Abstract

We present a closed-form image reconstruction method for single-pixel imaging based on the generalized inverse of the measurement matrix. Its numerical cost scales proportionally with the number of measured samples. Regularization of the inverse problem is obtained by minimizing the norms of the convolution between the reconstructed image and a set of spatial filters. The final reconstruction formula can be expressed in terms of matrix pseudoinverse. At high compression, this approach is an interesting alternative to the methods of compressive sensing based on l1-norm optimization, which are too slow for real-time applications. For instance, we demonstrate experimental single-pixel detection with real-time reconstruction obtained in parallel with measurement at a frame rate of 11 Hz for highly compressive measurements with a resolution of 256 × 256. To this end, we preselect the sampling functions to match the average spectrum obtained with an image database. The sampling functions are selected from the Walsh-Hadamard basis, from the discrete cosine basis, or from a subset of Morlet wavelets convolved with white noise. We show that by incorporating the quadratic criterion into the closed-form reconstruction formula, we can use binary rather than continuous sampling and reach similar reconstruction quality as is obtained by minimizing the total variation. This makes it possible to use cosine- or Morlet-based sampling with digital micromirror devices without advanced binarization methods.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref] [PubMed]

2018 (7)

2017 (6)

W. Yuwang, L. Yang, S. Jinli, S. Guohai, Q. Chang, and D. Qionghai, “High Speed Computational Ghost Imaging via Spatial Sweeping,” Sci. Rep. 7, 45325 (2017).
[Crossref]

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]

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

J. Senlin, H. Wangwei, W. Yunlong, H. Kaicheng, S. Qiushuai, Y. Cuifeng, L. Dongqi, Ye Qing, Z. Wenyuan, and T. Jianguo, “Hyperspectral imaging using the single-pixel Fourier transform technique,” Sci. Rep. 7, 45209 (2017).
[Crossref]

Q. Pian, R. Yao, N. Sinsuebphon, and X. Intes, “Compressive hyperspectral time-resolved wide-field fluorescence lifetime imaging,” Nat. Photon. 11, 411–414 (2017).
[Crossref]

D. Pastor, A. Pastuszczak, M. Mikolajczyk, and R. Kotynski, “Compressive phase-only filtering at extreme compression rates,” Opt. Commun. 383, 446–452 (2017).
[Crossref]

2016 (6)

M. Sun, M. Edgar, G. Gibson, N. R. B. Sun, R. Lamb, and M. Padget, “Single-pixel three-dimentional imaging with time-based depth resolution,” Nat. Commun. 7, 12010 (2016).
[Crossref]

L. Bian, J. Suo, G. Situ, Z. Li, J. Fan, F. Chen, and Q. Dai, “Multispectral imaging using a single bucket detector,” Sci. Rep. 6, 24752 (2016).
[Crossref] [PubMed]

Z. Li, J. Suo, X. Hu, C. Deng, J. Fan, and Q. Dai, “Effucient single-pixel multispectral imaging via non-mechanical spatio-spectral modulation,” Sci. Rep. 7, 41435 (2016).
[Crossref]

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]

D. J. Starling, I. Storer, and G. A. Howland, “Compressive sensing spectroscopy with a single pixel camera,” Appl. Opt. 55(19), 5198–5202 (2016).
[Crossref] [PubMed]

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] [PubMed]

2015 (4)

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] [PubMed]

W. Gong, “High-resolution pseudo-inverse ghost imaging,” Photonics Res. 3(5), 234 (2015).
[Crossref]

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

V. Durán, F. Soldevila, E. Irles, P. Clemente, E. Tajahuerce, P. Andrés, and J. Lancis, “Compressive imaging in scattering media,” Opt. Express 23(11), 14424–14433 (2015).
[Crossref] [PubMed]

2014 (3)

2013 (2)

F. Soldevila, E. Irles, V. Durán, P. Clemente, M. Fernández-Alonso, E. Tajahuerce, and J. Lancis, “Single-pixel polarimetric imaging spectrometer by compressive sensing,” Appl. Phys. B 113(3), 551–558 (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(6134), 844–847 (2013).
[Crossref] [PubMed]

2012 (1)

2009 (1)

S. Becker, J. Bobin, and E. J. Candes, “NESTA: a fast and accurate first-order method for sparse recovery,” SIAM J. Imaging Sci. 4(1), 1–39 (2009).
[Crossref]

2008 (5)

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

J. H. Shapiro, “Computational ghost imaging,” Phys. Rev. A 78, 061802 (2008).
[Crossref]

E. J. Candes and M. B. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25(2), 21–30 (2008).
[Crossref]

J. Romberg, “Imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 14–20 (2008).
[Crossref]

D. L. Donoho and Y. Tsaig, “Fast solution of ℓ1 -norm minimization problems when the solution may be sparse,” IEEE Trans. Inf. Theory 54(11), 4789–4812 (2008).
[Crossref]

2007 (1)

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

1985 (1)

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] [PubMed]

V. Durán, F. Soldevila, E. Irles, P. Clemente, E. Tajahuerce, P. Andrés, and J. Lancis, “Compressive imaging in scattering media,” Opt. Express 23(11), 14424–14433 (2015).
[Crossref] [PubMed]

Arridge, S.

Baraniuk, R.

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

Beard, P.

Becker, S.

S. Becker, J. Bobin, and E. J. Candes, “NESTA: a fast and accurate first-order method for sparse recovery,” SIAM J. Imaging Sci. 4(1), 1–39 (2009).
[Crossref]

Betcke, M.

Bian, L.

L. Bian, J. Suo, Q. Dai, and F. Chen, “Experimental comparison of single-pixel imaging algorithms,” J. Opt. Soc. Am. A 35(1), 78–87 (2018).
[Crossref]

L. Bian, J. Suo, G. Situ, Z. Li, J. Fan, F. Chen, and Q. Dai, “Multispectral imaging using a single bucket detector,” Sci. Rep. 6, 24752 (2016).
[Crossref] [PubMed]

Bobin, J.

J. Fade, E. Perrotin, and J. Bobin, “Polarizer-free two-pixel polarimetric camera by compressive sensing,” Appl. Opt. 57(7), B102–B113 (2018).
[Crossref] [PubMed]

S. Becker, J. Bobin, and E. J. Candes, “NESTA: a fast and accurate first-order method for sparse recovery,” SIAM J. Imaging Sci. 4(1), 1–39 (2009).
[Crossref]

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.

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

Candes, E.

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

Candes, E. J.

S. Becker, J. Bobin, and E. J. Candes, “NESTA: a fast and accurate first-order method for sparse recovery,” SIAM J. Imaging Sci. 4(1), 1–39 (2009).
[Crossref]

E. J. Candes and M. B. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25(2), 21–30 (2008).
[Crossref]

Cao, J.

Chang, Q.

W. Yuwang, L. Yang, S. Jinli, S. Guohai, Q. Chang, and D. Qionghai, “High Speed Computational Ghost Imaging via Spatial Sweeping,” Sci. Rep. 7, 45325 (2017).
[Crossref]

Chao, W.

Y. Wen-Kai, L. Xue-Feng, Y. Xu-Ri, W. Chao, Z. Yun, and Z. Guang-Jie, “Complementary compressive imaging for the telescopic system,” Sci. Rep. 4, 5834 (2014).

Chen, F.

L. Bian, J. Suo, Q. Dai, and F. Chen, “Experimental comparison of single-pixel imaging algorithms,” J. Opt. Soc. Am. A 35(1), 78–87 (2018).
[Crossref]

L. Bian, J. Suo, G. Situ, Z. Li, J. Fan, F. Chen, and Q. Dai, “Multispectral imaging using a single bucket detector,” Sci. Rep. 6, 24752 (2016).
[Crossref] [PubMed]

Chen, J.

Chen, W.

Clemente, 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] [PubMed]

V. Durán, F. Soldevila, E. Irles, P. Clemente, E. Tajahuerce, P. Andrés, and J. Lancis, “Compressive imaging in scattering media,” Opt. Express 23(11), 14424–14433 (2015).
[Crossref] [PubMed]

F. Soldevila, E. Irles, V. Durán, P. Clemente, M. Fernández-Alonso, E. Tajahuerce, and J. Lancis, “Single-pixel polarimetric imaging spectrometer by compressive sensing,” Appl. Phys. B 113(3), 551–558 (2013).
[Crossref]

V. Duran, P. Clemente, M. Fernandez-Alonso, E. Tajahuerce, and J. Lancis, “Single-pixel polarimetric imaging,” Opt. Lett. 37(5), 824–826 (2012).
[Crossref] [PubMed]

Cox, B.

Cuifeng, Y.

J. Senlin, H. Wangwei, W. Yunlong, H. Kaicheng, S. Qiushuai, Y. Cuifeng, L. Dongqi, Ye Qing, Z. Wenyuan, and T. Jianguo, “Hyperspectral imaging using the single-pixel Fourier transform technique,” Sci. Rep. 7, 45209 (2017).
[Crossref]

Czajkowski, K. M.

K. M. Czajkowski, A. Pastuszczak, and R. Kotynski, “Single-pixel imaging with Morlet wavelet correlated random patterns,” Sci. Rep. 8, 466 (2018).
[Crossref] [PubMed]

Dai, Q.

L. Bian, J. Suo, Q. Dai, and F. Chen, “Experimental comparison of single-pixel imaging algorithms,” J. Opt. Soc. Am. A 35(1), 78–87 (2018).
[Crossref]

Z. Li, J. Suo, X. Hu, C. Deng, J. Fan, and Q. Dai, “Effucient single-pixel multispectral imaging via non-mechanical spatio-spectral modulation,” Sci. Rep. 7, 41435 (2016).
[Crossref]

L. Bian, J. Suo, G. Situ, Z. Li, J. Fan, F. Chen, and Q. Dai, “Multispectral imaging using a single bucket detector,” Sci. Rep. 6, 24752 (2016).
[Crossref] [PubMed]

Daugman, J. G.

Davenport, M.

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

Deng, C.

Z. Li, J. Suo, X. Hu, C. Deng, J. Fan, and Q. Dai, “Effucient single-pixel multispectral imaging via non-mechanical spatio-spectral modulation,” Sci. Rep. 7, 41435 (2016).
[Crossref]

Dokmanic, I.

I. Dokmanic, M. Kolundzija, and M. Vetterli, “Beyond Moore-Penrose: Sparse pseudoinverse,” in “2013 IEEE International Conference on Acoustics, Speech and Signal Processing,” (IEEE, 2013), pp. 6526–6530.

Dongqi, L.

J. Senlin, H. Wangwei, W. Yunlong, H. Kaicheng, S. Qiushuai, Y. Cuifeng, L. Dongqi, Ye Qing, Z. Wenyuan, and T. Jianguo, “Hyperspectral imaging using the single-pixel Fourier transform technique,” Sci. Rep. 7, 45209 (2017).
[Crossref]

Donoho, D. L.

D. L. Donoho and Y. Tsaig, “Fast solution of ℓ1 -norm minimization problems when the solution may be sparse,” IEEE Trans. Inf. Theory 54(11), 4789–4812 (2008).
[Crossref]

Duarte, M.

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

Duran, V.

Durán, V.

V. Durán, F. Soldevila, E. Irles, P. Clemente, E. Tajahuerce, P. Andrés, and J. Lancis, “Compressive imaging in scattering media,” Opt. Express 23(11), 14424–14433 (2015).
[Crossref] [PubMed]

F. Soldevila, E. Irles, V. Durán, P. Clemente, M. Fernández-Alonso, E. Tajahuerce, and J. Lancis, “Single-pixel polarimetric imaging spectrometer by compressive sensing,” Appl. Phys. B 113(3), 551–558 (2013).
[Crossref]

Edgar, M.

M. Sun, M. Edgar, G. Gibson, N. R. B. Sun, R. Lamb, and M. Padget, “Single-pixel three-dimentional imaging with time-based depth resolution,” Nat. Commun. 7, 12010 (2016).
[Crossref]

Edgar, M. P.

C. F. Higham, R. Murray-Smith, M. J. Padgett, and M. P. Edgar,“Deep learning for real-time single-pixel video,” Sci. Rep. 8, 2369 (2018).
[Crossref] [PubMed]

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. 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] [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]

Eldar, Y. C.

Y. C. Eldar, Sampling theory, Beyond Bandlimted Systems(Cambridge University, 2015).

Fade, J.

Fan, J.

Z. Li, J. Suo, X. Hu, C. Deng, J. Fan, and Q. Dai, “Effucient single-pixel multispectral imaging via non-mechanical spatio-spectral modulation,” Sci. Rep. 7, 41435 (2016).
[Crossref]

L. Bian, J. Suo, G. Situ, Z. Li, J. Fan, F. Chen, and Q. Dai, “Multispectral imaging using a single bucket detector,” Sci. Rep. 6, 24752 (2016).
[Crossref] [PubMed]

Fernandez-Alonso, M.

Fernández-Alonso, M.

F. Soldevila, E. Irles, V. Durán, P. Clemente, M. Fernández-Alonso, E. Tajahuerce, and J. Lancis, “Single-pixel polarimetric imaging spectrometer by compressive sensing,” Appl. Phys. B 113(3), 551–558 (2013).
[Crossref]

Gao, F.

Gibson, G.

M. Sun, M. Edgar, G. Gibson, N. R. B. Sun, R. Lamb, and M. Padget, “Single-pixel three-dimentional imaging with time-based depth resolution,” Nat. Commun. 7, 12010 (2016).
[Crossref]

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. 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] [PubMed]

Gong, W.

W. Gong, “High-resolution pseudo-inverse ghost imaging,” Photonics Res. 3(5), 234 (2015).
[Crossref]

Guan, J.

Guang-Jie, Z.

Y. Wen-Kai, L. Xue-Feng, Y. Xu-Ri, W. Chao, Z. Yun, and Z. Guang-Jie, “Complementary compressive imaging for the telescopic system,” Sci. Rep. 4, 5834 (2014).

Guo, S.

Guohai, S.

W. Yuwang, L. Yang, S. Jinli, S. Guohai, Q. Chang, and D. Qionghai, “High Speed Computational Ghost Imaging via Spatial Sweeping,” Sci. Rep. 7, 45325 (2017).
[Crossref]

Han, X.

Hempler, N.

Higham, C. F.

C. F. Higham, R. Murray-Smith, M. J. Padgett, and M. P. Edgar,“Deep learning for real-time single-pixel video,” Sci. Rep. 8, 2369 (2018).
[Crossref] [PubMed]

Howland, G. A.

Hu, X.

Z. Li, J. Suo, X. Hu, C. Deng, J. Fan, and Q. Dai, “Effucient single-pixel multispectral imaging via non-mechanical spatio-spectral modulation,” Sci. Rep. 7, 41435 (2016).
[Crossref]

Huynh, N.

Intes, X.

Q. Pian, R. Yao, N. Sinsuebphon, and X. Intes, “Compressive hyperspectral time-resolved wide-field fluorescence lifetime imaging,” Nat. Photon. 11, 411–414 (2017).
[Crossref]

Irles, E.

V. Durán, F. Soldevila, E. Irles, P. Clemente, E. Tajahuerce, P. Andrés, and J. Lancis, “Compressive imaging in scattering media,” Opt. Express 23(11), 14424–14433 (2015).
[Crossref] [PubMed]

F. Soldevila, E. Irles, V. Durán, P. Clemente, M. Fernández-Alonso, E. Tajahuerce, and J. Lancis, “Single-pixel polarimetric imaging spectrometer by compressive sensing,” Appl. Phys. B 113(3), 551–558 (2013).
[Crossref]

Jian, W.

Jianguo, T.

J. Senlin, H. Wangwei, W. Yunlong, H. Kaicheng, S. Qiushuai, Y. Cuifeng, L. Dongqi, Ye Qing, Z. Wenyuan, and T. Jianguo, “Hyperspectral imaging using the single-pixel Fourier transform technique,” Sci. Rep. 7, 45209 (2017).
[Crossref]

Jinli, S.

W. Yuwang, L. Yang, S. Jinli, S. Guohai, Q. Chang, and D. Qionghai, “High Speed Computational Ghost Imaging via Spatial Sweeping,” Sci. Rep. 7, 45325 (2017).
[Crossref]

Kaicheng, H.

J. Senlin, H. Wangwei, W. Yunlong, H. Kaicheng, S. Qiushuai, Y. Cuifeng, L. Dongqi, Ye Qing, Z. Wenyuan, and T. Jianguo, “Hyperspectral imaging using the single-pixel Fourier transform technique,” Sci. Rep. 7, 45209 (2017).
[Crossref]

Kelly, K.

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

Kolundzija, M.

I. Dokmanic, M. Kolundzija, and M. Vetterli, “Beyond Moore-Penrose: Sparse pseudoinverse,” in “2013 IEEE International Conference on Acoustics, Speech and Signal Processing,” (IEEE, 2013), pp. 6526–6530.

Kotynski, R.

K. M. Czajkowski, A. Pastuszczak, and R. Kotynski, “Single-pixel imaging with Morlet wavelet correlated random patterns,” Sci. Rep. 8, 466 (2018).
[Crossref] [PubMed]

D. Pastor, A. Pastuszczak, M. Mikolajczyk, and R. Kotynski, “Compressive phase-only filtering at extreme compression rates,” Opt. Commun. 383, 446–452 (2017).
[Crossref]

Lamb, R.

M. Sun, M. Edgar, G. Gibson, N. R. B. Sun, R. Lamb, and M. Padget, “Single-pixel three-dimentional imaging with time-based depth resolution,” Nat. Commun. 7, 12010 (2016).
[Crossref]

Lancis, J.

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] [PubMed]

V. Durán, F. Soldevila, E. Irles, P. Clemente, E. Tajahuerce, P. Andrés, and J. Lancis, “Compressive imaging in scattering media,” Opt. Express 23(11), 14424–14433 (2015).
[Crossref] [PubMed]

F. Soldevila, E. Irles, V. Durán, P. Clemente, M. Fernández-Alonso, E. Tajahuerce, and J. Lancis, “Single-pixel polarimetric imaging spectrometer by compressive sensing,” Appl. Phys. B 113(3), 551–558 (2013).
[Crossref]

V. Duran, P. Clemente, M. Fernandez-Alonso, E. Tajahuerce, and J. Lancis, “Single-pixel polarimetric imaging,” Opt. Lett. 37(5), 824–826 (2012).
[Crossref] [PubMed]

Laska, J.

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

Li, L.

Li, Z.

Z. Li, J. Suo, X. Hu, C. Deng, J. Fan, and Q. Dai, “Effucient single-pixel multispectral imaging via non-mechanical spatio-spectral modulation,” Sci. Rep. 7, 41435 (2016).
[Crossref]

L. Bian, J. Suo, G. Situ, Z. Li, J. Fan, F. Chen, and Q. Dai, “Multispectral imaging using a single bucket detector,” Sci. Rep. 6, 24752 (2016).
[Crossref] [PubMed]

Liu, C.

Liu, J.

Liu, X.

X. Liu, J. Shi, X. Wu, and G. Zeng, “Fast first-photon ghost imaging,” Sci. Rep. 8, 5012 (2018).
[Crossref] [PubMed]

Ma, X.

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

Maker, G. T.

Malcolm, G. P. A.

Mikolajczyk, M.

D. Pastor, A. Pastuszczak, M. Mikolajczyk, and R. Kotynski, “Compressive phase-only filtering at extreme compression rates,” Opt. Commun. 383, 446–452 (2017).
[Crossref]

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] [PubMed]

Murray-Smith, R.

C. F. Higham, R. Murray-Smith, M. J. Padgett, and M. P. Edgar,“Deep learning for real-time single-pixel video,” Sci. Rep. 8, 2369 (2018).
[Crossref] [PubMed]

Padget, M.

M. Sun, M. Edgar, G. Gibson, N. R. B. Sun, R. Lamb, and M. Padget, “Single-pixel three-dimentional imaging with time-based depth resolution,” Nat. Commun. 7, 12010 (2016).
[Crossref]

Padgett, M.

Padgett, M. J.

C. F. Higham, R. Murray-Smith, M. J. Padgett, and M. P. Edgar,“Deep learning for real-time single-pixel video,” Sci. Rep. 8, 2369 (2018).
[Crossref] [PubMed]

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. 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] [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]

Pastor, D.

D. Pastor, A. Pastuszczak, M. Mikolajczyk, and R. Kotynski, “Compressive phase-only filtering at extreme compression rates,” Opt. Commun. 383, 446–452 (2017).
[Crossref]

Pastuszczak, A.

K. M. Czajkowski, A. Pastuszczak, and R. Kotynski, “Single-pixel imaging with Morlet wavelet correlated random patterns,” Sci. Rep. 8, 466 (2018).
[Crossref] [PubMed]

D. Pastor, A. Pastuszczak, M. Mikolajczyk, and R. Kotynski, “Compressive phase-only filtering at extreme compression rates,” Opt. Commun. 383, 446–452 (2017).
[Crossref]

Penuelas, J.

Perrotin, E.

Phillips, D. B.

Pian, Q.

Q. Pian, R. Yao, N. Sinsuebphon, and X. Intes, “Compressive hyperspectral time-resolved wide-field fluorescence lifetime imaging,” Nat. Photon. 11, 411–414 (2017).
[Crossref]

Qing, Ye

J. Senlin, H. Wangwei, W. Yunlong, H. Kaicheng, S. Qiushuai, Y. Cuifeng, L. Dongqi, Ye Qing, Z. Wenyuan, and T. Jianguo, “Hyperspectral imaging using the single-pixel Fourier transform technique,” Sci. Rep. 7, 45209 (2017).
[Crossref]

Qionghai, D.

W. Yuwang, L. Yang, S. Jinli, S. Guohai, Q. Chang, and D. Qionghai, “High Speed Computational Ghost Imaging via Spatial Sweeping,” Sci. Rep. 7, 45325 (2017).
[Crossref]

Qiushuai, S.

J. Senlin, H. Wangwei, W. Yunlong, H. Kaicheng, S. Qiushuai, Y. Cuifeng, L. Dongqi, Ye Qing, Z. Wenyuan, and T. Jianguo, “Hyperspectral imaging using the single-pixel Fourier transform technique,” Sci. Rep. 7, 45209 (2017).
[Crossref]

Radwell, N.

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] [PubMed]

Romberg, J.

J. Romberg, “Imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 14–20 (2008).
[Crossref]

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

Senlin, J.

J. Senlin, H. Wangwei, W. Yunlong, H. Kaicheng, S. Qiushuai, Y. Cuifeng, L. Dongqi, Ye Qing, Z. Wenyuan, and T. Jianguo, “Hyperspectral imaging using the single-pixel Fourier transform technique,” Sci. Rep. 7, 45209 (2017).
[Crossref]

Shapiro, J. H.

J. H. Shapiro, “Computational ghost imaging,” Phys. Rev. A 78, 061802 (2008).
[Crossref]

Shi, J.

X. Liu, J. Shi, X. Wu, and G. Zeng, “Fast first-photon ghost imaging,” Sci. Rep. 8, 5012 (2018).
[Crossref] [PubMed]

Sinsuebphon, N.

Q. Pian, R. Yao, N. Sinsuebphon, and X. Intes, “Compressive hyperspectral time-resolved wide-field fluorescence lifetime imaging,” Nat. Photon. 11, 411–414 (2017).
[Crossref]

Situ, G.

L. Bian, J. Suo, G. Situ, Z. Li, J. Fan, F. Chen, and Q. Dai, “Multispectral imaging using a single bucket detector,” Sci. Rep. 6, 24752 (2016).
[Crossref] [PubMed]

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] [PubMed]

V. Durán, F. Soldevila, E. Irles, P. Clemente, E. Tajahuerce, P. Andrés, and J. Lancis, “Compressive imaging in scattering media,” Opt. Express 23(11), 14424–14433 (2015).
[Crossref] [PubMed]

F. Soldevila, E. Irles, V. Durán, P. Clemente, M. Fernández-Alonso, E. Tajahuerce, and J. Lancis, “Single-pixel polarimetric imaging spectrometer by compressive sensing,” Appl. Phys. B 113(3), 551–558 (2013).
[Crossref]

Starling, D. J.

Storer, I.

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. 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] [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.

M. Sun, M. Edgar, G. Gibson, N. R. B. Sun, R. Lamb, and M. Padget, “Single-pixel three-dimentional imaging with time-based depth resolution,” Nat. Commun. 7, 12010 (2016).
[Crossref]

Sun, M.-J.

Sun, N. R. B.

M. Sun, M. Edgar, G. Gibson, N. R. B. Sun, R. Lamb, and M. Padget, “Single-pixel three-dimentional imaging with time-based depth resolution,” Nat. Commun. 7, 12010 (2016).
[Crossref]

Sun, T.

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

Suo, J.

L. Bian, J. Suo, Q. Dai, and F. Chen, “Experimental comparison of single-pixel imaging algorithms,” J. Opt. Soc. Am. A 35(1), 78–87 (2018).
[Crossref]

L. Bian, J. Suo, G. Situ, Z. Li, J. Fan, F. Chen, and Q. Dai, “Multispectral imaging using a single bucket detector,” Sci. Rep. 6, 24752 (2016).
[Crossref] [PubMed]

Z. Li, J. Suo, X. Hu, C. Deng, J. Fan, and Q. Dai, “Effucient single-pixel multispectral imaging via non-mechanical spatio-spectral modulation,” Sci. Rep. 7, 41435 (2016).
[Crossref]

Tajahuerce, E.

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] [PubMed]

V. Durán, F. Soldevila, E. Irles, P. Clemente, E. Tajahuerce, P. Andrés, and J. Lancis, “Compressive imaging in scattering media,” Opt. Express 23(11), 14424–14433 (2015).
[Crossref] [PubMed]

F. Soldevila, E. Irles, V. Durán, P. Clemente, M. Fernández-Alonso, E. Tajahuerce, and J. Lancis, “Single-pixel polarimetric imaging spectrometer by compressive sensing,” Appl. Phys. B 113(3), 551–558 (2013).
[Crossref]

V. Duran, P. Clemente, M. Fernandez-Alonso, E. Tajahuerce, and J. Lancis, “Single-pixel polarimetric imaging,” Opt. Lett. 37(5), 824–826 (2012).
[Crossref] [PubMed]

Takbar, D.

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

Tsaig, Y.

D. L. Donoho and Y. Tsaig, “Fast solution of ℓ1 -norm minimization problems when the solution may be sparse,” IEEE Trans. Inf. Theory 54(11), 4789–4812 (2008).
[Crossref]

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] [PubMed]

Vetterli, M.

I. Dokmanic, M. Kolundzija, and M. Vetterli, “Beyond Moore-Penrose: Sparse pseudoinverse,” in “2013 IEEE International Conference on Acoustics, Speech and Signal Processing,” (IEEE, 2013), pp. 6526–6530.

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]

Wakin, M. B.

E. J. Candes and M. B. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25(2), 21–30 (2008).
[Crossref]

Wang, X.

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

Wangwei, H.

J. Senlin, H. Wangwei, W. Yunlong, H. Kaicheng, S. Qiushuai, Y. Cuifeng, L. Dongqi, Ye Qing, Z. Wenyuan, and T. Jianguo, “Hyperspectral imaging using the single-pixel Fourier transform technique,” Sci. Rep. 7, 45209 (2017).
[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, 10669 (2015).
[Crossref] [PubMed]

Wen-Kai, Y.

Y. Wen-Kai, L. Xue-Feng, Y. Xu-Ri, W. Chao, Z. Yun, and Z. Guang-Jie, “Complementary compressive imaging for the telescopic system,” Sci. Rep. 4, 5834 (2014).

Wenyuan, Z.

J. Senlin, H. Wangwei, W. Yunlong, H. Kaicheng, S. Qiushuai, Y. Cuifeng, L. Dongqi, Ye Qing, Z. Wenyuan, and T. Jianguo, “Hyperspectral imaging using the single-pixel Fourier transform technique,” Sci. Rep. 7, 45209 (2017).
[Crossref]

Wu, X.

X. Liu, J. Shi, X. Wu, and G. Zeng, “Fast first-photon ghost imaging,” Sci. Rep. 8, 5012 (2018).
[Crossref] [PubMed]

Xiao, W.

Xu, Z.-H.

Xue-Feng, L.

Y. Wen-Kai, L. Xue-Feng, Y. Xu-Ri, W. Chao, Z. Yun, and Z. Guang-Jie, “Complementary compressive imaging for the telescopic system,” Sci. Rep. 4, 5834 (2014).

Xu-Ri, Y.

Y. Wen-Kai, L. Xue-Feng, Y. Xu-Ri, W. Chao, Z. Yun, and Z. Guang-Jie, “Complementary compressive imaging for the telescopic system,” Sci. Rep. 4, 5834 (2014).

Yang, L.

W. Yuwang, L. Yang, S. Jinli, S. Guohai, Q. Chang, and D. Qionghai, “High Speed Computational Ghost Imaging via Spatial Sweeping,” Sci. Rep. 7, 45325 (2017).
[Crossref]

Yao, R.

Q. Pian, R. Yao, N. Sinsuebphon, and X. Intes, “Compressive hyperspectral time-resolved wide-field fluorescence lifetime imaging,” Nat. Photon. 11, 411–414 (2017).
[Crossref]

Yun, Z.

Y. Wen-Kai, L. Xue-Feng, Y. Xu-Ri, W. Chao, Z. Yun, and Z. Guang-Jie, “Complementary compressive imaging for the telescopic system,” Sci. Rep. 4, 5834 (2014).

Yunlong, W.

J. Senlin, H. Wangwei, W. Yunlong, H. Kaicheng, S. Qiushuai, Y. Cuifeng, L. Dongqi, Ye Qing, Z. Wenyuan, and T. Jianguo, “Hyperspectral imaging using the single-pixel Fourier transform technique,” Sci. Rep. 7, 45209 (2017).
[Crossref]

Yuwang, W.

W. Yuwang, L. Yang, S. Jinli, S. Guohai, Q. Chang, and D. Qionghai, “High Speed Computational Ghost Imaging via Spatial Sweeping,” Sci. Rep. 7, 45325 (2017).
[Crossref]

Zeng, G.

X. Liu, J. Shi, X. Wu, and G. Zeng, “Fast first-photon ghost imaging,” Sci. Rep. 8, 5012 (2018).
[Crossref] [PubMed]

Zhang, C.

Zhang, E.

Zhang, Z.

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

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

Zheng, G.

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

Zhong, J.

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

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

Appl. Opt. (3)

Appl. Phys. B (1)

F. Soldevila, E. Irles, V. Durán, P. Clemente, M. Fernández-Alonso, E. Tajahuerce, and J. Lancis, “Single-pixel polarimetric imaging spectrometer by compressive sensing,” Appl. Phys. B 113(3), 551–558 (2013).
[Crossref]

IEEE Signal Process. Mag. (3)

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

E. J. Candes and M. B. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25(2), 21–30 (2008).
[Crossref]

J. Romberg, “Imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 14–20 (2008).
[Crossref]

IEEE Trans. Inf. Theory (1)

D. L. Donoho and Y. Tsaig, “Fast solution of ℓ1 -norm minimization problems when the solution may be sparse,” IEEE Trans. Inf. Theory 54(11), 4789–4812 (2008).
[Crossref]

Inverse Probl. (1)

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

J. Opt. Soc. Am. A (2)

Nat. Commun. (2)

M. Sun, M. Edgar, G. Gibson, N. R. B. Sun, R. Lamb, and M. Padget, “Single-pixel three-dimentional imaging with time-based depth resolution,” Nat. Commun. 7, 12010 (2016).
[Crossref]

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

Nat. Photon. (1)

Q. Pian, R. Yao, N. Sinsuebphon, and X. Intes, “Compressive hyperspectral time-resolved wide-field fluorescence lifetime imaging,” Nat. Photon. 11, 411–414 (2017).
[Crossref]

Opt. Commun. (1)

D. Pastor, A. Pastuszczak, M. Mikolajczyk, and R. Kotynski, “Compressive phase-only filtering at extreme compression rates,” Opt. Commun. 383, 446–452 (2017).
[Crossref]

Opt. Express (5)

Opt. Lett. (1)

Optica (1)

Photonics Res. (1)

W. Gong, “High-resolution pseudo-inverse ghost imaging,” Photonics Res. 3(5), 234 (2015).
[Crossref]

Phys. Rev. A (1)

J. H. Shapiro, “Computational ghost imaging,” Phys. Rev. A 78, 061802 (2008).
[Crossref]

Sci. Rep. (11)

L. Bian, J. Suo, G. Situ, Z. Li, J. Fan, F. Chen, and Q. Dai, “Multispectral imaging using a single bucket detector,” Sci. Rep. 6, 24752 (2016).
[Crossref] [PubMed]

Z. Li, J. Suo, X. Hu, C. Deng, J. Fan, and Q. Dai, “Effucient single-pixel multispectral imaging via non-mechanical spatio-spectral modulation,” Sci. Rep. 7, 41435 (2016).
[Crossref]

J. Senlin, H. Wangwei, W. Yunlong, H. Kaicheng, S. Qiushuai, Y. Cuifeng, L. Dongqi, Ye Qing, Z. Wenyuan, and T. Jianguo, “Hyperspectral imaging using the single-pixel Fourier transform technique,” Sci. Rep. 7, 45209 (2017).
[Crossref]

X. Liu, J. Shi, X. Wu, and G. Zeng, “Fast first-photon ghost imaging,” Sci. Rep. 8, 5012 (2018).
[Crossref] [PubMed]

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Supplementary Material (1)

NameDescription
» Visualization 1       Exemplary video captured with the single-pixel camera and reconstructed at 11.3 Hz with Fourier domain regularized inverse algorithm. Discrete cosine transform sampling has been used at 256x256 resolution and 3% compression ratio.

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Figures (10)

Fig. 1
Fig. 1 Filter Γ ^ ( ω x , ω y ) defined in Eq. (11) for various values of the parameter μ (logarithmic scale).
Fig. 2
Fig. 2 Fourier spectra of sampling functions used in various sampling schemes ( i | m ^ i | / m ^ i ) , where mi are the rows of the measurement matrix M, and the caret denotes the 2D Fourier transform. B denotes binarized sampling functions.
Fig. 3
Fig. 3 Single-pixel imaging at a compression ratio of 3%. Pseudoinverse and FDRI image reconstructions (top). The dependence of the reconstruction quality obtained with FDRI on the value of μ (bottom). Sampling functions consist of a subset of the binarized DCT basis. PSNR reaches maximal values for μ ∈ (0.5, 0.7).
Fig. 4
Fig. 4 Image reconstructions obtained with the proposed FDRI (top row) and with the pseudoinverse (bottom row) methods for DCT and Morlet wavelet-based sampling schemes. When the sampling functions are continuous, FDRI and pseudoinverse reconstructions have a similar quality. On the other hand, for binary sampling, the FDRI method is much better than the pseudoinverse. The compression ratio is always equal to 3%.
Fig. 5
Fig. 5 Numerical simulations of compressive imaging, presenting a comparison between various reconstruction methods for DCT sampling functions at a 3% compression ratio (top). The PSNR values and reconstruction times as a function of the number of sampling functions (bottom). The proposed method (FDRI) achieves performance similar to that of total variation regularization (NESTA), while the calculation time is decreased by a factor of ~ 70.
Fig. 6
Fig. 6 Comparison of peak signal-to-noise ratio (averaged over 49 test images) obtained for various sampling and reconstruction methods. The improvement gained by using the FDRI reconstruction method is especially visible for the binary sampling methods denoted with B.
Fig. 7
Fig. 7 Robustness of the FDRI, pseudoinverse, and TV (NESTA) reconstruction methods to additive Gaussian noise for the three kinds of binary sampling at a compression ratio of 3%. The PSNR averaged over 49 test images is plotted as a function of σy/μy, where σy is the standard deviation of the Gaussian noise and μy is the mean value of the measurement vector y.
Fig. 8
Fig. 8 Schematic view of the single-pixel camera. The DMD spatial light modulator samples the image with a set of binary patterns. A differential photodetection technique, with two photodetectors gathering the complementary optical signals reflected from the DMD in two directions, was used to increase the experimental SNR.
Fig. 9
Fig. 9 Comparison of reconstructions obtained with the FDRI and pseudoinverse methods for experimental data measured with an optical single-pixel camera with different types of sampling protocols at a resolution of 256 × 256 and compression ratios of 6% (top 6 images) and 3% (bottom 6 images).
Fig. 10
Fig. 10 Several representative video frames recorded with our optical single-pixel camera at a rate of 11.3 Hz and reconstructed on the fly using the proposed FDRI algorithm. The sampling patterns consist of 3% binarized DCT basis functions with a resolution 256 × 256. For full video see Visualization 1.

Equations (13)

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M · x = y ,
x 0 = arg min x E ( x ) subject to M · x = y .
E ( x ) = x * h 2 .
E ( x ) = x T C x = x ^ T C ^ x ^ ,
( x , λ ) = 1 2 x T C x λ * ( M x y ) .
x 0 = P y ,
P = C 1 M * ( M C 1 M * ) 1
P F * Γ ^ F ( M F * Γ ^ F ) + ,
E ( x ) = p α ( p ) x * h ( p ) 2 ,
Γ ^ i , j = δ i , j p α ( p ) | h ^ i ( p ) | 2 and C ^ i , j 1 = Γ ^ i , j 2 ,
Γ ^ i , j = δ i . j ( 1 μ ) ( sin 2 ( ω x ) + sin 2 ( ω y ) ) + μ 2 ω x 2 + ω y 2 2 π 2 + ε ,
g σ , n p , θ ( x , y ) = N e x 2 + y 2 2 σ 2 ( e i ( π n p / 2 σ ) ( x cos ( θ ) + y sin ( θ ) ) κ ) ,
σ = σ m i n + ( σ m a x σ m i n ) ω m a x ω ω m a x ω m i n ,

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