Abstract

A novel technique for Radon single-pixel imaging with projective sampling, which is based on the theorem of the Radon transform, is proposed. In contrast to current patterns in conventional single-pixel imaging systems, candy-striped patterns called Radon basis patterns, which are produced by projecting the 1D Hadamard functions along different angles, are employed in our proposed technique. Here, the patterns are loaded into a projection system and then illuminated onto an object. The light reflected from the object is detected by a single-pixel detector. An iterative reconstruction method is used to restore the object’s 1D projection functions by summing the 1D Hadamard functions and detected intensities. Next, the Radon spectrum of the object is recovered by arranging the 1D projection functions along the projection angle. Finally, the image of the object can be recovered using a filtered back-projection algorithm with the Radon spectrum. Experiments demonstrate that the proposed technique can obtain the information of the Radon spectrum and image of the object. Recognition directly in the Radon spectrum domain, rather than in the image domain, is fast and yields robust and high classification rates. A recognition experiment is performed by detecting the lines in one scene by searching the singular peaks in the Radon spectrum domain. According to the results, the lines in the scene can be easily detected in the Radon spectrum domain. Other shapes can also be detected by the characteristics of those shapes in the Radon spectrum domain.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (1)

L. Olivieri, J. S. Totero Gongora, A. Pasquazi, and M. Peccianti, “Time-Resolved Nonlinear Ghost Imaging,” ACS Photonics 5(8), 3379–3388 (2018).
[Crossref]

2017 (2)

2016 (5)

N. Huynh, E. Zhang, M. Betcke, S. Arridge, P. Beard, and B. Cox, “Single-pixel optical camera for video rate ultrasonic imaging,” Optica 3(1), 26–29 (2016).
[Crossref]

B. Lochocki, A. Gambin, S. Manzanera, E. Irles, E. Tajahuerce, J. Lancis, and P. Artal, “Single pixel camera ophthalmoscope,” Optica 3(10), 1056–1059 (2016).
[Crossref]

R. I. Stantchev, B. Sun, S. M. Hornett, P. A. Hobson, G. M. Gibson, M. J. Padgett, and E. Hendry, “Noninvasive, near-field terahertz imaging of hidden objects using a single-pixel detector,” Sci. Adv. 2(6), e1600190 (2016).
[Crossref] [PubMed]

M. J. Sun, M. P. Edgar, G. M. Gibson, B. Sun, N. Radwell, R. Lamb, and M. J. Padgett, “Single-pixel three-dimensional imaging with time-based depth resolution,” Nat. Commun. 7(1), 12010 (2016).
[Crossref] [PubMed]

H. Yu, R. Lu, S. Han, H. Xie, G. Du, T. Xiao, and D. Zhu, “Fourier-Transform Ghost Imaging with Hard X Rays,” Phys. Rev. Lett. 117(11), 113901 (2016).
[Crossref] [PubMed]

2015 (7)

P. A. Morris, R. S. Aspden, J. E. C. Bell, R. W. Boyd, and M. J. Padgett, “Imaging with a small number of photons,” Nat. Commun. 6(1), 5913 (2015).
[Crossref] [PubMed]

Z. Zhang, X. Ma, and J. Zhong, “Single-pixel imaging by means of Fourier spectrum acquisition,” Nat. Commun. 6(1), 6225 (2015).
[Crossref] [PubMed]

M. Plöschner, T. Tyc, and T. Cizmar, “Seeing through chaos in multimode fibres,” Nat. Photonics 9(8), 529–535 (2015).
[Crossref]

O. Bimber, “An image sensor based on optical Radon transform,” Comput Graph-Uk 53, 37–43 (2015).
[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(1), 10669 (2015).
[Crossref] [PubMed]

A. Koppelhuber and O. Bimber, “A classification sensor based on compressed optical Radon transform,” Opt. Express 23(7), 9397–9406 (2015).
[Crossref] [PubMed]

R. S. Aspden, N. R. Gemmell, P. A. Morris, D. S. Tasca, L. Mertens, M. G. Tanner, R. A. Kirkwood, A. Ruggeri, A. Tosi, R. W. Boyd, G. S. Buller, R. H. Hadfield, and M. J. Padgett, “Photon-sparse microscopy: visible light imaging using infrared illumination,” Optica 2(12), 1049–1052 (2015).
[Crossref]

2014 (3)

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(5), 285–289 (2014).
[Crossref]

T. Ilovitsh, A. Ilovitsh, J. Sheridan, and Z. Zalevsky, “Optical realization of the radon transform,” Opt. Express 22(26), 32301–32307 (2014).
[Crossref] [PubMed]

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(8), 605–609 (2014).
[Crossref]

2013 (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(6134), 844–847 (2013).
[Crossref] [PubMed]

2012 (2)

T. Cižmár and K. Dholakia, “Exploiting multimode waveguides for pure fibre-based imaging,” Nat. Commun. 3(1), 1027 (2012).
[Crossref] [PubMed]

Y. Kashter, O. Levi, and A. Stern, “Optical compressive change and motion detection,” Appl. Opt. 51(13), 2491–2496 (2012).
[Crossref] [PubMed]

2011 (1)

2009 (1)

J. D. Wu and S. H. Ye, “Driver identification using finger-vein patterns with Radon transform and neural network,” Expert Syst. Appl. 36(3), 5793–5799 (2009).
[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]

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93(12), 121105 (2008).
[Crossref]

2004 (1)

J. S. Seo, J. Haitsma, T. Kalker, and C. D. Yoo, “A robust image fingerprinting system using the Radon transform,” Signal Process-Image 19(4), 325–339 (2004).
[Crossref]

Arridge, S.

Artal, P.

Aspden, R. S.

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]

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93(12), 121105 (2008).
[Crossref]

Beard, P.

Bell, J. E. C.

P. A. Morris, R. S. Aspden, J. E. C. Bell, R. W. Boyd, and M. J. Padgett, “Imaging with a small number of photons,” Nat. Commun. 6(1), 5913 (2015).
[Crossref] [PubMed]

Betcke, M.

Bimber, O.

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(6134), 844–847 (2013).
[Crossref] [PubMed]

Bowman, R.

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(5), 285–289 (2014).
[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(6134), 844–847 (2013).
[Crossref] [PubMed]

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(1), 10669 (2015).
[Crossref] [PubMed]

Boyd, R. W.

Buller, G. S.

Chan, W. L.

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93(12), 121105 (2008).
[Crossref]

Charan, K.

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93(12), 121105 (2008).
[Crossref]

Cizmar, T.

M. Plöschner, T. Tyc, and T. Cizmar, “Seeing through chaos in multimode fibres,” Nat. Photonics 9(8), 529–535 (2015).
[Crossref]

Cižmár, T.

T. Cižmár and K. Dholakia, “Exploiting multimode waveguides for pure fibre-based imaging,” Nat. Commun. 3(1), 1027 (2012).
[Crossref] [PubMed]

Clemente, P.

Climent, V.

Cox, B.

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]

Dholakia, K.

T. Cižmár and K. Dholakia, “Exploiting multimode waveguides for pure fibre-based imaging,” Nat. Commun. 3(1), 1027 (2012).
[Crossref] [PubMed]

Du, G.

H. Yu, R. Lu, S. Han, H. Xie, G. Du, T. Xiao, and D. Zhu, “Fourier-Transform Ghost Imaging with Hard X Rays,” Phys. Rev. Lett. 117(11), 113901 (2016).
[Crossref] [PubMed]

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]

Edgar, M. P.

G. M. Gibson, B. Sun, M. P. Edgar, D. B. Phillips, N. Hempler, G. T. Maker, G. P. A. Malcolm, and M. J. Padgett, “Real-time imaging of methane gas leaks using a single-pixel camera,” Opt. Express 25(4), 2998–3005 (2017).
[Crossref] [PubMed]

M. J. Sun, M. P. Edgar, G. M. Gibson, B. Sun, N. Radwell, R. Lamb, and M. J. Padgett, “Single-pixel three-dimensional imaging with time-based depth resolution,” Nat. Commun. 7(1), 12010 (2016).
[Crossref] [PubMed]

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(1), 10669 (2015).
[Crossref] [PubMed]

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(5), 285–289 (2014).
[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(6134), 844–847 (2013).
[Crossref] [PubMed]

Egiazarian, K.

K. Egiazarian, A. Foi, and V. Katkovnik, “Compressed Sensing Image Reconstruction via Recursive Spatially Adaptive Filtering,” Proc. IEEE ICIP 2007, San Antonio (TX), USA, pp. 549–552, Sept. 2007.
[Crossref]

Foi, A.

K. Egiazarian, A. Foi, and V. Katkovnik, “Compressed Sensing Image Reconstruction via Recursive Spatially Adaptive Filtering,” Proc. IEEE ICIP 2007, San Antonio (TX), USA, pp. 549–552, Sept. 2007.
[Crossref]

Fu, L.

Gambin, A.

Gemmell, N. R.

Gibson, G. M.

G. M. Gibson, B. Sun, M. P. Edgar, D. B. Phillips, N. Hempler, G. T. Maker, G. P. A. Malcolm, and M. J. Padgett, “Real-time imaging of methane gas leaks using a single-pixel camera,” Opt. Express 25(4), 2998–3005 (2017).
[Crossref] [PubMed]

M. J. Sun, M. P. Edgar, G. M. Gibson, B. Sun, N. Radwell, R. Lamb, and M. J. Padgett, “Single-pixel three-dimensional imaging with time-based depth resolution,” Nat. Commun. 7(1), 12010 (2016).
[Crossref] [PubMed]

R. I. Stantchev, B. Sun, S. M. Hornett, P. A. Hobson, G. M. Gibson, M. J. Padgett, and E. Hendry, “Noninvasive, near-field terahertz imaging of hidden objects using a single-pixel detector,” Sci. Adv. 2(6), e1600190 (2016).
[Crossref] [PubMed]

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(1), 10669 (2015).
[Crossref] [PubMed]

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(5), 285–289 (2014).
[Crossref]

Guo, Q.

Hadfield, R. H.

Haitsma, J.

J. S. Seo, J. Haitsma, T. Kalker, and C. D. Yoo, “A robust image fingerprinting system using the Radon transform,” Signal Process-Image 19(4), 325–339 (2004).
[Crossref]

Han, S.

H. Yu, R. Lu, S. Han, H. Xie, G. Du, T. Xiao, and D. Zhu, “Fourier-Transform Ghost Imaging with Hard X Rays,” Phys. Rev. Lett. 117(11), 113901 (2016).
[Crossref] [PubMed]

Hempler, N.

Hendry, E.

R. I. Stantchev, B. Sun, S. M. Hornett, P. A. Hobson, G. M. Gibson, M. J. Padgett, and E. Hendry, “Noninvasive, near-field terahertz imaging of hidden objects using a single-pixel detector,” Sci. Adv. 2(6), e1600190 (2016).
[Crossref] [PubMed]

Hobson, P. A.

R. I. Stantchev, B. Sun, S. M. Hornett, P. A. Hobson, G. M. Gibson, M. J. Padgett, and E. Hendry, “Noninvasive, near-field terahertz imaging of hidden objects using a single-pixel detector,” Sci. Adv. 2(6), e1600190 (2016).
[Crossref] [PubMed]

Hornett, S. M.

R. I. Stantchev, B. Sun, S. M. Hornett, P. A. Hobson, G. M. Gibson, M. J. Padgett, and E. Hendry, “Noninvasive, near-field terahertz imaging of hidden objects using a single-pixel detector,” Sci. Adv. 2(6), e1600190 (2016).
[Crossref] [PubMed]

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(8), 605–609 (2014).
[Crossref]

Huynh, N.

Ilovitsh, A.

Ilovitsh, T.

Irles, E.

Kalker, T.

J. S. Seo, J. Haitsma, T. Kalker, and C. D. Yoo, “A robust image fingerprinting system using the Radon transform,” Signal Process-Image 19(4), 325–339 (2004).
[Crossref]

Kashter, Y.

Katkovnik, V.

K. Egiazarian, A. Foi, and V. Katkovnik, “Compressed Sensing Image Reconstruction via Recursive Spatially Adaptive Filtering,” Proc. IEEE ICIP 2007, San Antonio (TX), USA, pp. 549–552, Sept. 2007.
[Crossref]

Kelly, K. F.

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93(12), 121105 (2008).
[Crossref]

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]

Kirkwood, R. A.

Koppelhuber, A.

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(8), 605–609 (2014).
[Crossref]

Lamb, R.

M. J. Sun, M. P. Edgar, G. M. Gibson, B. Sun, N. Radwell, R. Lamb, and M. J. Padgett, “Single-pixel three-dimensional imaging with time-based depth resolution,” Nat. Commun. 7(1), 12010 (2016).
[Crossref] [PubMed]

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]

Levi, O.

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(8), 605–609 (2014).
[Crossref]

Lochocki, B.

Lu, R.

H. Yu, R. Lu, S. Han, H. Xie, G. Du, T. Xiao, and D. Zhu, “Fourier-Transform Ghost Imaging with Hard X Rays,” Phys. Rev. Lett. 117(11), 113901 (2016).
[Crossref] [PubMed]

Ma, X.

Z. Zhang, X. Ma, and J. Zhong, “Single-pixel imaging by means of Fourier spectrum acquisition,” Nat. Commun. 6(1), 6225 (2015).
[Crossref] [PubMed]

Maker, G. T.

Malcolm, G. P. A.

Manzanera, S.

Martínez-León, L.

Mertens, L.

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(1), 10669 (2015).
[Crossref] [PubMed]

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(5), 285–289 (2014).
[Crossref]

Mittleman, D. M.

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93(12), 121105 (2008).
[Crossref]

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(8), 605–609 (2014).
[Crossref]

Mori, Y.

Morris, P. A.

Olivieri, L.

L. Olivieri, J. S. Totero Gongora, A. Pasquazi, and M. Peccianti, “Time-Resolved Nonlinear Ghost Imaging,” ACS Photonics 5(8), 3379–3388 (2018).
[Crossref]

Padgett, M. J.

G. M. Gibson, B. Sun, M. P. Edgar, D. B. Phillips, N. Hempler, G. T. Maker, G. P. A. Malcolm, and M. J. Padgett, “Real-time imaging of methane gas leaks using a single-pixel camera,” Opt. Express 25(4), 2998–3005 (2017).
[Crossref] [PubMed]

M. J. Sun, M. P. Edgar, G. M. Gibson, B. Sun, N. Radwell, R. Lamb, and M. J. Padgett, “Single-pixel three-dimensional imaging with time-based depth resolution,” Nat. Commun. 7(1), 12010 (2016).
[Crossref] [PubMed]

R. I. Stantchev, B. Sun, S. M. Hornett, P. A. Hobson, G. M. Gibson, M. J. Padgett, and E. Hendry, “Noninvasive, near-field terahertz imaging of hidden objects using a single-pixel detector,” Sci. Adv. 2(6), e1600190 (2016).
[Crossref] [PubMed]

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(1), 10669 (2015).
[Crossref] [PubMed]

R. S. Aspden, N. R. Gemmell, P. A. Morris, D. S. Tasca, L. Mertens, M. G. Tanner, R. A. Kirkwood, A. Ruggeri, A. Tosi, R. W. Boyd, G. S. Buller, R. H. Hadfield, and M. J. Padgett, “Photon-sparse microscopy: visible light imaging using infrared illumination,” Optica 2(12), 1049–1052 (2015).
[Crossref]

P. A. Morris, R. S. Aspden, J. E. C. Bell, R. W. Boyd, and M. J. Padgett, “Imaging with a small number of photons,” Nat. Commun. 6(1), 5913 (2015).
[Crossref] [PubMed]

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(5), 285–289 (2014).
[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(6134), 844–847 (2013).
[Crossref] [PubMed]

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(8), 605–609 (2014).
[Crossref]

Pasquazi, A.

L. Olivieri, J. S. Totero Gongora, A. Pasquazi, and M. Peccianti, “Time-Resolved Nonlinear Ghost Imaging,” ACS Photonics 5(8), 3379–3388 (2018).
[Crossref]

Peccianti, M.

L. Olivieri, J. S. Totero Gongora, A. Pasquazi, and M. Peccianti, “Time-Resolved Nonlinear Ghost Imaging,” ACS Photonics 5(8), 3379–3388 (2018).
[Crossref]

Phillips, D. B.

Plöschner, M.

M. Plöschner, T. Tyc, and T. Cizmar, “Seeing through chaos in multimode fibres,” Nat. Photonics 9(8), 529–535 (2015).
[Crossref]

Radwell, N.

M. J. Sun, M. P. Edgar, G. M. Gibson, B. Sun, N. Radwell, R. Lamb, and M. J. Padgett, “Single-pixel three-dimensional imaging with time-based depth resolution,” Nat. Commun. 7(1), 12010 (2016).
[Crossref] [PubMed]

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(1), 10669 (2015).
[Crossref] [PubMed]

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(5), 285–289 (2014).
[Crossref]

Ruggeri, A.

Seo, J. S.

J. S. Seo, J. Haitsma, T. Kalker, and C. D. Yoo, “A robust image fingerprinting system using the Radon transform,” Signal Process-Image 19(4), 325–339 (2004).
[Crossref]

Sheridan, 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(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(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(8), 605–609 (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, “Noninvasive, near-field terahertz imaging of hidden objects using a single-pixel detector,” Sci. Adv. 2(6), e1600190 (2016).
[Crossref] [PubMed]

Stern, A.

Sun, B.

G. M. Gibson, B. Sun, M. P. Edgar, D. B. Phillips, N. Hempler, G. T. Maker, G. P. A. Malcolm, and M. J. Padgett, “Real-time imaging of methane gas leaks using a single-pixel camera,” Opt. Express 25(4), 2998–3005 (2017).
[Crossref] [PubMed]

M. J. Sun, M. P. Edgar, G. M. Gibson, B. Sun, N. Radwell, R. Lamb, and M. J. Padgett, “Single-pixel three-dimensional imaging with time-based depth resolution,” Nat. Commun. 7(1), 12010 (2016).
[Crossref] [PubMed]

R. I. Stantchev, B. Sun, S. M. Hornett, P. A. Hobson, G. M. Gibson, M. J. Padgett, and E. Hendry, “Noninvasive, near-field terahertz imaging of hidden objects using a single-pixel detector,” Sci. Adv. 2(6), e1600190 (2016).
[Crossref] [PubMed]

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(1), 10669 (2015).
[Crossref] [PubMed]

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(6134), 844–847 (2013).
[Crossref] [PubMed]

Sun, M. J.

M. J. Sun, M. P. Edgar, G. M. Gibson, B. Sun, N. Radwell, R. Lamb, and M. J. Padgett, “Single-pixel three-dimensional imaging with time-based depth resolution,” Nat. Commun. 7(1), 12010 (2016).
[Crossref] [PubMed]

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]

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93(12), 121105 (2008).
[Crossref]

Tanner, M. G.

Tasca, D. S.

Tian, N.

Tosi, A.

Totero Gongora, J. S.

L. Olivieri, J. S. Totero Gongora, A. Pasquazi, and M. Peccianti, “Time-Resolved Nonlinear Ghost Imaging,” ACS Photonics 5(8), 3379–3388 (2018).
[Crossref]

Tyc, T.

M. Plöschner, T. Tyc, and T. Cizmar, “Seeing through chaos in multimode fibres,” Nat. Photonics 9(8), 529–535 (2015).
[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(6134), 844–847 (2013).
[Crossref] [PubMed]

Wang, A.

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(8), 605–609 (2014).
[Crossref]

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(6134), 844–847 (2013).
[Crossref] [PubMed]

Welsh, S. S.

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(1), 10669 (2015).
[Crossref] [PubMed]

Wu, J. D.

J. D. Wu and S. H. Ye, “Driver identification using finger-vein patterns with Radon transform and neural network,” Expert Syst. Appl. 36(3), 5793–5799 (2009).
[Crossref]

Xiao, T.

H. Yu, R. Lu, S. Han, H. Xie, G. Du, T. Xiao, and D. Zhu, “Fourier-Transform Ghost Imaging with Hard X Rays,” Phys. Rev. Lett. 117(11), 113901 (2016).
[Crossref] [PubMed]

Xie, H.

H. Yu, R. Lu, S. Han, H. Xie, G. Du, T. Xiao, and D. Zhu, “Fourier-Transform Ghost Imaging with Hard X Rays,” Phys. Rev. Lett. 117(11), 113901 (2016).
[Crossref] [PubMed]

Xu, D.

Ye, S. H.

J. D. Wu and S. H. Ye, “Driver identification using finger-vein patterns with Radon transform and neural network,” Expert Syst. Appl. 36(3), 5793–5799 (2009).
[Crossref]

Yoo, C. D.

J. S. Seo, J. Haitsma, T. Kalker, and C. D. Yoo, “A robust image fingerprinting system using the Radon transform,” Signal Process-Image 19(4), 325–339 (2004).
[Crossref]

Yu, H.

H. Yu, R. Lu, S. Han, H. Xie, G. Du, T. Xiao, and D. Zhu, “Fourier-Transform Ghost Imaging with Hard X Rays,” Phys. Rev. Lett. 117(11), 113901 (2016).
[Crossref] [PubMed]

Zalevsky, Z.

Zhang, E.

Zhang, Z.

Z. Zhang, X. Ma, and J. Zhong, “Single-pixel imaging by means of Fourier spectrum acquisition,” Nat. Commun. 6(1), 6225 (2015).
[Crossref] [PubMed]

Zhong, J.

Z. Zhang, X. Ma, and J. Zhong, “Single-pixel imaging by means of Fourier spectrum acquisition,” Nat. Commun. 6(1), 6225 (2015).
[Crossref] [PubMed]

Zhu, D.

H. Yu, R. Lu, S. Han, H. Xie, G. Du, T. Xiao, and D. Zhu, “Fourier-Transform Ghost Imaging with Hard X Rays,” Phys. Rev. Lett. 117(11), 113901 (2016).
[Crossref] [PubMed]

ACS Photonics (1)

L. Olivieri, J. S. Totero Gongora, A. Pasquazi, and M. Peccianti, “Time-Resolved Nonlinear Ghost Imaging,” ACS Photonics 5(8), 3379–3388 (2018).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93(12), 121105 (2008).
[Crossref]

Comput Graph-Uk (1)

O. Bimber, “An image sensor based on optical Radon transform,” Comput Graph-Uk 53, 37–43 (2015).
[Crossref]

Expert Syst. Appl. (1)

J. D. Wu and S. H. Ye, “Driver identification using finger-vein patterns with Radon transform and neural network,” Expert Syst. Appl. 36(3), 5793–5799 (2009).
[Crossref]

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]

Nat. Commun. (4)

Z. Zhang, X. Ma, and J. Zhong, “Single-pixel imaging by means of Fourier spectrum acquisition,” Nat. Commun. 6(1), 6225 (2015).
[Crossref] [PubMed]

M. J. Sun, M. P. Edgar, G. M. Gibson, B. Sun, N. Radwell, R. Lamb, and M. J. Padgett, “Single-pixel three-dimensional imaging with time-based depth resolution,” Nat. Commun. 7(1), 12010 (2016).
[Crossref] [PubMed]

T. Cižmár and K. Dholakia, “Exploiting multimode waveguides for pure fibre-based imaging,” Nat. Commun. 3(1), 1027 (2012).
[Crossref] [PubMed]

P. A. Morris, R. S. Aspden, J. E. C. Bell, R. W. Boyd, and M. J. Padgett, “Imaging with a small number of photons,” Nat. Commun. 6(1), 5913 (2015).
[Crossref] [PubMed]

Nat. Photonics (2)

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(8), 605–609 (2014).
[Crossref]

M. Plöschner, T. Tyc, and T. Cizmar, “Seeing through chaos in multimode fibres,” Nat. Photonics 9(8), 529–535 (2015).
[Crossref]

Opt. Express (4)

Opt. Lett. (1)

Optica (4)

Phys. Rev. Lett. (1)

H. Yu, R. Lu, S. Han, H. Xie, G. Du, T. Xiao, and D. Zhu, “Fourier-Transform Ghost Imaging with Hard X Rays,” Phys. Rev. Lett. 117(11), 113901 (2016).
[Crossref] [PubMed]

Sci. Adv. (1)

R. I. Stantchev, B. Sun, S. M. Hornett, P. A. Hobson, G. M. Gibson, M. J. Padgett, and E. Hendry, “Noninvasive, near-field terahertz imaging of hidden objects using a single-pixel detector,” Sci. Adv. 2(6), e1600190 (2016).
[Crossref] [PubMed]

Sci. Rep. (1)

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(1), 10669 (2015).
[Crossref] [PubMed]

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(6134), 844–847 (2013).
[Crossref] [PubMed]

Signal Process-Image (1)

J. S. Seo, J. Haitsma, T. Kalker, and C. D. Yoo, “A robust image fingerprinting system using the Radon transform,” Signal Process-Image 19(4), 325–339 (2004).
[Crossref]

Other (8)

S. Tabbone and L. Wendling, “Technical symbols recognition using the two-dimensional radon transform,” Int C Patt Recog, 200–203 (2002).
[Crossref]

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (SIAM, 2001).

G. T. Herman, Fundamentals of Computerized Tomography: Image Reconstruction from Projections, 2nd edn. (Springer, 2010).

Beatty, Jen, “The Radon Transform and the Mathematics of Medical Imaging” (2012). Honors Theses. Paper 646.

K. Egiazarian, A. Foi, and V. Katkovnik, “Compressed Sensing Image Reconstruction via Recursive Spatially Adaptive Filtering,” Proc. IEEE ICIP 2007, San Antonio (TX), USA, pp. 549–552, Sept. 2007.
[Crossref]

C. M. Bishop, Pattern Recognition and Machine Learning (Springer-Verlag, 2006).

C. E. Rasmussen and C. K. I. Williams, Gaussian Processes for Machine Learning (Massachusetts Institute of Technology, 2006).

S. R. Deans, The Radon Transform and Some of Its Applications (Wiley, 1983).

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Figures (10)

Fig. 1
Fig. 1 A) Radon Transform diagram. Sonogram is the Radon spectrum. 1D projection function (1DPF) is one line of the sinogram image. A 2D projection function (2DPF) is obtained by projecting the 1DPF along the integral angle in 2D coordinates. B) Procedure of the proposed method: The letter C in the circle represents the correlation operation; HM: Hadamard matrix; 1DH: 1D Hadamard functions; PI: projective illumination. The 2D projective patterns under three integral angles (00, 450 and 900) are expressed as 2DS-0, 2DS-45 and 2DS-90.
Fig. 2
Fig. 2 Original information for simulation: A1 and A2 are original images; B1 and B2 are corresponding Radon spectrum.
Fig. 3
Fig. 3 Restoration results of binary image. The results in first and second lines are Radon spectrums and recovered images under random form original matrices and the numbers of projective patterns are 51200 × 180, 204800 × 180, 819200 × 180 and 3276800 × 180 for A to D rows, respectively. The results in third and fourth lines are Radon spectrums and recovered images under Hadamard form original matrices, and the numbers of projective patterns are 32 × 180, 64 × 180, 96 × 180 and 128 × 180 for A to D rows, respectively.
Fig. 4
Fig. 4 Restoration results of grayscale image. The results in first and second lines are Radon spectrums and recovered images under random form original matrices, and the numbers of projective patterns are 51200 × 180, 204800 × 180, 819200 × 180 and 3276800 × 180 for A to D rows, respectively. The results in third and fourth lines are Radon spectrums and recovered images under Hadamard form original matrices, and the numbers of projective patterns are 32 × 180, 64 × 180, 96 × 180 and 128 × 180 for A to D rows, respectively.
Fig. 5
Fig. 5 Grayscale images of the object reconstructed with different projection angle intervals. A1 to C2 (Top-to-Left) represent recovered results with projection angle intervals of 8, 6, 4, 2, 1, and 0.5 degrees, respectively.
Fig. 6
Fig. 6 The experimental system (A) and the process of projective patterning (B). Lim. Are. is circular limitative area; Pro. Patt. are projective patterns.
Fig. 7
Fig. 7 The information of the object reconstructed with different compressed rates. Sinogram is the RT information of the object, and FBP is the recovered image with the filtered back-projection method. Scale bar, 2 cm.
Fig. 8
Fig. 8 The images of the object reconstructed with different projection angle intervals and compressed rates. The blue numbers indicate the correlation coefficients between the recovered images and the reconstruction utilizing the complete patterns and projection angle interval of one degree. T2, T4, T6 and T8 indicate angle intervals of two, four, six and eight degrees, respectively. Scale bar, 2 cm.
Fig. 9
Fig. 9 Experimental results. The left image is the original noise image, the middle image is the sinogram information, and the right image is recovered by the filtered back-projection algorithm. Scale bar, 2 cm.
Fig. 10
Fig. 10 Straight line marking process: TP is threshold processing; MK_B, MK_G and MK_R represent the lines marked in blue, green and red, respectively. 2DPF-49, 2DPF-98 and 2DPF-98 are the 2D projection functions along angles of 49, 98 and 198 degrees, respectively. According to the abscissas and intercepts, the lines are marked, as shown in (A). According to the 2DPF, the lines are marked, as shown in (B).

Equations (14)

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

L=xcosθ'+ysinθ',
F(L,θ')= x,y f(x,y)δ(xcosθ'+ysinθ'L) ,
I θ' + (n)= x,y f(x,y) p n + (x,y;L,θ') ,
I θ' (n)= x,y f(x,y) p n (x,y;L,θ') ,
I θ' (n)= I θ' + (n) I θ' (n) = x,y f(x,y)[ p n + (x,y;L,θ') p n (x,y;L,θ')] = x,y f(x,y) p n (x,y;L,θ') ,
p n (x,y;L,θ')=C(R) T n,θ' (L)δ(xcosθ'+ysinθ'L).
I θ' (n)= x,y C(R) T n,θ' (L)f(x,y)δ(xcosθ'+ysinθ'L) .
I θ' (n)= x,y T n,θ' (L) F θ' (L) .
F θ' (L)= n T n,θ' (L) I θ' (n).
Bo(x,y)= 1 π 0 π o(xcosθ'+ysinθ',θ')dθ' .
B F θ' (L)= 1 π 0 π F θ' (L)dθ' .
f(x,y)= 1 2 B( F t 1 S F θ' (L))(x,y).
RMSE= x,y=1 M,N [ f r (x,y) f o (x,y)] 2 / M×N ,
r= m n ( A mn A ¯ )( B mn B ¯ ) m n ( A mn A ¯ ) 2 m n ( B mn B ¯ ) 2 ,

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