Abstract

A fast time-lens-based line-scan single-pixel camera with multi-wavelength source is proposed and experimentally demonstrated in this paper. A multi-wavelength laser instead of a mode-locked laser is used as the optical source. With a diffraction grating and dispersion compensating fibers, the spatial information of an object is converted into temporal waveforms which are then randomly encoded, temporally compressed and captured by a single-pixel photodetector. Two algorithms (the dictionary learning algorithm and the discrete cosine transform-based algorithm) for image reconstruction are employed, respectively. Results show that the dictionary learning algorithm has greater capability to reduce the number of compressive measurements than the DCT-based algorithm. The effective imaging frame rate increases from 200 kHz to 1 MHz, which shows a significant improvement in imaging speed over conventional single-pixel cameras.

© 2015 Optical Society of America

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References

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  1. D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006).
    [Crossref]
  2. E. J. Candes, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52(2), 489–509 (2006).
    [Crossref]
  3. E. J. Candes, “The restricted isometry property and its implications for compressed sensing,” C. R. Math. 346(9-10), 589–592 (2008).
    [Crossref]
  4. E. J. Candès and M. B. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25(2), 21–30 (2008).
    [Crossref]
  5. J. Romberg, “Imaging via compressive sampling [introduction to compressive sampling and recovery via convex programming],” IEEE Signal Process. Mag. 25(2), 14–20 (2008).
    [Crossref]
  6. M. Lustig, D. Donoho, and J. M. Pauly, “Sparse MRI: The application of compressed sensing for rapid MR imaging,” Magn. Reson. Med. 58(6), 1182–1195 (2007).
    [Crossref] [PubMed]
  7. M. Duarte, M. Davenport, D. Takhar, 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]
  8. K. Goda, K. K. Tsia, and B. Jalali, “Amplified dispersive Fourier-transform imaging for ultrafast displacement sensing and barcode reading,” Appl. Phys. Lett. 93(13), 131109 (2008).
    [Crossref]
  9. K. Goda, D. R. Solli, K. K. Tsia, and B. Jalali, “Theory of amplified dispersive Fourier transformation,” Phys. Rev. A 80(4), 043821 (2009).
    [Crossref]
  10. K. Goda, K. K. Tsia, and B. Jalali, “Serial time-encoded amplified imaging for real-time observation of fast dynamic phenomena,” Nature 458(7242), 1145–1149 (2009).
    [Crossref] [PubMed]
  11. K. Goda and B. Jalali, “Dispersive Fourier transformation for fast continuous single-shot measurements,” Nat. Photonics 7(2), 102–112 (2013).
    [Crossref]
  12. H. Chen, Z. Weng, Y. Liang, C. Lei, F. Xing, M. Chen, and S. Xie, “High speed single-pixel imaging via time domain compressive sampling,” in CLEO: 2014, OSA Technical Digest (Optical Society of America, 2014), paper JTh2A.132.
  13. B. T. Bosworth and M. A. Foster, “High-speed flow imaging utilizing spectral-encoding of ultrafast pulses and compressed sensing,” in CLEO: 2014, OSA Technical Digest (Optical Society of America, 2014), paper ATh4P.3.
  14. B. T. Bosworth, J. R. Stroud, D. N. Tran, T. D. Tran, S. Chin, and M. A. Foster, “High-speed flow microscopy using compressed sensing with ultrafast laser pulses,” Opt. Express 23(8), 10521–10532 (2015).
    [Crossref] [PubMed]
  15. M. Aharon, M. Elad, and A. Bruckstein, “K-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation,” IEEE Trans. Signal Process. 54(11), 4311–4322 (2006).
    [Crossref]
  16. J. M. Duarte-Carvajalino and G. Sapiro, “Learning to sense sparse signals: simultaneous sensing matrix and sparsifying dictionary optimization,” IEEE Trans. Image Process. 18(7), 1395–1408 (2009).
    [Crossref] [PubMed]
  17. K. K. Tsia, K. Goda, D. Capewell, and B. Jalali, “Performance of serial time-encoded amplified microscope,” Opt. Express 18(10), 10016–10028 (2010).
    [Crossref] [PubMed]

2015 (1)

2013 (1)

K. Goda and B. Jalali, “Dispersive Fourier transformation for fast continuous single-shot measurements,” Nat. Photonics 7(2), 102–112 (2013).
[Crossref]

2010 (1)

2009 (3)

J. M. Duarte-Carvajalino and G. Sapiro, “Learning to sense sparse signals: simultaneous sensing matrix and sparsifying dictionary optimization,” IEEE Trans. Image Process. 18(7), 1395–1408 (2009).
[Crossref] [PubMed]

K. Goda, D. R. Solli, K. K. Tsia, and B. Jalali, “Theory of amplified dispersive Fourier transformation,” Phys. Rev. A 80(4), 043821 (2009).
[Crossref]

K. Goda, K. K. Tsia, and B. Jalali, “Serial time-encoded amplified imaging for real-time observation of fast dynamic phenomena,” Nature 458(7242), 1145–1149 (2009).
[Crossref] [PubMed]

2008 (5)

E. J. Candes, “The restricted isometry property and its implications for compressed sensing,” C. R. Math. 346(9-10), 589–592 (2008).
[Crossref]

E. J. Candès 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 [introduction to compressive sampling and recovery via convex programming],” IEEE Signal Process. Mag. 25(2), 14–20 (2008).
[Crossref]

M. Duarte, M. Davenport, D. Takhar, 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]

K. Goda, K. K. Tsia, and B. Jalali, “Amplified dispersive Fourier-transform imaging for ultrafast displacement sensing and barcode reading,” Appl. Phys. Lett. 93(13), 131109 (2008).
[Crossref]

2007 (1)

M. Lustig, D. Donoho, and J. M. Pauly, “Sparse MRI: The application of compressed sensing for rapid MR imaging,” Magn. Reson. Med. 58(6), 1182–1195 (2007).
[Crossref] [PubMed]

2006 (3)

D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006).
[Crossref]

E. J. Candes, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52(2), 489–509 (2006).
[Crossref]

M. Aharon, M. Elad, and A. Bruckstein, “K-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation,” IEEE Trans. Signal Process. 54(11), 4311–4322 (2006).
[Crossref]

Aharon, M.

M. Aharon, M. Elad, and A. Bruckstein, “K-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation,” IEEE Trans. Signal Process. 54(11), 4311–4322 (2006).
[Crossref]

Baraniuk, R.

M. Duarte, M. Davenport, D. Takhar, 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]

Bosworth, B. T.

Bruckstein, A.

M. Aharon, M. Elad, and A. Bruckstein, “K-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation,” IEEE Trans. Signal Process. 54(11), 4311–4322 (2006).
[Crossref]

Candes, E. J.

E. J. Candes, “The restricted isometry property and its implications for compressed sensing,” C. R. Math. 346(9-10), 589–592 (2008).
[Crossref]

E. J. Candes, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52(2), 489–509 (2006).
[Crossref]

Candès, E. J.

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

Capewell, D.

Chin, S.

Davenport, M.

M. Duarte, M. Davenport, D. Takhar, 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]

Donoho, D.

M. Lustig, D. Donoho, and J. M. Pauly, “Sparse MRI: The application of compressed sensing for rapid MR imaging,” Magn. Reson. Med. 58(6), 1182–1195 (2007).
[Crossref] [PubMed]

Donoho, D. L.

D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006).
[Crossref]

Duarte, M.

M. Duarte, M. Davenport, D. Takhar, 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]

Duarte-Carvajalino, J. M.

J. M. Duarte-Carvajalino and G. Sapiro, “Learning to sense sparse signals: simultaneous sensing matrix and sparsifying dictionary optimization,” IEEE Trans. Image Process. 18(7), 1395–1408 (2009).
[Crossref] [PubMed]

Elad, M.

M. Aharon, M. Elad, and A. Bruckstein, “K-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation,” IEEE Trans. Signal Process. 54(11), 4311–4322 (2006).
[Crossref]

Foster, M. A.

Goda, K.

K. Goda and B. Jalali, “Dispersive Fourier transformation for fast continuous single-shot measurements,” Nat. Photonics 7(2), 102–112 (2013).
[Crossref]

K. K. Tsia, K. Goda, D. Capewell, and B. Jalali, “Performance of serial time-encoded amplified microscope,” Opt. Express 18(10), 10016–10028 (2010).
[Crossref] [PubMed]

K. Goda, D. R. Solli, K. K. Tsia, and B. Jalali, “Theory of amplified dispersive Fourier transformation,” Phys. Rev. A 80(4), 043821 (2009).
[Crossref]

K. Goda, K. K. Tsia, and B. Jalali, “Serial time-encoded amplified imaging for real-time observation of fast dynamic phenomena,” Nature 458(7242), 1145–1149 (2009).
[Crossref] [PubMed]

K. Goda, K. K. Tsia, and B. Jalali, “Amplified dispersive Fourier-transform imaging for ultrafast displacement sensing and barcode reading,” Appl. Phys. Lett. 93(13), 131109 (2008).
[Crossref]

Jalali, B.

K. Goda and B. Jalali, “Dispersive Fourier transformation for fast continuous single-shot measurements,” Nat. Photonics 7(2), 102–112 (2013).
[Crossref]

K. K. Tsia, K. Goda, D. Capewell, and B. Jalali, “Performance of serial time-encoded amplified microscope,” Opt. Express 18(10), 10016–10028 (2010).
[Crossref] [PubMed]

K. Goda, D. R. Solli, K. K. Tsia, and B. Jalali, “Theory of amplified dispersive Fourier transformation,” Phys. Rev. A 80(4), 043821 (2009).
[Crossref]

K. Goda, K. K. Tsia, and B. Jalali, “Serial time-encoded amplified imaging for real-time observation of fast dynamic phenomena,” Nature 458(7242), 1145–1149 (2009).
[Crossref] [PubMed]

K. Goda, K. K. Tsia, and B. Jalali, “Amplified dispersive Fourier-transform imaging for ultrafast displacement sensing and barcode reading,” Appl. Phys. Lett. 93(13), 131109 (2008).
[Crossref]

Kelly, K.

M. Duarte, M. Davenport, D. Takhar, 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]

Laska, J.

M. Duarte, M. Davenport, D. Takhar, 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]

Lustig, M.

M. Lustig, D. Donoho, and J. M. Pauly, “Sparse MRI: The application of compressed sensing for rapid MR imaging,” Magn. Reson. Med. 58(6), 1182–1195 (2007).
[Crossref] [PubMed]

Pauly, J. M.

M. Lustig, D. Donoho, and J. M. Pauly, “Sparse MRI: The application of compressed sensing for rapid MR imaging,” Magn. Reson. Med. 58(6), 1182–1195 (2007).
[Crossref] [PubMed]

Romberg, J.

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

E. J. Candes, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52(2), 489–509 (2006).
[Crossref]

Sapiro, G.

J. M. Duarte-Carvajalino and G. Sapiro, “Learning to sense sparse signals: simultaneous sensing matrix and sparsifying dictionary optimization,” IEEE Trans. Image Process. 18(7), 1395–1408 (2009).
[Crossref] [PubMed]

Solli, D. R.

K. Goda, D. R. Solli, K. K. Tsia, and B. Jalali, “Theory of amplified dispersive Fourier transformation,” Phys. Rev. A 80(4), 043821 (2009).
[Crossref]

Stroud, J. R.

Sun, T.

M. Duarte, M. Davenport, D. Takhar, 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]

Takhar, D.

M. Duarte, M. Davenport, D. Takhar, 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]

Tao, T.

E. J. Candes, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52(2), 489–509 (2006).
[Crossref]

Tran, D. N.

Tran, T. D.

Tsia, K. K.

K. K. Tsia, K. Goda, D. Capewell, and B. Jalali, “Performance of serial time-encoded amplified microscope,” Opt. Express 18(10), 10016–10028 (2010).
[Crossref] [PubMed]

K. Goda, D. R. Solli, K. K. Tsia, and B. Jalali, “Theory of amplified dispersive Fourier transformation,” Phys. Rev. A 80(4), 043821 (2009).
[Crossref]

K. Goda, K. K. Tsia, and B. Jalali, “Serial time-encoded amplified imaging for real-time observation of fast dynamic phenomena,” Nature 458(7242), 1145–1149 (2009).
[Crossref] [PubMed]

K. Goda, K. K. Tsia, and B. Jalali, “Amplified dispersive Fourier-transform imaging for ultrafast displacement sensing and barcode reading,” Appl. Phys. Lett. 93(13), 131109 (2008).
[Crossref]

Wakin, M. B.

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

Appl. Phys. Lett. (1)

K. Goda, K. K. Tsia, and B. Jalali, “Amplified dispersive Fourier-transform imaging for ultrafast displacement sensing and barcode reading,” Appl. Phys. Lett. 93(13), 131109 (2008).
[Crossref]

C. R. Math. (1)

E. J. Candes, “The restricted isometry property and its implications for compressed sensing,” C. R. Math. 346(9-10), 589–592 (2008).
[Crossref]

IEEE Signal Process. Mag. (3)

E. J. Candès 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 [introduction to compressive sampling and recovery via convex programming],” IEEE Signal Process. Mag. 25(2), 14–20 (2008).
[Crossref]

M. Duarte, M. Davenport, D. Takhar, 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]

IEEE Trans. Image Process. (1)

J. M. Duarte-Carvajalino and G. Sapiro, “Learning to sense sparse signals: simultaneous sensing matrix and sparsifying dictionary optimization,” IEEE Trans. Image Process. 18(7), 1395–1408 (2009).
[Crossref] [PubMed]

IEEE Trans. Inf. Theory (2)

D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006).
[Crossref]

E. J. Candes, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52(2), 489–509 (2006).
[Crossref]

IEEE Trans. Signal Process. (1)

M. Aharon, M. Elad, and A. Bruckstein, “K-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation,” IEEE Trans. Signal Process. 54(11), 4311–4322 (2006).
[Crossref]

Magn. Reson. Med. (1)

M. Lustig, D. Donoho, and J. M. Pauly, “Sparse MRI: The application of compressed sensing for rapid MR imaging,” Magn. Reson. Med. 58(6), 1182–1195 (2007).
[Crossref] [PubMed]

Nat. Photonics (1)

K. Goda and B. Jalali, “Dispersive Fourier transformation for fast continuous single-shot measurements,” Nat. Photonics 7(2), 102–112 (2013).
[Crossref]

Nature (1)

K. Goda, K. K. Tsia, and B. Jalali, “Serial time-encoded amplified imaging for real-time observation of fast dynamic phenomena,” Nature 458(7242), 1145–1149 (2009).
[Crossref] [PubMed]

Opt. Express (2)

Phys. Rev. A (1)

K. Goda, D. R. Solli, K. K. Tsia, and B. Jalali, “Theory of amplified dispersive Fourier transformation,” Phys. Rev. A 80(4), 043821 (2009).
[Crossref]

Other (2)

H. Chen, Z. Weng, Y. Liang, C. Lei, F. Xing, M. Chen, and S. Xie, “High speed single-pixel imaging via time domain compressive sampling,” in CLEO: 2014, OSA Technical Digest (Optical Society of America, 2014), paper JTh2A.132.

B. T. Bosworth and M. A. Foster, “High-speed flow imaging utilizing spectral-encoding of ultrafast pulses and compressed sensing,” in CLEO: 2014, OSA Technical Digest (Optical Society of America, 2014), paper ATh4P.3.

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Figures (6)

Fig. 1
Fig. 1 The sparsity levels of 256 DCT-coded images. Inset: the tested 2D image.
Fig. 2
Fig. 2 Experimental setup of the proposed compressive imaging system. PPG: pulse pattern generator, OPM: optical phase modulator, OTD: optical time delay, MZM: Mach-Zehnder modulator, EDFA: Erbium-doped fiber amplifier, Cir: circulator, DCF: dispersion compensating fiber, SMF: single mode fiber, PD: photodetector, ADC: analog-to-digital converter, DSP: digital signal processor.
Fig. 3
Fig. 3 The optical spectra (a) before the cascade modulation and (b) after the cascade modulation.
Fig. 4
Fig. 4 The temporal waveforms and the spectrum of optical pulses before random modulation (left) and after compression (right). (a) A 20-MHz optical pulse train whose spectrum is encoded with a spatial image (b) The temporal waveform of an optical pulse after dispersion. (c) The optical spectrum of one dispersed pulse. (d) The optical pulses after compression. (e) The temporal profile of one compressed pulse. (f) The optical spectrum of a pulse after compression.
Fig. 5
Fig. 5 Image reconstruction with different number of compressive measurements. (a) 80 measurements. (b) 100 measurements. (c) 150 measurements. (d) 200 measurements.
Fig. 6
Fig. 6 Image reconstruction with the over-complete dictionary and the DCT basis at different compression ratios. (a) Sample images used for training the dictionary. (b) The patches taken from the tested images. (c) Image reconstruction with the over-complete dictionary and the DCT basis at different compression ratios (10%, 20%, 40%, 50%, 60%).

Equations (5)

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x = ψ θ
y = Φ x + e
min θ θ 1 subject to y - Φ Ψ θ 2 σ
min Ψ Θ X - Ψ Θ F 2 subject to i , θ i 0 S
N = Δ λ | D | R P R B S

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