M. P. Edgar, G. M. Gibson, B. Sun, N. Radwell, R. Lamb, and M. J. Padgett, “Single-pixel 3D imaging with time-based depth resolution,” Nat. Commun. 7, 1–10 (2016).

M. P. Edgar, G. M. Gibson, R. W. Bowman, B. Sun, N. Radwell, K. J. Mitchell, S. S. Welsh, and M. J. Padgett, “Simultaneous real-time visible and infrared video with single-pixel detectors,” Sci. Rep. 5, 10669 (2015).
[Crossref]

N. Radwell, K. J. Mitchell, G. M. Gibson, M. P. Edgar, R. Bowman, and M. J. Padgett, “Single-pixel infrared and visible microscope,” Optica 1, 285–289 (2014).
[Crossref]

Rodríguez, A. D.

Romberg, J.

E. Candès and J. Romberg, “Sparsity and incoherence in compressive sampling,” Inverse Probl. 23, 969–985 (2007).
[Crossref]

Sankaranarayanan, A. C.

J. Wang, M. Gupta, and A. C. Sankaranarayanan, “LiSens—A scalable architecture for video compressive sensing,” arXiv (2015).

Sarvotham, S.

M. B. Wakin, J. N. Laska, M. F. Duarte, D. Baron, S. Sarvotham, D. Takhar, K. F. Kelly, and R. G. Baraniuk, “An architecture for compressive imaging,” in International Conference on Image Processing (IEEE, 2006), pp. 1273–1276.

Shapiro, J. H.

Shibuya, K.

K. Shibuya, K. Nakae, Y. Mizutani, and T. Iwata, “Comparison of reconstructed images between ghost imaging and Hadamard transform imaging,” Opt. Rev. 22, 897–902 (2015).
[Crossref]

Soldevila, F.

F. Soldevila, P. Clemente, E. Tajahuerce, N. Uribe-Patarroyo, P. Andrés, and J. Lancis, “Computational imaging with a balanced detector,” Sci. Rep. 6, 29181 (2016).
[Crossref]

E. Tajahuerce, V. Durán, P. Clemente, E. Irles, F. Soldevila, P. Andrés, and J. Lancis, “Image transmission through dynamic scattering media by single-pixel photodetection,” Opt. Express 22, 16945–16955 (2014).
[Crossref]

Stantchev, R. I.

R. I. Stantchev, B. Sun, S. M. Hornett, P. A. Hobson, G. M. Gibson, M. J. Padgett, and E. Hendry, “Non-invasive, near-field terahertz imaging of hidden objects using a single pixel detector,” arXiv (2015).

Streeter, L.

Sun, B.

M. J. Sun, M. P. Edgar, G. M. Gibson, B. Sun, N. Radwell, R. Lamb, and M. J. Padgett, “Single-pixel 3D imaging with time-based depth resolution,” Nat. Commun. 7, 1–10 (2016).

M. P. Edgar, G. M. Gibson, R. W. Bowman, B. Sun, N. Radwell, K. J. Mitchell, S. S. Welsh, and M. J. Padgett, “Simultaneous real-time visible and infrared video with single-pixel detectors,” Sci. Rep. 5, 10669 (2015).
[Crossref]

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, “3D computational imaging with single-pixel detectors,” Science 340, 844–847 (2013).
[Crossref]

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

B. Sun, S. S. Welsh, M. P. Edgar, J. H. Shapiro, and M. J. Padgett, “Normalized ghost imaging,” Opt. Express 20, 16892–16901 (2012).
[Crossref]

R. I. Stantchev, B. Sun, S. M. Hornett, P. A. Hobson, G. M. Gibson, M. J. Padgett, and E. Hendry, “Non-invasive, near-field terahertz imaging of hidden objects using a single pixel detector,” arXiv (2015).

Sun, M. J.

M. J. Sun, M. P. Edgar, G. M. Gibson, B. Sun, N. Radwell, R. Lamb, and M. J. Padgett, “Single-pixel 3D imaging with time-based depth resolution,” Nat. Commun. 7, 1–10 (2016).

M. J. Sun, M. P. Edgar, D. B. Phillips, G. M. Gibson, and M. J. Padgett, “Improving the signal-to-noise ratio of single-pixel imaging using digital microscanning,” Opt. Express 24, 10476–10485 (2016).
[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]

Tajahuerce, E.

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]

M. B. Wakin, J. N. Laska, M. F. Duarte, D. Baron, S. Sarvotham, D. Takhar, K. F. Kelly, and R. G. Baraniuk, “An architecture for compressive imaging,” in International Conference on Image Processing (IEEE, 2006), pp. 1273–1276.

Uribe-Patarroyo, N.

F. Soldevila, P. Clemente, E. Tajahuerce, N. Uribe-Patarroyo, P. Andrés, and J. Lancis, “Computational imaging with a balanced detector,” Sci. Rep. 6, 29181 (2016).
[Crossref]

Vittert, L. E.

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, “3D computational imaging with single-pixel detectors,” Science 340, 844–847 (2013).
[Crossref]

Wakin, M. B.

M. B. Wakin, J. N. Laska, M. F. Duarte, D. Baron, S. Sarvotham, D. Takhar, K. F. Kelly, and R. G. Baraniuk, “An architecture for compressive imaging,” in International Conference on Image Processing (IEEE, 2006), pp. 1273–1276.

Wang, C.

W. K. Yu, X. F. Liu, X. R. Yao, C. Wang, Y. Zhai, and G. J. Zhai, “Complementary compressive imaging for the telescopic system,” Sci. Rep. 4, 5834 (2014).

Wang, J.

J. Wang, M. Gupta, and A. C. Sankaranarayanan, “LiSens—A scalable architecture for video compressive sensing,” arXiv (2015).

Welsh, S.

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, “3D computational imaging with single-pixel detectors,” Science 340, 844–847 (2013).
[Crossref]

Welsh, S. S.

Willett, R. M.

R. M. Willett, R. F. Marcia, and J. M. Nichols, “Compressed sensing for practical optical imaging systems: a tutorial,” Opt. Eng. 50, 72601–72613 (2011).
[Crossref]

Wu, L. A.

W. K. Yu, X. R. Yao, X. F. Liu, R. M. Lan, L. A. Wu, G. J. Zhai, and Q. Zhao, “Compressive microscopic imaging with “positive-negative” light modulation,” Opt. Commun. 371, 105–111 (2016).
[Crossref]

Xu, W.

H. Yu, Y. Liu, Y. Peng, W. Xu, and M. Zhang, “A portable single-pixel camera based on coarse-to-fine coding light,” in IEEE International Conference on Imaging Systems and Techniques (IST) (2015), pp. 1–5.

Yao, X. R.

W. K. Yu, X. R. Yao, X. F. Liu, R. M. Lan, L. A. Wu, G. J. Zhai, and Q. Zhao, “Compressive microscopic imaging with “positive-negative” light modulation,” Opt. Commun. 371, 105–111 (2016).
[Crossref]

W. K. Yu, X. F. Liu, X. R. Yao, C. Wang, Y. Zhai, and G. J. Zhai, “Complementary compressive imaging for the telescopic system,” Sci. Rep. 4, 5834 (2014).

Yu, H.

H. Yu, Y. Liu, Y. Peng, W. Xu, and M. Zhang, “A portable single-pixel camera based on coarse-to-fine coding light,” in IEEE International Conference on Imaging Systems and Techniques (IST) (2015), pp. 1–5.

Yu, W. K.

W. K. Yu, X. R. Yao, X. F. Liu, R. M. Lan, L. A. Wu, G. J. Zhai, and Q. Zhao, “Compressive microscopic imaging with “positive-negative” light modulation,” Opt. Commun. 371, 105–111 (2016).
[Crossref]

W. K. Yu, X. F. Liu, X. R. Yao, C. Wang, Y. Zhai, and G. J. Zhai, “Complementary compressive imaging for the telescopic system,” Sci. Rep. 4, 5834 (2014).

Zhai, G. J.

W. K. Yu, X. R. Yao, X. F. Liu, R. M. Lan, L. A. Wu, G. J. Zhai, and Q. Zhao, “Compressive microscopic imaging with “positive-negative” light modulation,” Opt. Commun. 371, 105–111 (2016).
[Crossref]

W. K. Yu, X. F. Liu, X. R. Yao, C. Wang, Y. Zhai, and G. J. Zhai, “Complementary compressive imaging for the telescopic system,” Sci. Rep. 4, 5834 (2014).

Zhai, Y.

W. K. Yu, X. F. Liu, X. R. Yao, C. Wang, Y. Zhai, and G. J. Zhai, “Complementary compressive imaging for the telescopic system,” Sci. Rep. 4, 5834 (2014).

Zhang, E.

Zhang, M.

H. Yu, Y. Liu, Y. Peng, W. Xu, and M. Zhang, “A portable single-pixel camera based on coarse-to-fine coding light,” in IEEE International Conference on Imaging Systems and Techniques (IST) (2015), pp. 1–5.

Zhang, Z.

Z. Zhang, X. Ma, and J. Zhong, “Single-pixel imaging by means of Fourier spectrum acquisition,” Nat. Commun. 6, 1–6 (2015).

Zhao, Q.

W. K. Yu, X. R. Yao, X. F. Liu, R. M. Lan, L. A. Wu, G. J. Zhai, and Q. Zhao, “Compressive microscopic imaging with “positive-negative” light modulation,” Opt. Commun. 371, 105–111 (2016).
[Crossref]

Zheng, G.

Zhong, J.

Z. Zhang, X. Ma, and J. Zhong, “Single-pixel imaging by means of Fourier spectrum acquisition,” Nat. Commun. 6, 1–6 (2015).

Appl. Comput. Harmon. Anal. (1)

R. Coifman, F. Geshwind, and Y. Meyer, “Noiselets,” Appl. Comput. Harmon. Anal. 10, 27–44 (2001).
[Crossref]

Appl. Opt. (1)

Biomed. Opt. Express (1)

IEEE Signal Process. Mag. (1)

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]

Inverse Probl. (1)

E. Candès and J. Romberg, “Sparsity and incoherence in compressive sampling,” Inverse Probl. 23, 969–985 (2007).
[Crossref]

Math. Comput. Simul. (1)

C. F. Chen and W. K. Leung, “Algorithms for converting sequence-, dyadic-, and Hadamard-ordered Walsh functions,” Math. Comput. Simul. 27, 471–478 (1985).
[Crossref]

Nat. Commun. (2)

Z. Zhang, X. Ma, and J. Zhong, “Single-pixel imaging by means of Fourier spectrum acquisition,” Nat. Commun. 6, 1–6 (2015).

M. J. Sun, M. P. Edgar, G. M. Gibson, B. Sun, N. Radwell, R. Lamb, and M. J. Padgett, “Single-pixel 3D imaging with time-based depth resolution,” Nat. Commun. 7, 1–10 (2016).

Opt. Commun. (1)

W. K. Yu, X. R. Yao, X. F. Liu, R. M. Lan, L. A. Wu, G. J. Zhai, and Q. Zhao, “Compressive microscopic imaging with “positive-negative” light modulation,” Opt. Commun. 371, 105–111 (2016).
[Crossref]

Opt. Eng. (1)

R. M. Willett, R. F. Marcia, and J. M. Nichols, “Compressed sensing for practical optical imaging systems: a tutorial,” Opt. Eng. 50, 72601–72613 (2011).
[Crossref]

Opt. Express (5)

Opt. Lett. (1)

Opt. Rev. (1)

K. Shibuya, K. Nakae, Y. Mizutani, and T. Iwata, “Comparison of reconstructed images between ghost imaging and Hadamard transform imaging,” Opt. Rev. 22, 897–902 (2015).
[Crossref]

Optica (3)

Phys. Rev. Lett. (1)

F. Ferri, D. Magatti, L. A. Lugiato, and A. Gatti, “Differential ghost imaging,” Phys. Rev. Lett. 104, 1–4 (2010).
[Crossref]

Proc. IEEE (1)

W. K. Pratt, J. Kane, and H. C. Andrews, “Hadamard transform image coding,” Proc. IEEE 57, 58–68 (1969).
[Crossref]

Sci. Rep. (3)

M. P. Edgar, G. M. Gibson, R. W. Bowman, B. Sun, N. Radwell, K. J. Mitchell, S. S. Welsh, and M. J. Padgett, “Simultaneous real-time visible and infrared video with single-pixel detectors,” Sci. Rep. 5, 10669 (2015).
[Crossref]

F. Soldevila, P. Clemente, E. Tajahuerce, N. Uribe-Patarroyo, P. Andrés, and J. Lancis, “Computational imaging with a balanced detector,” Sci. Rep. 6, 29181 (2016).
[Crossref]

W. K. Yu, X. F. Liu, X. R. Yao, C. Wang, Y. Zhai, and G. J. Zhai, “Complementary compressive imaging for the telescopic system,” Sci. Rep. 4, 5834 (2014).

Science (1)

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, “3D computational imaging with single-pixel detectors,” Science 340, 844–847 (2013).
[Crossref]

Work. Inf. Opt. (1)

K. Nitta, S. Hayashi, and O. Matoba, “Divided Hadamard pattern illumination for fewer times measurements,” Work. Inf. Opt. 20152, 1–3 (2015).

Other (8)

T. Ritter, “Walsh–Hadamard transforms: a literature survey,” http://www.ciphersbyritter.com/RES/WALHAD.HTM .

R. G. Baraniuk, K. F. Kelly, R. F. Bridge, S. Chatterjee, and L. McMackin, “Dual-port measurements of light reflected from micromirror array,” U.S. patent8717466 B2 (4September, 2014).

J. Wang, M. Gupta, and A. C. Sankaranarayanan, “LiSens—A scalable architecture for video compressive sensing,” arXiv (2015).

X. Miao and B. Amirparviz, “Single pixel camera,” U.S. patentUS20150042834 A1 (12February2015).

H. Yu, Y. Liu, Y. Peng, W. Xu, and M. Zhang, “A portable single-pixel camera based on coarse-to-fine coding light,” in IEEE International Conference on Imaging Systems and Techniques (IST) (2015), pp. 1–5.

R. I. Stantchev, B. Sun, S. M. Hornett, P. A. Hobson, G. M. Gibson, M. J. Padgett, and E. Hendry, “Non-invasive, near-field terahertz imaging of hidden objects using a single pixel detector,” arXiv (2015).

S. J. Olivas, Y. Rachlin, L. Gu, B. Gardiner, R. Dawson, J. P. Laine, and J. Ford, Single Pixel Compressive Imaging of Laboratory and Natural Light Scenes (2013).

M. B. Wakin, J. N. Laska, M. F. Duarte, D. Baron, S. Sarvotham, D. Takhar, K. F. Kelly, and R. G. Baraniuk, “An architecture for compressive imaging,” in International Conference on Image Processing (IEEE, 2006), pp. 1273–1276.

Supplementary Material (3)

NameDescription
» Visualization 1: MP4 (961 KB)      Video N=32, 22 fps.
» Visualization 2: MP4 (1616 KB)      Video N = 64, 5.5 fps.
» Visualization 3: MP4 (1709 KB)      Video N = 128, 0.75 fps.

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Figures (9)

Fig. 1.
Fig. 1. Experimental system used to image a back illuminated object (inset: Siemens star) onto the DMD with a lens f1. The detectors d1 and d2 collect the reflected light coming from the DMD.

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Fig. 2.
Fig. 2. Test image with four grayscale values used during simulation.

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Fig. 3.
Fig. 3. Results of N 2 = 16 patterns measuring the test object displayed in Fig. 2. The first row indicates the measurements performed with only positive ( + 1 and 0) patterns where only positive values are measured (intensity values above each pattern). The second row shows the received measurements from positive and inverted ( + 1 and − 1 ) patterns and the corresponding intensity values.

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Fig. 4.
Fig. 4. (a) Intensity data of 16 positive Hadamard patterns. (b) Data of (a) after the mean is subtracted. (c) Data of 16 positive and inverted Hadamard patterns. (d) The difference between the simulated data of (b) and the real data of (c).

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Fig. 5.
Fig. 5. Three simulations where different Gaussian white noise is added to the original signal [graphs 4(b) and 4(c)]. The first row displays the original signal with the added noise (blue) and the difference to the original signal (red) for method A. The bottom row shows the original signal with added noise for method B (green) and the difference from the original signal (red). Please note the difference in the y-axis scale.

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Fig. 6.
Fig. 6. Reconstructed images after noise is introduced. The top row shows the reconstructed images using method A, and the bottom row when method B is used. The numbers below the images show the correlation coefficient compared to the reference image in Fig. 2, based on Eq. (3) of [19].

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Fig. 7.
Fig. 7. Reconstructed images for N = 32 , up-sampled to 256 × 256    px . (a) Positive detector. (b) Negative detector. (c) Reconstruction after the negative data is subtracted from the positive data, resulting in a higher contrast image with fewer artifacts. Correlation coefficient below the images compared to (c).

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Fig. 8.
Fig. 8. Image reconstruction for (a)  N = 64 , (b)  N = 128 , and (c)  N = 256 . All images are up-scaled to 256 × 256    px (except images with N = 256 ). Imaging time is indicated. Images (d) and (e) are reconstructed with maximum resolution, 1    px ≃ 13.68    μm .

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Fig. 9.
Fig. 9. Adaptive imaging results for N = 256 . t is the time, which is needed to display the percentage of pattern. The numbers in the last row are the correlation coefficients compared to the first image (100%).

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Tables (2)

Tables Icon

Table 1. Comparison of Theoretical and Experimentally Obtained FPS

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Table 2. T(heoretical) Versus E(xperimental) FPS Results While Applying Adaptive Imaging Using Two Detectors

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Equations (1)

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Image ( m , n ) = ∑ i N 2 intensity i × pattern i ( m , n ) ,

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