Abstract

A single-pixel compressive imaging technique that uses differential modulation based on the transformation of discrete orthogonal Krawtchouk moments is proposed. In this method, two sets of Krawtchouk basis patterns are used to differentially modulate the light source, then the Krawtchouk moments of the target object are acquired from the light intensities measured by a single-pixel detector. The target image is reconstructed by applying an inverse Krawtchouk moment transform represented in the matrix form. The proposed technique is verified by both computational simulations and laboratory experiments. The results show that this technique can retrieve an image from compressive measurements and the real-time reconstruction. The background noise can be removed by the differential measurement to realize the excellent image quality. Moreover, the proposed technique is especially suitable for the single-pixel imaging application that requires the extraction of the characteristics at the region-of-interest.

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

Full Article  |  PDF Article
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References

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  5. 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 meta material spatial light modulators,” Nat. Photonics 8(8), 605–609 (2014).
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    [Crossref]
  19. J. Huang, D. Shi, K. Yuan, S. Hu, and Y. Wang, “Computational-weighted Fourier single-pixel imaging via binary illumination,” Opt. Express 26(13), 16547–16559 (2018).
    [Crossref]
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    [Crossref]
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    [Crossref]
  22. G. A. Papakostas, E. G. Karakasis, and D. E. Koulouriotis, “Accurate and speedy computation of image Legendre moments for computer vision applications,” Image and Vision Comput. 28(3), 414–423 (2010).
    [Crossref]
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    [Crossref]
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    [Crossref]
  25. P. T. Yap, R. Paramesran, and S. H. Ong, “Image analysis by Krawtchouk moments,” IEEE Trans. on Image Process. 12(11), 1367–1377 (2003).
    [Crossref]
  26. R. Koekoek and R. F. Swarttouw, “The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue,” arXiv preprint math 9602214 (1996).
  27. X. Wang, M. L. Xu, B. Q. Li, H. L. Zhai, J. J. Liu, and S. Y. Li, “Prediction of phosphorylation sites based on Krawtchouk image moments,” Proteins 85(12), 2231–2238 (2017).
    [Crossref]
  28. I. Batioua, R. Benouini, K. Zenkouar, A. Zahi, and E. F. Hakim, “3D image analysis by separable discrete orthogonal moments based on Krawtchouk and Tchebichef polynomials,” Pattern Recognit. 71, 264–277 (2017).
    [Crossref]
  29. S. H. Abdulhussain, A. R. Ramli, S. A. R. Al-Haddad, B. M. Mahmmod, and W. A. Jassim, “Fast recursive computation of Krawtchouk Polynomials,” J. Math. Imaging Vis. 60(3), 285–303 (2018).
    [Crossref]
  30. S. P. Priyal and P. K. Bora, “A robust static hand gesture recognition system using geometry based normalizations and Krawtchouk moments,” Pattern Recognit. 46(8), 2202–2219 (2013).
    [Crossref]
  31. G. Zhang, Z. Luo, B. Fu, B. Li, J. Liao, X. Fan, and Z. Xi, “A symmetry and bi-recursive algorithm of accurately computing Krawtchouk moments,” Pattern Recognit. Lett. 31(7), 548–554 (2010).
    [Crossref]

2019 (1)

R. Benouini, I. Batioua, K. Zenkouar, A. Zahi, S. Najah, and H. Qjidaa, “Fractional-order orthogonal Chebyshev moments and moments invariants for image representation and pattern recognition,” Pattern Recognit. 86, 332–343 (2019).
[Crossref]

2018 (5)

S. Golabi, M. S. Helfroush, and H. Danyali, “Non-unit mapped radial moments platform for robust, geometric invariant image watermarking and reversible data hiding,” Inf. Sci. 447, 104–116 (2018).
[Crossref]

V. A. Coutinho, R. J. Cintra, F. M. Bayer, P. A. M. Oliveira, R. S. Oliveira, and A. Madanayake, “Pruned discrete Tchebichef transform approximation for image compression,” Circuits Syst. Signal Process 37(10), 4363–4383 (2018).
[Crossref]

S. H. Abdulhussain, A. R. Ramli, S. A. R. Al-Haddad, B. M. Mahmmod, and W. A. Jassim, “Fast recursive computation of Krawtchouk Polynomials,” J. Math. Imaging Vis. 60(3), 285–303 (2018).
[Crossref]

B. Xu, H. Jiang, H. Zhao, X. Li, and S. Zhu, “Projector-defocusing rectification for Fourier single-pixel imaging,” Opt. Express 26(4), 5005–5017 (2018).
[Crossref]

J. Huang, D. Shi, K. Yuan, S. Hu, and Y. Wang, “Computational-weighted Fourier single-pixel imaging via binary illumination,” Opt. Express 26(13), 16547–16559 (2018).
[Crossref]

2017 (8)

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]

L. Martínez-León, P. Clemente, Y. Mori, V. Climent, J. Lancis, and E. Tajahuerce, “Single-pixel digital holography with phase-encoded illumination,” Opt. Express 25(5), 4975–4984 (2017).
[Crossref]

Z. Zhang, X. Wang, G. Zheng, and J. Zhong, “Hadamard single-pixel imaging versus Fourier single-pixel imaging,” Opt. Express 25(16), 19619–19639 (2017).
[Crossref]

K. Fan, J. Y. Suen, and W. J. Padilla, “Graphene metamaterial spatial light modulator for infrared single pixel imaging,” Opt. Express 25(21), 25318–25325 (2017).
[Crossref]

X. Wang, M. L. Xu, B. Q. Li, H. L. Zhai, J. J. Liu, and S. Y. Li, “Prediction of phosphorylation sites based on Krawtchouk image moments,” Proteins 85(12), 2231–2238 (2017).
[Crossref]

I. Batioua, R. Benouini, K. Zenkouar, A. Zahi, and E. F. Hakim, “3D image analysis by separable discrete orthogonal moments based on Krawtchouk and Tchebichef polynomials,” Pattern Recognit. 71, 264–277 (2017).
[Crossref]

Z. Zhang, X. Wang, G. Zheng, and J. Zhong, “Fast Fourier single-pixel imaging via binary illumination,” Sci. Rep. 7(1), 12029 (2017).
[Crossref]

B. Liu, Z. Yang, X. Liu, and L. Wu, “Coloured computational imaging with single-pixel detectors based on a 2D discrete cosine transform,” J. Mod. Opt. 64(3), 259–264 (2017).
[Crossref]

2016 (2)

X. Liu, W. Yu, X. Yao, B. Dai, L. Li, C. Wang, and G. Zhai, “Measurement dimensions compressed spectral imaging with a single point detector,” Opt. Commun. 365, 173–179 (2016).
[Crossref]

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

2015 (2)

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

S. M. M. Khamoushi, Y. Nosrati, and S. H. Tavassoli, “Sinusoidal ghost imaging,” Opt. Lett. 40(15), 3452–3455 (2015).
[Crossref]

2014 (2)

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]

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 meta material spatial light modulators,” Nat. Photonics 8(8), 605–609 (2014).
[Crossref]

2013 (1)

S. P. Priyal and P. K. Bora, “A robust static hand gesture recognition system using geometry based normalizations and Krawtchouk moments,” Pattern Recognit. 46(8), 2202–2219 (2013).
[Crossref]

2011 (2)

2010 (2)

G. Zhang, Z. Luo, B. Fu, B. Li, J. Liao, X. Fan, and Z. Xi, “A symmetry and bi-recursive algorithm of accurately computing Krawtchouk moments,” Pattern Recognit. Lett. 31(7), 548–554 (2010).
[Crossref]

G. A. Papakostas, E. G. Karakasis, and D. E. Koulouriotis, “Accurate and speedy computation of image Legendre moments for computer vision applications,” Image and Vision Comput. 28(3), 414–423 (2010).
[Crossref]

2009 (1)

D. Needell and J. A. Tropp, “CoSaMP: Iterative signal recovery from incomplete and inaccurate samples,” Appl. Comput. Harmon. Anal 26(3), 301–321 (2009).
[Crossref]

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)

J. A. Tropp and A. C. Gilbert, “Signal recovery from random measurements via orthogonal matching pursuit,” IEEE Trans. Inf. Theory 53(12), 4655–4666 (2007).
[Crossref]

2003 (1)

P. T. Yap, R. Paramesran, and S. H. Ong, “Image analysis by Krawtchouk moments,” IEEE Trans. on Image Process. 12(11), 1367–1377 (2003).
[Crossref]

Abdulhussain, S. H.

S. H. Abdulhussain, A. R. Ramli, S. A. R. Al-Haddad, B. M. Mahmmod, and W. A. Jassim, “Fast recursive computation of Krawtchouk Polynomials,” J. Math. Imaging Vis. 60(3), 285–303 (2018).
[Crossref]

Abolbashari, M.

Al-Haddad, S. A. R.

S. H. Abdulhussain, A. R. Ramli, S. A. R. Al-Haddad, B. M. Mahmmod, and W. A. Jassim, “Fast recursive computation of Krawtchouk Polynomials,” J. Math. Imaging Vis. 60(3), 285–303 (2018).
[Crossref]

Araújo, F. M.

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]

Batioua, I.

R. Benouini, I. Batioua, K. Zenkouar, A. Zahi, S. Najah, and H. Qjidaa, “Fractional-order orthogonal Chebyshev moments and moments invariants for image representation and pattern recognition,” Pattern Recognit. 86, 332–343 (2019).
[Crossref]

I. Batioua, R. Benouini, K. Zenkouar, A. Zahi, and E. F. Hakim, “3D image analysis by separable discrete orthogonal moments based on Krawtchouk and Tchebichef polynomials,” Pattern Recognit. 71, 264–277 (2017).
[Crossref]

Bayer, F. M.

V. A. Coutinho, R. J. Cintra, F. M. Bayer, P. A. M. Oliveira, R. S. Oliveira, and A. Madanayake, “Pruned discrete Tchebichef transform approximation for image compression,” Circuits Syst. Signal Process 37(10), 4363–4383 (2018).
[Crossref]

Benouini, R.

R. Benouini, I. Batioua, K. Zenkouar, A. Zahi, S. Najah, and H. Qjidaa, “Fractional-order orthogonal Chebyshev moments and moments invariants for image representation and pattern recognition,” Pattern Recognit. 86, 332–343 (2019).
[Crossref]

I. Batioua, R. Benouini, K. Zenkouar, A. Zahi, and E. F. Hakim, “3D image analysis by separable discrete orthogonal moments based on Krawtchouk and Tchebichef polynomials,” Pattern Recognit. 71, 264–277 (2017).
[Crossref]

Bora, P. K.

S. P. Priyal and P. K. Bora, “A robust static hand gesture recognition system using geometry based normalizations and Krawtchouk moments,” Pattern Recognit. 46(8), 2202–2219 (2013).
[Crossref]

Bowman, R.

Cintra, R. J.

V. A. Coutinho, R. J. Cintra, F. M. Bayer, P. A. M. Oliveira, R. S. Oliveira, and A. Madanayake, “Pruned discrete Tchebichef transform approximation for image compression,” Circuits Syst. Signal Process 37(10), 4363–4383 (2018).
[Crossref]

Clemente, P.

Climent, V.

Correia, M. V.

Coutinho, V. A.

V. A. Coutinho, R. J. Cintra, F. M. Bayer, P. A. M. Oliveira, R. S. Oliveira, and A. Madanayake, “Pruned discrete Tchebichef transform approximation for image compression,” Circuits Syst. Signal Process 37(10), 4363–4383 (2018).
[Crossref]

Dai, B.

X. Liu, W. Yu, X. Yao, B. Dai, L. Li, C. Wang, and G. Zhai, “Measurement dimensions compressed spectral imaging with a single point detector,” Opt. Commun. 365, 173–179 (2016).
[Crossref]

Danyali, H.

S. Golabi, M. S. Helfroush, and H. Danyali, “Non-unit mapped radial moments platform for robust, geometric invariant image watermarking and reversible data hiding,” Inf. Sci. 447, 104–116 (2018).
[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]

Dixon, P. B.

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.

Fan, K.

Fan, X.

G. Zhang, Z. Luo, B. Fu, B. Li, J. Liao, X. Fan, and Z. Xi, “A symmetry and bi-recursive algorithm of accurately computing Krawtchouk moments,” Pattern Recognit. Lett. 31(7), 548–554 (2010).
[Crossref]

Farahi, F.

Fu, B.

G. Zhang, Z. Luo, B. Fu, B. Li, J. Liao, X. Fan, and Z. Xi, “A symmetry and bi-recursive algorithm of accurately computing Krawtchouk moments,” Pattern Recognit. Lett. 31(7), 548–554 (2010).
[Crossref]

Gibson, G. M.

Gilbert, A. C.

J. A. Tropp and A. C. Gilbert, “Signal recovery from random measurements via orthogonal matching pursuit,” IEEE Trans. Inf. Theory 53(12), 4655–4666 (2007).
[Crossref]

Golabi, S.

S. Golabi, M. S. Helfroush, and H. Danyali, “Non-unit mapped radial moments platform for robust, geometric invariant image watermarking and reversible data hiding,” Inf. Sci. 447, 104–116 (2018).
[Crossref]

Hakim, E. F.

I. Batioua, R. Benouini, K. Zenkouar, A. Zahi, and E. F. Hakim, “3D image analysis by separable discrete orthogonal moments based on Krawtchouk and Tchebichef polynomials,” Pattern Recognit. 71, 264–277 (2017).
[Crossref]

Helfroush, M. S.

S. Golabi, M. S. Helfroush, and H. Danyali, “Non-unit mapped radial moments platform for robust, geometric invariant image watermarking and reversible data hiding,” Inf. Sci. 447, 104–116 (2018).
[Crossref]

Hempler, N.

Howell, J. C.

Howland, G. A.

Hu, S.

Huang, J.

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 meta material spatial light modulators,” Nat. Photonics 8(8), 605–609 (2014).
[Crossref]

Jassim, W. A.

S. H. Abdulhussain, A. R. Ramli, S. A. R. Al-Haddad, B. M. Mahmmod, and W. A. Jassim, “Fast recursive computation of Krawtchouk Polynomials,” J. Math. Imaging Vis. 60(3), 285–303 (2018).
[Crossref]

Jiang, H.

Karakasis, E. G.

G. A. Papakostas, E. G. Karakasis, and D. E. Koulouriotis, “Accurate and speedy computation of image Legendre moments for computer vision applications,” Image and Vision Comput. 28(3), 414–423 (2010).
[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]

Khamoushi, S. M. M.

Koekoek, R.

R. Koekoek and R. F. Swarttouw, “The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue,” arXiv preprint math 9602214 (1996).

Koulouriotis, D. E.

G. A. Papakostas, E. G. Karakasis, and D. E. Koulouriotis, “Accurate and speedy computation of image Legendre moments for computer vision applications,” Image and Vision Comput. 28(3), 414–423 (2010).
[Crossref]

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 meta material spatial light modulators,” Nat. Photonics 8(8), 605–609 (2014).
[Crossref]

Lan, R.

W. Yu, X. Yao, X. Liu, R. Lan, L. Wu, G. 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]

Li, B.

G. Zhang, Z. Luo, B. Fu, B. Li, J. Liao, X. Fan, and Z. Xi, “A symmetry and bi-recursive algorithm of accurately computing Krawtchouk moments,” Pattern Recognit. Lett. 31(7), 548–554 (2010).
[Crossref]

Li, B. Q.

X. Wang, M. L. Xu, B. Q. Li, H. L. Zhai, J. J. Liu, and S. Y. Li, “Prediction of phosphorylation sites based on Krawtchouk image moments,” Proteins 85(12), 2231–2238 (2017).
[Crossref]

Li, C. B.

C. B. Li, “An efficient algorithm for total variation regularization with applications to the single pixel camera and compressive sensing,” (Masters of Science thesis), Rice University, Houston: TX, USA (2010).

Li, L.

X. Liu, W. Yu, X. Yao, B. Dai, L. Li, C. Wang, and G. Zhai, “Measurement dimensions compressed spectral imaging with a single point detector,” Opt. Commun. 365, 173–179 (2016).
[Crossref]

Li, S. Y.

X. Wang, M. L. Xu, B. Q. Li, H. L. Zhai, J. J. Liu, and S. Y. Li, “Prediction of phosphorylation sites based on Krawtchouk image moments,” Proteins 85(12), 2231–2238 (2017).
[Crossref]

Li, X.

Liao, J.

G. Zhang, Z. Luo, B. Fu, B. Li, J. Liao, X. Fan, and Z. Xi, “A symmetry and bi-recursive algorithm of accurately computing Krawtchouk moments,” Pattern Recognit. Lett. 31(7), 548–554 (2010).
[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 meta material spatial light modulators,” Nat. Photonics 8(8), 605–609 (2014).
[Crossref]

Liu, B.

B. Liu, Z. Yang, X. Liu, and L. Wu, “Coloured computational imaging with single-pixel detectors based on a 2D discrete cosine transform,” J. Mod. Opt. 64(3), 259–264 (2017).
[Crossref]

Liu, J. J.

X. Wang, M. L. Xu, B. Q. Li, H. L. Zhai, J. J. Liu, and S. Y. Li, “Prediction of phosphorylation sites based on Krawtchouk image moments,” Proteins 85(12), 2231–2238 (2017).
[Crossref]

Liu, X.

B. Liu, Z. Yang, X. Liu, and L. Wu, “Coloured computational imaging with single-pixel detectors based on a 2D discrete cosine transform,” J. Mod. Opt. 64(3), 259–264 (2017).
[Crossref]

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

X. Liu, W. Yu, X. Yao, B. Dai, L. Li, C. Wang, and G. Zhai, “Measurement dimensions compressed spectral imaging with a single point detector,” Opt. Commun. 365, 173–179 (2016).
[Crossref]

Luo, Z.

G. Zhang, Z. Luo, B. Fu, B. Li, J. Liao, X. Fan, and Z. Xi, “A symmetry and bi-recursive algorithm of accurately computing Krawtchouk moments,” Pattern Recognit. Lett. 31(7), 548–554 (2010).
[Crossref]

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]

Madanayake, A.

V. A. Coutinho, R. J. Cintra, F. M. Bayer, P. A. M. Oliveira, R. S. Oliveira, and A. Madanayake, “Pruned discrete Tchebichef transform approximation for image compression,” Circuits Syst. Signal Process 37(10), 4363–4383 (2018).
[Crossref]

Magalhães, F.

Mahmmod, B. M.

S. H. Abdulhussain, A. R. Ramli, S. A. R. Al-Haddad, B. M. Mahmmod, and W. A. Jassim, “Fast recursive computation of Krawtchouk Polynomials,” J. Math. Imaging Vis. 60(3), 285–303 (2018).
[Crossref]

Maker, G. T.

Malcolm, G. P. A.

Martínez-León, L.

Mitchell, K. J.

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 meta material spatial light modulators,” Nat. Photonics 8(8), 605–609 (2014).
[Crossref]

Mori, Y.

Najah, S.

R. Benouini, I. Batioua, K. Zenkouar, A. Zahi, S. Najah, and H. Qjidaa, “Fractional-order orthogonal Chebyshev moments and moments invariants for image representation and pattern recognition,” Pattern Recognit. 86, 332–343 (2019).
[Crossref]

Needell, D.

D. Needell and J. A. Tropp, “CoSaMP: Iterative signal recovery from incomplete and inaccurate samples,” Appl. Comput. Harmon. Anal 26(3), 301–321 (2009).
[Crossref]

Nosrati, Y.

Oliveira, P. A. M.

V. A. Coutinho, R. J. Cintra, F. M. Bayer, P. A. M. Oliveira, R. S. Oliveira, and A. Madanayake, “Pruned discrete Tchebichef transform approximation for image compression,” Circuits Syst. Signal Process 37(10), 4363–4383 (2018).
[Crossref]

Oliveira, R. S.

V. A. Coutinho, R. J. Cintra, F. M. Bayer, P. A. M. Oliveira, R. S. Oliveira, and A. Madanayake, “Pruned discrete Tchebichef transform approximation for image compression,” Circuits Syst. Signal Process 37(10), 4363–4383 (2018).
[Crossref]

Ong, S. H.

P. T. Yap, R. Paramesran, and S. H. Ong, “Image analysis by Krawtchouk moments,” IEEE Trans. on Image Process. 12(11), 1367–1377 (2003).
[Crossref]

Padgett, M. J.

Padilla, W. J.

K. Fan, J. Y. Suen, and W. J. Padilla, “Graphene metamaterial spatial light modulator for infrared single pixel imaging,” Opt. Express 25(21), 25318–25325 (2017).
[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 meta material spatial light modulators,” Nat. Photonics 8(8), 605–609 (2014).
[Crossref]

Papakostas, G. A.

G. A. Papakostas, E. G. Karakasis, and D. E. Koulouriotis, “Accurate and speedy computation of image Legendre moments for computer vision applications,” Image and Vision Comput. 28(3), 414–423 (2010).
[Crossref]

Paramesran, R.

P. T. Yap, R. Paramesran, and S. H. Ong, “Image analysis by Krawtchouk moments,” IEEE Trans. on Image Process. 12(11), 1367–1377 (2003).
[Crossref]

Phillips, D. B.

Priyal, S. P.

S. P. Priyal and P. K. Bora, “A robust static hand gesture recognition system using geometry based normalizations and Krawtchouk moments,” Pattern Recognit. 46(8), 2202–2219 (2013).
[Crossref]

Qjidaa, H.

R. Benouini, I. Batioua, K. Zenkouar, A. Zahi, S. Najah, and H. Qjidaa, “Fractional-order orthogonal Chebyshev moments and moments invariants for image representation and pattern recognition,” Pattern Recognit. 86, 332–343 (2019).
[Crossref]

Radwell, N.

Ramli, A. R.

S. H. Abdulhussain, A. R. Ramli, S. A. R. Al-Haddad, B. M. Mahmmod, and W. A. Jassim, “Fast recursive computation of Krawtchouk Polynomials,” J. Math. Imaging Vis. 60(3), 285–303 (2018).
[Crossref]

Shi, D.

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 meta material 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 meta material 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 meta material spatial light modulators,” Nat. Photonics 8(8), 605–609 (2014).
[Crossref]

Suen, J. Y.

Sun, B.

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]

Swarttouw, R. F.

R. Koekoek and R. F. Swarttouw, “The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue,” arXiv preprint math 9602214 (1996).

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]

Tavassoli, S. H.

Tropp, J. A.

D. Needell and J. A. Tropp, “CoSaMP: Iterative signal recovery from incomplete and inaccurate samples,” Appl. Comput. Harmon. Anal 26(3), 301–321 (2009).
[Crossref]

J. A. Tropp and A. C. Gilbert, “Signal recovery from random measurements via orthogonal matching pursuit,” IEEE Trans. Inf. Theory 53(12), 4655–4666 (2007).
[Crossref]

Wang, C.

X. Liu, W. Yu, X. Yao, B. Dai, L. Li, C. Wang, and G. Zhai, “Measurement dimensions compressed spectral imaging with a single point detector,” Opt. Commun. 365, 173–179 (2016).
[Crossref]

Wang, X.

Z. Zhang, X. Wang, G. Zheng, and J. Zhong, “Fast Fourier single-pixel imaging via binary illumination,” Sci. Rep. 7(1), 12029 (2017).
[Crossref]

Z. Zhang, X. Wang, G. Zheng, and J. Zhong, “Hadamard single-pixel imaging versus Fourier single-pixel imaging,” Opt. Express 25(16), 19619–19639 (2017).
[Crossref]

X. Wang, M. L. Xu, B. Q. Li, H. L. Zhai, J. J. Liu, and S. Y. Li, “Prediction of phosphorylation sites based on Krawtchouk image moments,” Proteins 85(12), 2231–2238 (2017).
[Crossref]

Wang, Y.

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 meta material spatial light modulators,” Nat. Photonics 8(8), 605–609 (2014).
[Crossref]

Wu, L.

B. Liu, Z. Yang, X. Liu, and L. Wu, “Coloured computational imaging with single-pixel detectors based on a 2D discrete cosine transform,” J. Mod. Opt. 64(3), 259–264 (2017).
[Crossref]

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

Xi, Z.

G. Zhang, Z. Luo, B. Fu, B. Li, J. Liao, X. Fan, and Z. Xi, “A symmetry and bi-recursive algorithm of accurately computing Krawtchouk moments,” Pattern Recognit. Lett. 31(7), 548–554 (2010).
[Crossref]

Xu, B.

Xu, M. L.

X. Wang, M. L. Xu, B. Q. Li, H. L. Zhai, J. J. Liu, and S. Y. Li, “Prediction of phosphorylation sites based on Krawtchouk image moments,” Proteins 85(12), 2231–2238 (2017).
[Crossref]

Yang, Z.

B. Liu, Z. Yang, X. Liu, and L. Wu, “Coloured computational imaging with single-pixel detectors based on a 2D discrete cosine transform,” J. Mod. Opt. 64(3), 259–264 (2017).
[Crossref]

Yao, X.

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

X. Liu, W. Yu, X. Yao, B. Dai, L. Li, C. Wang, and G. Zhai, “Measurement dimensions compressed spectral imaging with a single point detector,” Opt. Commun. 365, 173–179 (2016).
[Crossref]

Yap, P. T.

P. T. Yap, R. Paramesran, and S. H. Ong, “Image analysis by Krawtchouk moments,” IEEE Trans. on Image Process. 12(11), 1367–1377 (2003).
[Crossref]

Yu, W.

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

X. Liu, W. Yu, X. Yao, B. Dai, L. Li, C. Wang, and G. Zhai, “Measurement dimensions compressed spectral imaging with a single point detector,” Opt. Commun. 365, 173–179 (2016).
[Crossref]

Yuan, K.

Zahi, A.

R. Benouini, I. Batioua, K. Zenkouar, A. Zahi, S. Najah, and H. Qjidaa, “Fractional-order orthogonal Chebyshev moments and moments invariants for image representation and pattern recognition,” Pattern Recognit. 86, 332–343 (2019).
[Crossref]

I. Batioua, R. Benouini, K. Zenkouar, A. Zahi, and E. F. Hakim, “3D image analysis by separable discrete orthogonal moments based on Krawtchouk and Tchebichef polynomials,” Pattern Recognit. 71, 264–277 (2017).
[Crossref]

Zenkouar, K.

R. Benouini, I. Batioua, K. Zenkouar, A. Zahi, S. Najah, and H. Qjidaa, “Fractional-order orthogonal Chebyshev moments and moments invariants for image representation and pattern recognition,” Pattern Recognit. 86, 332–343 (2019).
[Crossref]

I. Batioua, R. Benouini, K. Zenkouar, A. Zahi, and E. F. Hakim, “3D image analysis by separable discrete orthogonal moments based on Krawtchouk and Tchebichef polynomials,” Pattern Recognit. 71, 264–277 (2017).
[Crossref]

Zhai, G.

X. Liu, W. Yu, X. Yao, B. Dai, L. Li, C. Wang, and G. Zhai, “Measurement dimensions compressed spectral imaging with a single point detector,” Opt. Commun. 365, 173–179 (2016).
[Crossref]

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

Zhai, H. L.

X. Wang, M. L. Xu, B. Q. Li, H. L. Zhai, J. J. Liu, and S. Y. Li, “Prediction of phosphorylation sites based on Krawtchouk image moments,” Proteins 85(12), 2231–2238 (2017).
[Crossref]

Zhang, G.

G. Zhang, Z. Luo, B. Fu, B. Li, J. Liao, X. Fan, and Z. Xi, “A symmetry and bi-recursive algorithm of accurately computing Krawtchouk moments,” Pattern Recognit. Lett. 31(7), 548–554 (2010).
[Crossref]

Zhang, Z.

Z. Zhang, X. Wang, G. Zheng, and J. Zhong, “Hadamard single-pixel imaging versus Fourier single-pixel imaging,” Opt. Express 25(16), 19619–19639 (2017).
[Crossref]

Z. Zhang, X. Wang, G. Zheng, and J. Zhong, “Fast Fourier single-pixel imaging via binary illumination,” Sci. Rep. 7(1), 12029 (2017).
[Crossref]

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

Zhao, H.

Zhao, Q.

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

Zheng, G.

Z. Zhang, X. Wang, G. Zheng, and J. Zhong, “Fast Fourier single-pixel imaging via binary illumination,” Sci. Rep. 7(1), 12029 (2017).
[Crossref]

Z. Zhang, X. Wang, G. Zheng, and J. Zhong, “Hadamard single-pixel imaging versus Fourier single-pixel imaging,” Opt. Express 25(16), 19619–19639 (2017).
[Crossref]

Zhong, J.

Z. Zhang, X. Wang, G. Zheng, and J. Zhong, “Hadamard single-pixel imaging versus Fourier single-pixel imaging,” Opt. Express 25(16), 19619–19639 (2017).
[Crossref]

Z. Zhang, X. Wang, G. Zheng, and J. Zhong, “Fast Fourier single-pixel imaging via binary illumination,” Sci. Rep. 7(1), 12029 (2017).
[Crossref]

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

Zhu, S.

Appl. Comput. Harmon. Anal (1)

D. Needell and J. A. Tropp, “CoSaMP: Iterative signal recovery from incomplete and inaccurate samples,” Appl. Comput. Harmon. Anal 26(3), 301–321 (2009).
[Crossref]

Appl. Opt. (2)

Circuits Syst. Signal Process (1)

V. A. Coutinho, R. J. Cintra, F. M. Bayer, P. A. M. Oliveira, R. S. Oliveira, and A. Madanayake, “Pruned discrete Tchebichef transform approximation for image compression,” Circuits Syst. Signal Process 37(10), 4363–4383 (2018).
[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]

IEEE Trans. Inf. Theory (1)

J. A. Tropp and A. C. Gilbert, “Signal recovery from random measurements via orthogonal matching pursuit,” IEEE Trans. Inf. Theory 53(12), 4655–4666 (2007).
[Crossref]

IEEE Trans. on Image Process. (1)

P. T. Yap, R. Paramesran, and S. H. Ong, “Image analysis by Krawtchouk moments,” IEEE Trans. on Image Process. 12(11), 1367–1377 (2003).
[Crossref]

Image and Vision Comput. (1)

G. A. Papakostas, E. G. Karakasis, and D. E. Koulouriotis, “Accurate and speedy computation of image Legendre moments for computer vision applications,” Image and Vision Comput. 28(3), 414–423 (2010).
[Crossref]

Inf. Sci. (1)

S. Golabi, M. S. Helfroush, and H. Danyali, “Non-unit mapped radial moments platform for robust, geometric invariant image watermarking and reversible data hiding,” Inf. Sci. 447, 104–116 (2018).
[Crossref]

J. Math. Imaging Vis. (1)

S. H. Abdulhussain, A. R. Ramli, S. A. R. Al-Haddad, B. M. Mahmmod, and W. A. Jassim, “Fast recursive computation of Krawtchouk Polynomials,” J. Math. Imaging Vis. 60(3), 285–303 (2018).
[Crossref]

J. Mod. Opt. (1)

B. Liu, Z. Yang, X. Liu, and L. Wu, “Coloured computational imaging with single-pixel detectors based on a 2D discrete cosine transform,” J. Mod. Opt. 64(3), 259–264 (2017).
[Crossref]

Nat. Commun. (1)

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

Nat. Photonics (1)

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 meta material spatial light modulators,” Nat. Photonics 8(8), 605–609 (2014).
[Crossref]

Opt. Commun. (2)

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

X. Liu, W. Yu, X. Yao, B. Dai, L. Li, C. Wang, and G. Zhai, “Measurement dimensions compressed spectral imaging with a single point detector,” Opt. Commun. 365, 173–179 (2016).
[Crossref]

Opt. Express (6)

Opt. Lett. (1)

Optica (1)

Pattern Recognit. (3)

S. P. Priyal and P. K. Bora, “A robust static hand gesture recognition system using geometry based normalizations and Krawtchouk moments,” Pattern Recognit. 46(8), 2202–2219 (2013).
[Crossref]

R. Benouini, I. Batioua, K. Zenkouar, A. Zahi, S. Najah, and H. Qjidaa, “Fractional-order orthogonal Chebyshev moments and moments invariants for image representation and pattern recognition,” Pattern Recognit. 86, 332–343 (2019).
[Crossref]

I. Batioua, R. Benouini, K. Zenkouar, A. Zahi, and E. F. Hakim, “3D image analysis by separable discrete orthogonal moments based on Krawtchouk and Tchebichef polynomials,” Pattern Recognit. 71, 264–277 (2017).
[Crossref]

Pattern Recognit. Lett. (1)

G. Zhang, Z. Luo, B. Fu, B. Li, J. Liao, X. Fan, and Z. Xi, “A symmetry and bi-recursive algorithm of accurately computing Krawtchouk moments,” Pattern Recognit. Lett. 31(7), 548–554 (2010).
[Crossref]

Proteins (1)

X. Wang, M. L. Xu, B. Q. Li, H. L. Zhai, J. J. Liu, and S. Y. Li, “Prediction of phosphorylation sites based on Krawtchouk image moments,” Proteins 85(12), 2231–2238 (2017).
[Crossref]

Sci. Rep. (1)

Z. Zhang, X. Wang, G. Zheng, and J. Zhong, “Fast Fourier single-pixel imaging via binary illumination,” Sci. Rep. 7(1), 12029 (2017).
[Crossref]

Other (2)

C. B. Li, “An efficient algorithm for total variation regularization with applications to the single pixel camera and compressive sensing,” (Masters of Science thesis), Rice University, Houston: TX, USA (2010).

R. Koekoek and R. F. Swarttouw, “The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue,” arXiv preprint math 9602214 (1996).

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Figures (9)

Fig. 1.
Fig. 1. Part of the Krawtchouk basis patterns for $N$ = $M$ = 128 and $p_1$ = $p_2$ = 0.5. (a) Part of the patterns $P(x,\;y;n,\;m)$ generated from Eq. (15); (b) The pair of patterns ${P^+}(x,\;y;n,\;m)$ and ${P^-}(x,\;y;n,\;m)$ split from $P(x,\;y;n,\;m)$ by Eq. (17).
Fig. 2.
Fig. 2. Procedure of single-pixel imaging based on Krawtchouk moments ($N$ = 128, $M$ = 128; $p_1$ = 0.5, $p_2$ = 0.5). (a) Complete sampling ($N_{max}$ = 128, $M_{max}$ = 128); (b) Compressive sampling ($N_{max}$ = 41, $M_{max}$ = 41).
Fig. 3.
Fig. 3. The Krawtchouk moments and the reconstructed images of Peppers and Cameraman images at different sampling rates.(KM: Krawtchouk Moments; RI: Reconstructed image).
Fig. 4.
Fig. 4. The region-of-interest image reconstruction results of the krawtchouk moments with different parameters $p_1$ and $p_2$.
Fig. 5.
Fig. 5. Comparison of reconstruction results of USAF and Dog images by KM-SPI and Fourier-SPI method.
Fig. 6.
Fig. 6. The influence of the quantization bits in the imaging results.
Fig. 7.
Fig. 7. RMSEs under different quantization bits.
Fig. 8.
Fig. 8. Schematic of the experimental system of the proposed method.
Fig. 9.
Fig. 9. Reconstructed images of single-pixel compressive imaging experiments. (a) Reconstruction images of Fourier-SPI method; (b)Reconstruction images of KM-SPI method.

Tables (2)

Tables Icon

Table 1. Comparisons of RMSEs of the reconstruction results at different sampling rates.

Tables Icon

Table 2. Comparisons of reconstructed computational time (Unit: s).

Equations (22)

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

K n ( x ; p , N ) = k = 0 N a k , n , p x k = 2 F 1 ( n , x ; N ; 1 p )
2 F 1 ( a , b ; c ; z ) = k = 0 ( a ) k ( b ) k ( c ) k z k k !
( a ) k = a ( a + 1 ) ( a + k 1 ) = Γ ( a + k ) Γ ( a )
ω ( x ; p , N ) = ( N x ) p x ( 1 p ) ( N x )
x = 0 N ω ( x ; p , N ) K n ( x ; p , N ) K m ( x ; p , N ) = ρ ( n ; p , N ) δ n m
ρ ( n ; p , N ) = ( 1 ) n ( 1 p p ) n n ! ( N ) n
K ¯ n ( x ; p , N ) = K n ( x ; p , N ) ω ( x ; p , N ) ρ ( n ; p , N )
x = 0 N K ¯ n ( x ; p , N ) K ¯ m ( x ; p , N ) = δ n m
K ¯ n ( x ; p , N 1 ) = A n K ¯ n 1 ( x ; p , N 1 ) B n K ¯ n 2 ( x ; p , N 1 ) K ¯ 0 ( x ; p , N 1 ) = ω ( x ; p , N 1 ) K ¯ 1 ( x ; p , N 1 ) = ω ( x ; p , N 1 ) ( N 1 ) p x ( N 1 ) p ( 1 p )
ω ( x + 1 ; p , N ) = ( N x x + 1 ) p 1 p ω ( x ; p , N )
Q n m = x = 0 N 1 y = 0 M 1 K ¯ n ( x ; p 1 , N 1 ) K ¯ m ( y ; p 2 , M 1 ) f ( x , y )
f ( x , y ) = n = 0 N m a x 1 m = 0 M m a x 1 K ¯ n ( x ; p 1 , N 1 ) K ¯ m ( y ; p 2 , M 1 ) Q n m
K ¯ n ( x ; p , N 1 ) = ( 1 ) n K ¯ n ( N 1 x ; p , N 1 )
K ¯ n ( x ; p , N 1 ) = ( 1 ) x K ¯ N 1 n ( x ; p , N 1 )
P ( x , y ; n , m ) = K ¯ n ( x ; p 1 , N 1 ) K ¯ m ( y ; p 2 , M 1 )
E ( n i , m j ) = E 0 + t E R ( n i , m j ) = E 0 + t x = 0 N 1 y = 0 M 1 P ( x , y ; n i , m j ) I ( x , y )
P ( x , y ; n , m ) = P + ( x , y ; n , m ) P ( x , y ; n , m )
E ( n i , m j ) = E + ( n i , m j ) E ( n i , m j ) = ( E 0 + t x = 0 N 1 y = 0 M 1 P + ( x , y ; n i , m j ) I ( x , y ) ) ( E 0 + t x = 0 N 1 y = 0 M 1 P ( x , y ; n i , m j ) I ( x , y ) ) = t x = 0 N 1 y = 0 M 1 P + ( x , y ; n i , m j ) I ( x , y ) t x = 0 N 1 y = 0 M 1 P ( x , y ; n i , m j ) I ( x , y )
I K ( n , m ) = x = 0 N 1 y = 0 M 1 K ¯ n ( x ; p 1 , N 1 ) K ¯ m ( y ; p 2 , M 1 ) I ( x , y ) = 1 t E ( n , m )
I R ( x , y ) = n = 0 N m a x 1 m = 0 M m a x 1 K ¯ n ( x ; p 1 , N 1 ) K ¯ m ( y ; p 2 , M 1 ) E ( n , m ) = t n = 0 N m a x 1 m = 0 M m a x 1 K ¯ n ( x ; p 1 , N 1 ) K ¯ m ( y ; p 2 , M 1 ) I K ( n , m ) = t I ( x , y ) I ( x , y )
I R = K m T E K n
R M S E = x = 1 M y = 1 N [ I R ( x , y ) I ( x , y ) ] 2 M N

Metrics