Abstract

We demonstrate a compressed sensing, photon counting lidar system based on the single-pixel camera. Our technique recovers both depth and intensity maps from a single under-sampled set of incoherent, linear projections of a scene of interest at ultra-low light levels around 0.5 picowatts. Only two-dimensional reconstructions are required to image a three-dimensional scene. We demonstrate intensity imaging and depth mapping at 256 × 256 pixel transverse resolution with acquisition times as short as 3 seconds. We also show novelty filtering, reconstructing only the difference between two instances of a scene. Finally, we acquire 32 × 32 pixel real-time video for three-dimensional object tracking at 14 frames-per-second.

© 2013 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. C. Amann, T. Bosch, M. Lescure, R. Myllyla, and M. Rioux, “Laser ranging: a critical review of usual techniques for distance measurement,” Opt. Eng.40, 10–19 (2001).
    [CrossRef]
  2. C. Mallet and F. Bretar, “Full-waveform topographic lidar: State-of-the-art,” ISPRS Journal of Photogrammetry and Remote Sensing64, 1–16 (2009).
    [CrossRef]
  3. S. Hussmann and T. Liepert, “Three-dimensional TOF robot vision system,” IEEE Trans. Instrum. Meas.58, 141–146 (2009).
    [CrossRef]
  4. S. Foix, G. Alenya, and C. Torras, “Lock-in time-of-flight (TOF) cameras: A survey,” IEEE Sensors J.11, 1917–1926 (2011).
    [CrossRef]
  5. B. Schwarz, “Mapping the world in 3D,” Nat. Photonics4, 429–430 (2010).
    [CrossRef]
  6. A. McCarthy, N. J. Krichel, N. R. Gemmell, X. Ren, M. G. Tanner, S. N. Dorenbos, V. Zwiller, R. H. Hadfield, and G. S. Buller, “Kilometer-range, high resolution depth imaging via 1560 nm wavelength single-photon detection,” Opt. Express21, 8904–8915 (2013).
    [CrossRef] [PubMed]
  7. M. Richard and W. Davis, “Jigsaw: A foliage-penetrating 3D imaging laser radar system,” Lincoln Laboratory Journal15, 1 (2005).
  8. M. Vaidyanathan, S. Blask, T. Higgins, W. Clifton, D. Davidsohn, R. Carson, V. Reynolds, J. Pfannenstiel, R. Cannata, R. Marino, J. Drover, R. Hatch, D. Schue, R. Freehart, G. Rowe, J. Mooney, C. Hart, B. Stanley, J. McLaughlin, E. I. Lee, J. Berenholtz, B. Aull, J. Zayhowski, A. Vasile, P. Ramaswami, K. Ingersoll, T. Amoruso, I. Khan, W. Davis, and R. Heinrichs, “Jigsaw phase III: a miniaturized airborne 3-D imaging laser radar with photon-counting sensitivity for foliage penetration,” Proc. SPIE6550, 65500N (2007).
    [CrossRef]
  9. M. Entwistle, M. A. Itzler, J. Chen, M. Owens, K. Patel, X. Jiang, K. Slomkowski, and S. Rangwala, “Geiger-mode APD camera system for single-photon 3D ladar imaging,” Proc. SPIE8375, 83750D (2012).
  10. M. A. Itzler, M. Entwistle, M. Owens, K. Patel, X. Jiang, K. Slomkowski, S. Rangwala, P. F. Zalud, T. Senko, J. Tower, and J. Ferraro, “Comparison of 32 × 128 and 32 × 32 geiger-mode APD FPAS for single photon 3D ladar imaging,” Proc. SPIE8033, 80330G (2011).
    [CrossRef]
  11. 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, 83–91 (2008).
    [CrossRef]
  12. M. Sarkis and K. Diepold, “Depth map compression via compressed sensing,” in Proceedings of 16th IEEE International Conference on Image Processing, (IEEE, 2009), pp. 737–740.
  13. A. Kirmani, A. Colaço, F. N. C. Wong, and V. K. Goyal, “Exploiting sparsity in time-of-flight range acquisition using a single time-resolved sensor,” Opt. Express19, 21485–21507 (2011).
    [CrossRef] [PubMed]
  14. G. A. Howland, P. B. Dixon, and J. C. Howell, “Photon-counting compressive sensing laser radar for 3D imaging,” Appl. Opt.50, 5917–5920 (2011).
    [CrossRef] [PubMed]
  15. L. Li, L. Wu, X. Wang, and E. Dang, “Gated viewing laser imaging with compressive sensing,” Appl. Opt.51, 2706–2712 (2012).
    [CrossRef] [PubMed]
  16. W. R. Babbitt, Z. W. Barber, and C. Renner, “Compressive laser ranging,” Opt. Lett.36, 4794–4796 (2011).
    [CrossRef] [PubMed]
  17. D. L. Donoho, “Compressed Sensing,” IEEE Trans. Inf. Theory52, 1289–1306 (2006).
    [CrossRef]
  18. E. Candés and J. Romberg, “Sparsity and incoherence in compressive sampling,” Inverse Probl.23, 969 (2007).
    [CrossRef]
  19. M. Lustig, D. Donoho, and J. M. Pauly, “Sparse MRI: The application of compressed sensing for rapid MR imaging,” Magn. Reson. Med58, 1182–1195 (2007).
    [CrossRef] [PubMed]
  20. J. Bobin, J.-L. Starck, and R. Ottensamer, “Compressed sensing in astronomy,” IEEE J. Sel. Topics Signal Process.2, 718–726 (2008).
    [CrossRef]
  21. S. T. Flammia, D. Gross, Y.-K. Liu, and J. Eisert, “Quantum tomography via compressed sensing: error bounds, sample complexity and efficient estimators,” New J. Phys.14, 095022 (2012).
    [CrossRef]
  22. G. A. Howland and J. C. Howell, “Efficient high-dimensional entanglement imaging with a compressive-sensing double-pixel camera,” Phys. Rev. X3, 011013 (2013).
    [CrossRef]
  23. M. A. T. Figueiredo, R. D. Nowak, and S. J. Wright, “Gradient Projection for Sparse Reconstruction: Application to Compressed Sensing and Other Inverse Problems,” IEEE J. Sel. Topics Signal Process.1, 586–597 (2007).
    [CrossRef]
  24. D. Donoho and I. Johnstone, “Threshold selection for wavelet shrinkage of noisy data,” in Proceedings of the 16th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, (IEEE1994), 1A24–A25
  25. C. Li, W. Yin, and Y. Zhang, “TVAL3: TV minimization by augmented lagrangian and alternating direction algorithms,” http://www.caam.rice.edu/~optimization/L1/TVAL3/ .
  26. Z. T. Harmony, R. F. Marcia, and R. F. Willett, “Sparse poisson intensity reconstruction algorithms” in Proceedings of the IEEE/SP 15th Workshop on Statistical Signal Processing (IEEE2009), pp 634–637.
  27. D. L. Donoho, A. Maleki, and A. Montanari, “The Noise- Sensitivity Phase Transition in Compressed Sensing”, IEEE Trans. Inf. Theory57, 6920 (2011).
    [CrossRef]
  28. V. Cevher, A. Sankaranarayanan, M. F. Duarte, D. Reddy, R. G. Baraniuk, and R. Chellappa, “Compressive sensing for background subtraction,” in Computer Vision - ECCV 2008 Lecture Notes in Computer Science (Springer, 2008) pp. 155–168.
    [CrossRef]
  29. O. S. Magaña-Loaiza, G. A. Howland, M. Malik, J. C. Howell, and R. W. Boyd, “Compressive object tracking using entangled photons,” Appl. Phys. Lett.102, 231104 (2013).
    [CrossRef]

2013 (3)

A. McCarthy, N. J. Krichel, N. R. Gemmell, X. Ren, M. G. Tanner, S. N. Dorenbos, V. Zwiller, R. H. Hadfield, and G. S. Buller, “Kilometer-range, high resolution depth imaging via 1560 nm wavelength single-photon detection,” Opt. Express21, 8904–8915 (2013).
[CrossRef] [PubMed]

G. A. Howland and J. C. Howell, “Efficient high-dimensional entanglement imaging with a compressive-sensing double-pixel camera,” Phys. Rev. X3, 011013 (2013).
[CrossRef]

O. S. Magaña-Loaiza, G. A. Howland, M. Malik, J. C. Howell, and R. W. Boyd, “Compressive object tracking using entangled photons,” Appl. Phys. Lett.102, 231104 (2013).
[CrossRef]

2012 (3)

S. T. Flammia, D. Gross, Y.-K. Liu, and J. Eisert, “Quantum tomography via compressed sensing: error bounds, sample complexity and efficient estimators,” New J. Phys.14, 095022 (2012).
[CrossRef]

M. Entwistle, M. A. Itzler, J. Chen, M. Owens, K. Patel, X. Jiang, K. Slomkowski, and S. Rangwala, “Geiger-mode APD camera system for single-photon 3D ladar imaging,” Proc. SPIE8375, 83750D (2012).

L. Li, L. Wu, X. Wang, and E. Dang, “Gated viewing laser imaging with compressive sensing,” Appl. Opt.51, 2706–2712 (2012).
[CrossRef] [PubMed]

2011 (6)

W. R. Babbitt, Z. W. Barber, and C. Renner, “Compressive laser ranging,” Opt. Lett.36, 4794–4796 (2011).
[CrossRef] [PubMed]

M. A. Itzler, M. Entwistle, M. Owens, K. Patel, X. Jiang, K. Slomkowski, S. Rangwala, P. F. Zalud, T. Senko, J. Tower, and J. Ferraro, “Comparison of 32 × 128 and 32 × 32 geiger-mode APD FPAS for single photon 3D ladar imaging,” Proc. SPIE8033, 80330G (2011).
[CrossRef]

A. Kirmani, A. Colaço, F. N. C. Wong, and V. K. Goyal, “Exploiting sparsity in time-of-flight range acquisition using a single time-resolved sensor,” Opt. Express19, 21485–21507 (2011).
[CrossRef] [PubMed]

G. A. Howland, P. B. Dixon, and J. C. Howell, “Photon-counting compressive sensing laser radar for 3D imaging,” Appl. Opt.50, 5917–5920 (2011).
[CrossRef] [PubMed]

S. Foix, G. Alenya, and C. Torras, “Lock-in time-of-flight (TOF) cameras: A survey,” IEEE Sensors J.11, 1917–1926 (2011).
[CrossRef]

D. L. Donoho, A. Maleki, and A. Montanari, “The Noise- Sensitivity Phase Transition in Compressed Sensing”, IEEE Trans. Inf. Theory57, 6920 (2011).
[CrossRef]

2010 (1)

B. Schwarz, “Mapping the world in 3D,” Nat. Photonics4, 429–430 (2010).
[CrossRef]

2009 (2)

C. Mallet and F. Bretar, “Full-waveform topographic lidar: State-of-the-art,” ISPRS Journal of Photogrammetry and Remote Sensing64, 1–16 (2009).
[CrossRef]

S. Hussmann and T. Liepert, “Three-dimensional TOF robot vision system,” IEEE Trans. Instrum. Meas.58, 141–146 (2009).
[CrossRef]

2008 (2)

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, 83–91 (2008).
[CrossRef]

J. Bobin, J.-L. Starck, and R. Ottensamer, “Compressed sensing in astronomy,” IEEE J. Sel. Topics Signal Process.2, 718–726 (2008).
[CrossRef]

2007 (4)

M. A. T. Figueiredo, R. D. Nowak, and S. J. Wright, “Gradient Projection for Sparse Reconstruction: Application to Compressed Sensing and Other Inverse Problems,” IEEE J. Sel. Topics Signal Process.1, 586–597 (2007).
[CrossRef]

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

M. Lustig, D. Donoho, and J. M. Pauly, “Sparse MRI: The application of compressed sensing for rapid MR imaging,” Magn. Reson. Med58, 1182–1195 (2007).
[CrossRef] [PubMed]

M. Vaidyanathan, S. Blask, T. Higgins, W. Clifton, D. Davidsohn, R. Carson, V. Reynolds, J. Pfannenstiel, R. Cannata, R. Marino, J. Drover, R. Hatch, D. Schue, R. Freehart, G. Rowe, J. Mooney, C. Hart, B. Stanley, J. McLaughlin, E. I. Lee, J. Berenholtz, B. Aull, J. Zayhowski, A. Vasile, P. Ramaswami, K. Ingersoll, T. Amoruso, I. Khan, W. Davis, and R. Heinrichs, “Jigsaw phase III: a miniaturized airborne 3-D imaging laser radar with photon-counting sensitivity for foliage penetration,” Proc. SPIE6550, 65500N (2007).
[CrossRef]

2006 (1)

D. L. Donoho, “Compressed Sensing,” IEEE Trans. Inf. Theory52, 1289–1306 (2006).
[CrossRef]

2005 (1)

M. Richard and W. Davis, “Jigsaw: A foliage-penetrating 3D imaging laser radar system,” Lincoln Laboratory Journal15, 1 (2005).

2001 (1)

M. C. Amann, T. Bosch, M. Lescure, R. Myllyla, and M. Rioux, “Laser ranging: a critical review of usual techniques for distance measurement,” Opt. Eng.40, 10–19 (2001).
[CrossRef]

Alenya, G.

S. Foix, G. Alenya, and C. Torras, “Lock-in time-of-flight (TOF) cameras: A survey,” IEEE Sensors J.11, 1917–1926 (2011).
[CrossRef]

Amann, M. C.

M. C. Amann, T. Bosch, M. Lescure, R. Myllyla, and M. Rioux, “Laser ranging: a critical review of usual techniques for distance measurement,” Opt. Eng.40, 10–19 (2001).
[CrossRef]

Amoruso, T.

M. Vaidyanathan, S. Blask, T. Higgins, W. Clifton, D. Davidsohn, R. Carson, V. Reynolds, J. Pfannenstiel, R. Cannata, R. Marino, J. Drover, R. Hatch, D. Schue, R. Freehart, G. Rowe, J. Mooney, C. Hart, B. Stanley, J. McLaughlin, E. I. Lee, J. Berenholtz, B. Aull, J. Zayhowski, A. Vasile, P. Ramaswami, K. Ingersoll, T. Amoruso, I. Khan, W. Davis, and R. Heinrichs, “Jigsaw phase III: a miniaturized airborne 3-D imaging laser radar with photon-counting sensitivity for foliage penetration,” Proc. SPIE6550, 65500N (2007).
[CrossRef]

Aull, B.

M. Vaidyanathan, S. Blask, T. Higgins, W. Clifton, D. Davidsohn, R. Carson, V. Reynolds, J. Pfannenstiel, R. Cannata, R. Marino, J. Drover, R. Hatch, D. Schue, R. Freehart, G. Rowe, J. Mooney, C. Hart, B. Stanley, J. McLaughlin, E. I. Lee, J. Berenholtz, B. Aull, J. Zayhowski, A. Vasile, P. Ramaswami, K. Ingersoll, T. Amoruso, I. Khan, W. Davis, and R. Heinrichs, “Jigsaw phase III: a miniaturized airborne 3-D imaging laser radar with photon-counting sensitivity for foliage penetration,” Proc. SPIE6550, 65500N (2007).
[CrossRef]

Babbitt, W. R.

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, 83–91 (2008).
[CrossRef]

Baraniuk, R. G.

V. Cevher, A. Sankaranarayanan, M. F. Duarte, D. Reddy, R. G. Baraniuk, and R. Chellappa, “Compressive sensing for background subtraction,” in Computer Vision - ECCV 2008 Lecture Notes in Computer Science (Springer, 2008) pp. 155–168.
[CrossRef]

Barber, Z. W.

Berenholtz, J.

M. Vaidyanathan, S. Blask, T. Higgins, W. Clifton, D. Davidsohn, R. Carson, V. Reynolds, J. Pfannenstiel, R. Cannata, R. Marino, J. Drover, R. Hatch, D. Schue, R. Freehart, G. Rowe, J. Mooney, C. Hart, B. Stanley, J. McLaughlin, E. I. Lee, J. Berenholtz, B. Aull, J. Zayhowski, A. Vasile, P. Ramaswami, K. Ingersoll, T. Amoruso, I. Khan, W. Davis, and R. Heinrichs, “Jigsaw phase III: a miniaturized airborne 3-D imaging laser radar with photon-counting sensitivity for foliage penetration,” Proc. SPIE6550, 65500N (2007).
[CrossRef]

Blask, S.

M. Vaidyanathan, S. Blask, T. Higgins, W. Clifton, D. Davidsohn, R. Carson, V. Reynolds, J. Pfannenstiel, R. Cannata, R. Marino, J. Drover, R. Hatch, D. Schue, R. Freehart, G. Rowe, J. Mooney, C. Hart, B. Stanley, J. McLaughlin, E. I. Lee, J. Berenholtz, B. Aull, J. Zayhowski, A. Vasile, P. Ramaswami, K. Ingersoll, T. Amoruso, I. Khan, W. Davis, and R. Heinrichs, “Jigsaw phase III: a miniaturized airborne 3-D imaging laser radar with photon-counting sensitivity for foliage penetration,” Proc. SPIE6550, 65500N (2007).
[CrossRef]

Bobin, J.

J. Bobin, J.-L. Starck, and R. Ottensamer, “Compressed sensing in astronomy,” IEEE J. Sel. Topics Signal Process.2, 718–726 (2008).
[CrossRef]

Bosch, T.

M. C. Amann, T. Bosch, M. Lescure, R. Myllyla, and M. Rioux, “Laser ranging: a critical review of usual techniques for distance measurement,” Opt. Eng.40, 10–19 (2001).
[CrossRef]

Boyd, R. W.

O. S. Magaña-Loaiza, G. A. Howland, M. Malik, J. C. Howell, and R. W. Boyd, “Compressive object tracking using entangled photons,” Appl. Phys. Lett.102, 231104 (2013).
[CrossRef]

Bretar, F.

C. Mallet and F. Bretar, “Full-waveform topographic lidar: State-of-the-art,” ISPRS Journal of Photogrammetry and Remote Sensing64, 1–16 (2009).
[CrossRef]

Buller, G. S.

Candés, E.

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

Cannata, R.

M. Vaidyanathan, S. Blask, T. Higgins, W. Clifton, D. Davidsohn, R. Carson, V. Reynolds, J. Pfannenstiel, R. Cannata, R. Marino, J. Drover, R. Hatch, D. Schue, R. Freehart, G. Rowe, J. Mooney, C. Hart, B. Stanley, J. McLaughlin, E. I. Lee, J. Berenholtz, B. Aull, J. Zayhowski, A. Vasile, P. Ramaswami, K. Ingersoll, T. Amoruso, I. Khan, W. Davis, and R. Heinrichs, “Jigsaw phase III: a miniaturized airborne 3-D imaging laser radar with photon-counting sensitivity for foliage penetration,” Proc. SPIE6550, 65500N (2007).
[CrossRef]

Carson, R.

M. Vaidyanathan, S. Blask, T. Higgins, W. Clifton, D. Davidsohn, R. Carson, V. Reynolds, J. Pfannenstiel, R. Cannata, R. Marino, J. Drover, R. Hatch, D. Schue, R. Freehart, G. Rowe, J. Mooney, C. Hart, B. Stanley, J. McLaughlin, E. I. Lee, J. Berenholtz, B. Aull, J. Zayhowski, A. Vasile, P. Ramaswami, K. Ingersoll, T. Amoruso, I. Khan, W. Davis, and R. Heinrichs, “Jigsaw phase III: a miniaturized airborne 3-D imaging laser radar with photon-counting sensitivity for foliage penetration,” Proc. SPIE6550, 65500N (2007).
[CrossRef]

Cevher, V.

V. Cevher, A. Sankaranarayanan, M. F. Duarte, D. Reddy, R. G. Baraniuk, and R. Chellappa, “Compressive sensing for background subtraction,” in Computer Vision - ECCV 2008 Lecture Notes in Computer Science (Springer, 2008) pp. 155–168.
[CrossRef]

Chellappa, R.

V. Cevher, A. Sankaranarayanan, M. F. Duarte, D. Reddy, R. G. Baraniuk, and R. Chellappa, “Compressive sensing for background subtraction,” in Computer Vision - ECCV 2008 Lecture Notes in Computer Science (Springer, 2008) pp. 155–168.
[CrossRef]

Chen, J.

M. Entwistle, M. A. Itzler, J. Chen, M. Owens, K. Patel, X. Jiang, K. Slomkowski, and S. Rangwala, “Geiger-mode APD camera system for single-photon 3D ladar imaging,” Proc. SPIE8375, 83750D (2012).

Clifton, W.

M. Vaidyanathan, S. Blask, T. Higgins, W. Clifton, D. Davidsohn, R. Carson, V. Reynolds, J. Pfannenstiel, R. Cannata, R. Marino, J. Drover, R. Hatch, D. Schue, R. Freehart, G. Rowe, J. Mooney, C. Hart, B. Stanley, J. McLaughlin, E. I. Lee, J. Berenholtz, B. Aull, J. Zayhowski, A. Vasile, P. Ramaswami, K. Ingersoll, T. Amoruso, I. Khan, W. Davis, and R. Heinrichs, “Jigsaw phase III: a miniaturized airborne 3-D imaging laser radar with photon-counting sensitivity for foliage penetration,” Proc. SPIE6550, 65500N (2007).
[CrossRef]

Colaço, A.

Dang, E.

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, 83–91 (2008).
[CrossRef]

Davidsohn, D.

M. Vaidyanathan, S. Blask, T. Higgins, W. Clifton, D. Davidsohn, R. Carson, V. Reynolds, J. Pfannenstiel, R. Cannata, R. Marino, J. Drover, R. Hatch, D. Schue, R. Freehart, G. Rowe, J. Mooney, C. Hart, B. Stanley, J. McLaughlin, E. I. Lee, J. Berenholtz, B. Aull, J. Zayhowski, A. Vasile, P. Ramaswami, K. Ingersoll, T. Amoruso, I. Khan, W. Davis, and R. Heinrichs, “Jigsaw phase III: a miniaturized airborne 3-D imaging laser radar with photon-counting sensitivity for foliage penetration,” Proc. SPIE6550, 65500N (2007).
[CrossRef]

Davis, W.

M. Vaidyanathan, S. Blask, T. Higgins, W. Clifton, D. Davidsohn, R. Carson, V. Reynolds, J. Pfannenstiel, R. Cannata, R. Marino, J. Drover, R. Hatch, D. Schue, R. Freehart, G. Rowe, J. Mooney, C. Hart, B. Stanley, J. McLaughlin, E. I. Lee, J. Berenholtz, B. Aull, J. Zayhowski, A. Vasile, P. Ramaswami, K. Ingersoll, T. Amoruso, I. Khan, W. Davis, and R. Heinrichs, “Jigsaw phase III: a miniaturized airborne 3-D imaging laser radar with photon-counting sensitivity for foliage penetration,” Proc. SPIE6550, 65500N (2007).
[CrossRef]

M. Richard and W. Davis, “Jigsaw: A foliage-penetrating 3D imaging laser radar system,” Lincoln Laboratory Journal15, 1 (2005).

Diepold, K.

M. Sarkis and K. Diepold, “Depth map compression via compressed sensing,” in Proceedings of 16th IEEE International Conference on Image Processing, (IEEE, 2009), pp. 737–740.

Dixon, P. B.

Donoho, D.

M. Lustig, D. Donoho, and J. M. Pauly, “Sparse MRI: The application of compressed sensing for rapid MR imaging,” Magn. Reson. Med58, 1182–1195 (2007).
[CrossRef] [PubMed]

D. Donoho and I. Johnstone, “Threshold selection for wavelet shrinkage of noisy data,” in Proceedings of the 16th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, (IEEE1994), 1A24–A25

Donoho, D. L.

D. L. Donoho, A. Maleki, and A. Montanari, “The Noise- Sensitivity Phase Transition in Compressed Sensing”, IEEE Trans. Inf. Theory57, 6920 (2011).
[CrossRef]

D. L. Donoho, “Compressed Sensing,” IEEE Trans. Inf. Theory52, 1289–1306 (2006).
[CrossRef]

Dorenbos, S. N.

Drover, J.

M. Vaidyanathan, S. Blask, T. Higgins, W. Clifton, D. Davidsohn, R. Carson, V. Reynolds, J. Pfannenstiel, R. Cannata, R. Marino, J. Drover, R. Hatch, D. Schue, R. Freehart, G. Rowe, J. Mooney, C. Hart, B. Stanley, J. McLaughlin, E. I. Lee, J. Berenholtz, B. Aull, J. Zayhowski, A. Vasile, P. Ramaswami, K. Ingersoll, T. Amoruso, I. Khan, W. Davis, and R. Heinrichs, “Jigsaw phase III: a miniaturized airborne 3-D imaging laser radar with photon-counting sensitivity for foliage penetration,” Proc. SPIE6550, 65500N (2007).
[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, 83–91 (2008).
[CrossRef]

Duarte, M. F.

V. Cevher, A. Sankaranarayanan, M. F. Duarte, D. Reddy, R. G. Baraniuk, and R. Chellappa, “Compressive sensing for background subtraction,” in Computer Vision - ECCV 2008 Lecture Notes in Computer Science (Springer, 2008) pp. 155–168.
[CrossRef]

Eisert, J.

S. T. Flammia, D. Gross, Y.-K. Liu, and J. Eisert, “Quantum tomography via compressed sensing: error bounds, sample complexity and efficient estimators,” New J. Phys.14, 095022 (2012).
[CrossRef]

Entwistle, M.

M. Entwistle, M. A. Itzler, J. Chen, M. Owens, K. Patel, X. Jiang, K. Slomkowski, and S. Rangwala, “Geiger-mode APD camera system for single-photon 3D ladar imaging,” Proc. SPIE8375, 83750D (2012).

M. A. Itzler, M. Entwistle, M. Owens, K. Patel, X. Jiang, K. Slomkowski, S. Rangwala, P. F. Zalud, T. Senko, J. Tower, and J. Ferraro, “Comparison of 32 × 128 and 32 × 32 geiger-mode APD FPAS for single photon 3D ladar imaging,” Proc. SPIE8033, 80330G (2011).
[CrossRef]

Ferraro, J.

M. A. Itzler, M. Entwistle, M. Owens, K. Patel, X. Jiang, K. Slomkowski, S. Rangwala, P. F. Zalud, T. Senko, J. Tower, and J. Ferraro, “Comparison of 32 × 128 and 32 × 32 geiger-mode APD FPAS for single photon 3D ladar imaging,” Proc. SPIE8033, 80330G (2011).
[CrossRef]

Figueiredo, M. A. T.

M. A. T. Figueiredo, R. D. Nowak, and S. J. Wright, “Gradient Projection for Sparse Reconstruction: Application to Compressed Sensing and Other Inverse Problems,” IEEE J. Sel. Topics Signal Process.1, 586–597 (2007).
[CrossRef]

Flammia, S. T.

S. T. Flammia, D. Gross, Y.-K. Liu, and J. Eisert, “Quantum tomography via compressed sensing: error bounds, sample complexity and efficient estimators,” New J. Phys.14, 095022 (2012).
[CrossRef]

Foix, S.

S. Foix, G. Alenya, and C. Torras, “Lock-in time-of-flight (TOF) cameras: A survey,” IEEE Sensors J.11, 1917–1926 (2011).
[CrossRef]

Freehart, R.

M. Vaidyanathan, S. Blask, T. Higgins, W. Clifton, D. Davidsohn, R. Carson, V. Reynolds, J. Pfannenstiel, R. Cannata, R. Marino, J. Drover, R. Hatch, D. Schue, R. Freehart, G. Rowe, J. Mooney, C. Hart, B. Stanley, J. McLaughlin, E. I. Lee, J. Berenholtz, B. Aull, J. Zayhowski, A. Vasile, P. Ramaswami, K. Ingersoll, T. Amoruso, I. Khan, W. Davis, and R. Heinrichs, “Jigsaw phase III: a miniaturized airborne 3-D imaging laser radar with photon-counting sensitivity for foliage penetration,” Proc. SPIE6550, 65500N (2007).
[CrossRef]

Gemmell, N. R.

Goyal, V. K.

Gross, D.

S. T. Flammia, D. Gross, Y.-K. Liu, and J. Eisert, “Quantum tomography via compressed sensing: error bounds, sample complexity and efficient estimators,” New J. Phys.14, 095022 (2012).
[CrossRef]

Hadfield, R. H.

Harmony, Z. T.

Z. T. Harmony, R. F. Marcia, and R. F. Willett, “Sparse poisson intensity reconstruction algorithms” in Proceedings of the IEEE/SP 15th Workshop on Statistical Signal Processing (IEEE2009), pp 634–637.

Hart, C.

M. Vaidyanathan, S. Blask, T. Higgins, W. Clifton, D. Davidsohn, R. Carson, V. Reynolds, J. Pfannenstiel, R. Cannata, R. Marino, J. Drover, R. Hatch, D. Schue, R. Freehart, G. Rowe, J. Mooney, C. Hart, B. Stanley, J. McLaughlin, E. I. Lee, J. Berenholtz, B. Aull, J. Zayhowski, A. Vasile, P. Ramaswami, K. Ingersoll, T. Amoruso, I. Khan, W. Davis, and R. Heinrichs, “Jigsaw phase III: a miniaturized airborne 3-D imaging laser radar with photon-counting sensitivity for foliage penetration,” Proc. SPIE6550, 65500N (2007).
[CrossRef]

Hatch, R.

M. Vaidyanathan, S. Blask, T. Higgins, W. Clifton, D. Davidsohn, R. Carson, V. Reynolds, J. Pfannenstiel, R. Cannata, R. Marino, J. Drover, R. Hatch, D. Schue, R. Freehart, G. Rowe, J. Mooney, C. Hart, B. Stanley, J. McLaughlin, E. I. Lee, J. Berenholtz, B. Aull, J. Zayhowski, A. Vasile, P. Ramaswami, K. Ingersoll, T. Amoruso, I. Khan, W. Davis, and R. Heinrichs, “Jigsaw phase III: a miniaturized airborne 3-D imaging laser radar with photon-counting sensitivity for foliage penetration,” Proc. SPIE6550, 65500N (2007).
[CrossRef]

Heinrichs, R.

M. Vaidyanathan, S. Blask, T. Higgins, W. Clifton, D. Davidsohn, R. Carson, V. Reynolds, J. Pfannenstiel, R. Cannata, R. Marino, J. Drover, R. Hatch, D. Schue, R. Freehart, G. Rowe, J. Mooney, C. Hart, B. Stanley, J. McLaughlin, E. I. Lee, J. Berenholtz, B. Aull, J. Zayhowski, A. Vasile, P. Ramaswami, K. Ingersoll, T. Amoruso, I. Khan, W. Davis, and R. Heinrichs, “Jigsaw phase III: a miniaturized airborne 3-D imaging laser radar with photon-counting sensitivity for foliage penetration,” Proc. SPIE6550, 65500N (2007).
[CrossRef]

Higgins, T.

M. Vaidyanathan, S. Blask, T. Higgins, W. Clifton, D. Davidsohn, R. Carson, V. Reynolds, J. Pfannenstiel, R. Cannata, R. Marino, J. Drover, R. Hatch, D. Schue, R. Freehart, G. Rowe, J. Mooney, C. Hart, B. Stanley, J. McLaughlin, E. I. Lee, J. Berenholtz, B. Aull, J. Zayhowski, A. Vasile, P. Ramaswami, K. Ingersoll, T. Amoruso, I. Khan, W. Davis, and R. Heinrichs, “Jigsaw phase III: a miniaturized airborne 3-D imaging laser radar with photon-counting sensitivity for foliage penetration,” Proc. SPIE6550, 65500N (2007).
[CrossRef]

Howell, J. C.

G. A. Howland and J. C. Howell, “Efficient high-dimensional entanglement imaging with a compressive-sensing double-pixel camera,” Phys. Rev. X3, 011013 (2013).
[CrossRef]

O. S. Magaña-Loaiza, G. A. Howland, M. Malik, J. C. Howell, and R. W. Boyd, “Compressive object tracking using entangled photons,” Appl. Phys. Lett.102, 231104 (2013).
[CrossRef]

G. A. Howland, P. B. Dixon, and J. C. Howell, “Photon-counting compressive sensing laser radar for 3D imaging,” Appl. Opt.50, 5917–5920 (2011).
[CrossRef] [PubMed]

Howland, G. A.

O. S. Magaña-Loaiza, G. A. Howland, M. Malik, J. C. Howell, and R. W. Boyd, “Compressive object tracking using entangled photons,” Appl. Phys. Lett.102, 231104 (2013).
[CrossRef]

G. A. Howland and J. C. Howell, “Efficient high-dimensional entanglement imaging with a compressive-sensing double-pixel camera,” Phys. Rev. X3, 011013 (2013).
[CrossRef]

G. A. Howland, P. B. Dixon, and J. C. Howell, “Photon-counting compressive sensing laser radar for 3D imaging,” Appl. Opt.50, 5917–5920 (2011).
[CrossRef] [PubMed]

Hussmann, S.

S. Hussmann and T. Liepert, “Three-dimensional TOF robot vision system,” IEEE Trans. Instrum. Meas.58, 141–146 (2009).
[CrossRef]

Ingersoll, K.

M. Vaidyanathan, S. Blask, T. Higgins, W. Clifton, D. Davidsohn, R. Carson, V. Reynolds, J. Pfannenstiel, R. Cannata, R. Marino, J. Drover, R. Hatch, D. Schue, R. Freehart, G. Rowe, J. Mooney, C. Hart, B. Stanley, J. McLaughlin, E. I. Lee, J. Berenholtz, B. Aull, J. Zayhowski, A. Vasile, P. Ramaswami, K. Ingersoll, T. Amoruso, I. Khan, W. Davis, and R. Heinrichs, “Jigsaw phase III: a miniaturized airborne 3-D imaging laser radar with photon-counting sensitivity for foliage penetration,” Proc. SPIE6550, 65500N (2007).
[CrossRef]

Itzler, M. A.

M. Entwistle, M. A. Itzler, J. Chen, M. Owens, K. Patel, X. Jiang, K. Slomkowski, and S. Rangwala, “Geiger-mode APD camera system for single-photon 3D ladar imaging,” Proc. SPIE8375, 83750D (2012).

M. A. Itzler, M. Entwistle, M. Owens, K. Patel, X. Jiang, K. Slomkowski, S. Rangwala, P. F. Zalud, T. Senko, J. Tower, and J. Ferraro, “Comparison of 32 × 128 and 32 × 32 geiger-mode APD FPAS for single photon 3D ladar imaging,” Proc. SPIE8033, 80330G (2011).
[CrossRef]

Jiang, X.

M. Entwistle, M. A. Itzler, J. Chen, M. Owens, K. Patel, X. Jiang, K. Slomkowski, and S. Rangwala, “Geiger-mode APD camera system for single-photon 3D ladar imaging,” Proc. SPIE8375, 83750D (2012).

M. A. Itzler, M. Entwistle, M. Owens, K. Patel, X. Jiang, K. Slomkowski, S. Rangwala, P. F. Zalud, T. Senko, J. Tower, and J. Ferraro, “Comparison of 32 × 128 and 32 × 32 geiger-mode APD FPAS for single photon 3D ladar imaging,” Proc. SPIE8033, 80330G (2011).
[CrossRef]

Johnstone, I.

D. Donoho and I. Johnstone, “Threshold selection for wavelet shrinkage of noisy data,” in Proceedings of the 16th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, (IEEE1994), 1A24–A25

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, 83–91 (2008).
[CrossRef]

Khan, I.

M. Vaidyanathan, S. Blask, T. Higgins, W. Clifton, D. Davidsohn, R. Carson, V. Reynolds, J. Pfannenstiel, R. Cannata, R. Marino, J. Drover, R. Hatch, D. Schue, R. Freehart, G. Rowe, J. Mooney, C. Hart, B. Stanley, J. McLaughlin, E. I. Lee, J. Berenholtz, B. Aull, J. Zayhowski, A. Vasile, P. Ramaswami, K. Ingersoll, T. Amoruso, I. Khan, W. Davis, and R. Heinrichs, “Jigsaw phase III: a miniaturized airborne 3-D imaging laser radar with photon-counting sensitivity for foliage penetration,” Proc. SPIE6550, 65500N (2007).
[CrossRef]

Kirmani, A.

Krichel, N. J.

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, 83–91 (2008).
[CrossRef]

Lee, E. I.

M. Vaidyanathan, S. Blask, T. Higgins, W. Clifton, D. Davidsohn, R. Carson, V. Reynolds, J. Pfannenstiel, R. Cannata, R. Marino, J. Drover, R. Hatch, D. Schue, R. Freehart, G. Rowe, J. Mooney, C. Hart, B. Stanley, J. McLaughlin, E. I. Lee, J. Berenholtz, B. Aull, J. Zayhowski, A. Vasile, P. Ramaswami, K. Ingersoll, T. Amoruso, I. Khan, W. Davis, and R. Heinrichs, “Jigsaw phase III: a miniaturized airborne 3-D imaging laser radar with photon-counting sensitivity for foliage penetration,” Proc. SPIE6550, 65500N (2007).
[CrossRef]

Lescure, M.

M. C. Amann, T. Bosch, M. Lescure, R. Myllyla, and M. Rioux, “Laser ranging: a critical review of usual techniques for distance measurement,” Opt. Eng.40, 10–19 (2001).
[CrossRef]

Li, L.

Liepert, T.

S. Hussmann and T. Liepert, “Three-dimensional TOF robot vision system,” IEEE Trans. Instrum. Meas.58, 141–146 (2009).
[CrossRef]

Liu, Y.-K.

S. T. Flammia, D. Gross, Y.-K. Liu, and J. Eisert, “Quantum tomography via compressed sensing: error bounds, sample complexity and efficient estimators,” New J. Phys.14, 095022 (2012).
[CrossRef]

Lustig, M.

M. Lustig, D. Donoho, and J. M. Pauly, “Sparse MRI: The application of compressed sensing for rapid MR imaging,” Magn. Reson. Med58, 1182–1195 (2007).
[CrossRef] [PubMed]

Magaña-Loaiza, O. S.

O. S. Magaña-Loaiza, G. A. Howland, M. Malik, J. C. Howell, and R. W. Boyd, “Compressive object tracking using entangled photons,” Appl. Phys. Lett.102, 231104 (2013).
[CrossRef]

Maleki, A.

D. L. Donoho, A. Maleki, and A. Montanari, “The Noise- Sensitivity Phase Transition in Compressed Sensing”, IEEE Trans. Inf. Theory57, 6920 (2011).
[CrossRef]

Malik, M.

O. S. Magaña-Loaiza, G. A. Howland, M. Malik, J. C. Howell, and R. W. Boyd, “Compressive object tracking using entangled photons,” Appl. Phys. Lett.102, 231104 (2013).
[CrossRef]

Mallet, C.

C. Mallet and F. Bretar, “Full-waveform topographic lidar: State-of-the-art,” ISPRS Journal of Photogrammetry and Remote Sensing64, 1–16 (2009).
[CrossRef]

Marcia, R. F.

Z. T. Harmony, R. F. Marcia, and R. F. Willett, “Sparse poisson intensity reconstruction algorithms” in Proceedings of the IEEE/SP 15th Workshop on Statistical Signal Processing (IEEE2009), pp 634–637.

Marino, R.

M. Vaidyanathan, S. Blask, T. Higgins, W. Clifton, D. Davidsohn, R. Carson, V. Reynolds, J. Pfannenstiel, R. Cannata, R. Marino, J. Drover, R. Hatch, D. Schue, R. Freehart, G. Rowe, J. Mooney, C. Hart, B. Stanley, J. McLaughlin, E. I. Lee, J. Berenholtz, B. Aull, J. Zayhowski, A. Vasile, P. Ramaswami, K. Ingersoll, T. Amoruso, I. Khan, W. Davis, and R. Heinrichs, “Jigsaw phase III: a miniaturized airborne 3-D imaging laser radar with photon-counting sensitivity for foliage penetration,” Proc. SPIE6550, 65500N (2007).
[CrossRef]

McCarthy, A.

McLaughlin, J.

M. Vaidyanathan, S. Blask, T. Higgins, W. Clifton, D. Davidsohn, R. Carson, V. Reynolds, J. Pfannenstiel, R. Cannata, R. Marino, J. Drover, R. Hatch, D. Schue, R. Freehart, G. Rowe, J. Mooney, C. Hart, B. Stanley, J. McLaughlin, E. I. Lee, J. Berenholtz, B. Aull, J. Zayhowski, A. Vasile, P. Ramaswami, K. Ingersoll, T. Amoruso, I. Khan, W. Davis, and R. Heinrichs, “Jigsaw phase III: a miniaturized airborne 3-D imaging laser radar with photon-counting sensitivity for foliage penetration,” Proc. SPIE6550, 65500N (2007).
[CrossRef]

Montanari, A.

D. L. Donoho, A. Maleki, and A. Montanari, “The Noise- Sensitivity Phase Transition in Compressed Sensing”, IEEE Trans. Inf. Theory57, 6920 (2011).
[CrossRef]

Mooney, J.

M. Vaidyanathan, S. Blask, T. Higgins, W. Clifton, D. Davidsohn, R. Carson, V. Reynolds, J. Pfannenstiel, R. Cannata, R. Marino, J. Drover, R. Hatch, D. Schue, R. Freehart, G. Rowe, J. Mooney, C. Hart, B. Stanley, J. McLaughlin, E. I. Lee, J. Berenholtz, B. Aull, J. Zayhowski, A. Vasile, P. Ramaswami, K. Ingersoll, T. Amoruso, I. Khan, W. Davis, and R. Heinrichs, “Jigsaw phase III: a miniaturized airborne 3-D imaging laser radar with photon-counting sensitivity for foliage penetration,” Proc. SPIE6550, 65500N (2007).
[CrossRef]

Myllyla, R.

M. C. Amann, T. Bosch, M. Lescure, R. Myllyla, and M. Rioux, “Laser ranging: a critical review of usual techniques for distance measurement,” Opt. Eng.40, 10–19 (2001).
[CrossRef]

Nowak, R. D.

M. A. T. Figueiredo, R. D. Nowak, and S. J. Wright, “Gradient Projection for Sparse Reconstruction: Application to Compressed Sensing and Other Inverse Problems,” IEEE J. Sel. Topics Signal Process.1, 586–597 (2007).
[CrossRef]

Ottensamer, R.

J. Bobin, J.-L. Starck, and R. Ottensamer, “Compressed sensing in astronomy,” IEEE J. Sel. Topics Signal Process.2, 718–726 (2008).
[CrossRef]

Owens, M.

M. Entwistle, M. A. Itzler, J. Chen, M. Owens, K. Patel, X. Jiang, K. Slomkowski, and S. Rangwala, “Geiger-mode APD camera system for single-photon 3D ladar imaging,” Proc. SPIE8375, 83750D (2012).

M. A. Itzler, M. Entwistle, M. Owens, K. Patel, X. Jiang, K. Slomkowski, S. Rangwala, P. F. Zalud, T. Senko, J. Tower, and J. Ferraro, “Comparison of 32 × 128 and 32 × 32 geiger-mode APD FPAS for single photon 3D ladar imaging,” Proc. SPIE8033, 80330G (2011).
[CrossRef]

Patel, K.

M. Entwistle, M. A. Itzler, J. Chen, M. Owens, K. Patel, X. Jiang, K. Slomkowski, and S. Rangwala, “Geiger-mode APD camera system for single-photon 3D ladar imaging,” Proc. SPIE8375, 83750D (2012).

M. A. Itzler, M. Entwistle, M. Owens, K. Patel, X. Jiang, K. Slomkowski, S. Rangwala, P. F. Zalud, T. Senko, J. Tower, and J. Ferraro, “Comparison of 32 × 128 and 32 × 32 geiger-mode APD FPAS for single photon 3D ladar imaging,” Proc. SPIE8033, 80330G (2011).
[CrossRef]

Pauly, J. M.

M. Lustig, D. Donoho, and J. M. Pauly, “Sparse MRI: The application of compressed sensing for rapid MR imaging,” Magn. Reson. Med58, 1182–1195 (2007).
[CrossRef] [PubMed]

Pfannenstiel, J.

M. Vaidyanathan, S. Blask, T. Higgins, W. Clifton, D. Davidsohn, R. Carson, V. Reynolds, J. Pfannenstiel, R. Cannata, R. Marino, J. Drover, R. Hatch, D. Schue, R. Freehart, G. Rowe, J. Mooney, C. Hart, B. Stanley, J. McLaughlin, E. I. Lee, J. Berenholtz, B. Aull, J. Zayhowski, A. Vasile, P. Ramaswami, K. Ingersoll, T. Amoruso, I. Khan, W. Davis, and R. Heinrichs, “Jigsaw phase III: a miniaturized airborne 3-D imaging laser radar with photon-counting sensitivity for foliage penetration,” Proc. SPIE6550, 65500N (2007).
[CrossRef]

Ramaswami, P.

M. Vaidyanathan, S. Blask, T. Higgins, W. Clifton, D. Davidsohn, R. Carson, V. Reynolds, J. Pfannenstiel, R. Cannata, R. Marino, J. Drover, R. Hatch, D. Schue, R. Freehart, G. Rowe, J. Mooney, C. Hart, B. Stanley, J. McLaughlin, E. I. Lee, J. Berenholtz, B. Aull, J. Zayhowski, A. Vasile, P. Ramaswami, K. Ingersoll, T. Amoruso, I. Khan, W. Davis, and R. Heinrichs, “Jigsaw phase III: a miniaturized airborne 3-D imaging laser radar with photon-counting sensitivity for foliage penetration,” Proc. SPIE6550, 65500N (2007).
[CrossRef]

Rangwala, S.

M. Entwistle, M. A. Itzler, J. Chen, M. Owens, K. Patel, X. Jiang, K. Slomkowski, and S. Rangwala, “Geiger-mode APD camera system for single-photon 3D ladar imaging,” Proc. SPIE8375, 83750D (2012).

M. A. Itzler, M. Entwistle, M. Owens, K. Patel, X. Jiang, K. Slomkowski, S. Rangwala, P. F. Zalud, T. Senko, J. Tower, and J. Ferraro, “Comparison of 32 × 128 and 32 × 32 geiger-mode APD FPAS for single photon 3D ladar imaging,” Proc. SPIE8033, 80330G (2011).
[CrossRef]

Reddy, D.

V. Cevher, A. Sankaranarayanan, M. F. Duarte, D. Reddy, R. G. Baraniuk, and R. Chellappa, “Compressive sensing for background subtraction,” in Computer Vision - ECCV 2008 Lecture Notes in Computer Science (Springer, 2008) pp. 155–168.
[CrossRef]

Ren, X.

Renner, C.

Reynolds, V.

M. Vaidyanathan, S. Blask, T. Higgins, W. Clifton, D. Davidsohn, R. Carson, V. Reynolds, J. Pfannenstiel, R. Cannata, R. Marino, J. Drover, R. Hatch, D. Schue, R. Freehart, G. Rowe, J. Mooney, C. Hart, B. Stanley, J. McLaughlin, E. I. Lee, J. Berenholtz, B. Aull, J. Zayhowski, A. Vasile, P. Ramaswami, K. Ingersoll, T. Amoruso, I. Khan, W. Davis, and R. Heinrichs, “Jigsaw phase III: a miniaturized airborne 3-D imaging laser radar with photon-counting sensitivity for foliage penetration,” Proc. SPIE6550, 65500N (2007).
[CrossRef]

Richard, M.

M. Richard and W. Davis, “Jigsaw: A foliage-penetrating 3D imaging laser radar system,” Lincoln Laboratory Journal15, 1 (2005).

Rioux, M.

M. C. Amann, T. Bosch, M. Lescure, R. Myllyla, and M. Rioux, “Laser ranging: a critical review of usual techniques for distance measurement,” Opt. Eng.40, 10–19 (2001).
[CrossRef]

Romberg, J.

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

Rowe, G.

M. Vaidyanathan, S. Blask, T. Higgins, W. Clifton, D. Davidsohn, R. Carson, V. Reynolds, J. Pfannenstiel, R. Cannata, R. Marino, J. Drover, R. Hatch, D. Schue, R. Freehart, G. Rowe, J. Mooney, C. Hart, B. Stanley, J. McLaughlin, E. I. Lee, J. Berenholtz, B. Aull, J. Zayhowski, A. Vasile, P. Ramaswami, K. Ingersoll, T. Amoruso, I. Khan, W. Davis, and R. Heinrichs, “Jigsaw phase III: a miniaturized airborne 3-D imaging laser radar with photon-counting sensitivity for foliage penetration,” Proc. SPIE6550, 65500N (2007).
[CrossRef]

Sankaranarayanan, A.

V. Cevher, A. Sankaranarayanan, M. F. Duarte, D. Reddy, R. G. Baraniuk, and R. Chellappa, “Compressive sensing for background subtraction,” in Computer Vision - ECCV 2008 Lecture Notes in Computer Science (Springer, 2008) pp. 155–168.
[CrossRef]

Sarkis, M.

M. Sarkis and K. Diepold, “Depth map compression via compressed sensing,” in Proceedings of 16th IEEE International Conference on Image Processing, (IEEE, 2009), pp. 737–740.

Schue, D.

M. Vaidyanathan, S. Blask, T. Higgins, W. Clifton, D. Davidsohn, R. Carson, V. Reynolds, J. Pfannenstiel, R. Cannata, R. Marino, J. Drover, R. Hatch, D. Schue, R. Freehart, G. Rowe, J. Mooney, C. Hart, B. Stanley, J. McLaughlin, E. I. Lee, J. Berenholtz, B. Aull, J. Zayhowski, A. Vasile, P. Ramaswami, K. Ingersoll, T. Amoruso, I. Khan, W. Davis, and R. Heinrichs, “Jigsaw phase III: a miniaturized airborne 3-D imaging laser radar with photon-counting sensitivity for foliage penetration,” Proc. SPIE6550, 65500N (2007).
[CrossRef]

Schwarz, B.

B. Schwarz, “Mapping the world in 3D,” Nat. Photonics4, 429–430 (2010).
[CrossRef]

Senko, T.

M. A. Itzler, M. Entwistle, M. Owens, K. Patel, X. Jiang, K. Slomkowski, S. Rangwala, P. F. Zalud, T. Senko, J. Tower, and J. Ferraro, “Comparison of 32 × 128 and 32 × 32 geiger-mode APD FPAS for single photon 3D ladar imaging,” Proc. SPIE8033, 80330G (2011).
[CrossRef]

Slomkowski, K.

M. Entwistle, M. A. Itzler, J. Chen, M. Owens, K. Patel, X. Jiang, K. Slomkowski, and S. Rangwala, “Geiger-mode APD camera system for single-photon 3D ladar imaging,” Proc. SPIE8375, 83750D (2012).

M. A. Itzler, M. Entwistle, M. Owens, K. Patel, X. Jiang, K. Slomkowski, S. Rangwala, P. F. Zalud, T. Senko, J. Tower, and J. Ferraro, “Comparison of 32 × 128 and 32 × 32 geiger-mode APD FPAS for single photon 3D ladar imaging,” Proc. SPIE8033, 80330G (2011).
[CrossRef]

Stanley, B.

M. Vaidyanathan, S. Blask, T. Higgins, W. Clifton, D. Davidsohn, R. Carson, V. Reynolds, J. Pfannenstiel, R. Cannata, R. Marino, J. Drover, R. Hatch, D. Schue, R. Freehart, G. Rowe, J. Mooney, C. Hart, B. Stanley, J. McLaughlin, E. I. Lee, J. Berenholtz, B. Aull, J. Zayhowski, A. Vasile, P. Ramaswami, K. Ingersoll, T. Amoruso, I. Khan, W. Davis, and R. Heinrichs, “Jigsaw phase III: a miniaturized airborne 3-D imaging laser radar with photon-counting sensitivity for foliage penetration,” Proc. SPIE6550, 65500N (2007).
[CrossRef]

Starck, J.-L.

J. Bobin, J.-L. Starck, and R. Ottensamer, “Compressed sensing in astronomy,” IEEE J. Sel. Topics Signal Process.2, 718–726 (2008).
[CrossRef]

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, 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, 83–91 (2008).
[CrossRef]

Tanner, M. G.

Torras, C.

S. Foix, G. Alenya, and C. Torras, “Lock-in time-of-flight (TOF) cameras: A survey,” IEEE Sensors J.11, 1917–1926 (2011).
[CrossRef]

Tower, J.

M. A. Itzler, M. Entwistle, M. Owens, K. Patel, X. Jiang, K. Slomkowski, S. Rangwala, P. F. Zalud, T. Senko, J. Tower, and J. Ferraro, “Comparison of 32 × 128 and 32 × 32 geiger-mode APD FPAS for single photon 3D ladar imaging,” Proc. SPIE8033, 80330G (2011).
[CrossRef]

Vaidyanathan, M.

M. Vaidyanathan, S. Blask, T. Higgins, W. Clifton, D. Davidsohn, R. Carson, V. Reynolds, J. Pfannenstiel, R. Cannata, R. Marino, J. Drover, R. Hatch, D. Schue, R. Freehart, G. Rowe, J. Mooney, C. Hart, B. Stanley, J. McLaughlin, E. I. Lee, J. Berenholtz, B. Aull, J. Zayhowski, A. Vasile, P. Ramaswami, K. Ingersoll, T. Amoruso, I. Khan, W. Davis, and R. Heinrichs, “Jigsaw phase III: a miniaturized airborne 3-D imaging laser radar with photon-counting sensitivity for foliage penetration,” Proc. SPIE6550, 65500N (2007).
[CrossRef]

Vasile, A.

M. Vaidyanathan, S. Blask, T. Higgins, W. Clifton, D. Davidsohn, R. Carson, V. Reynolds, J. Pfannenstiel, R. Cannata, R. Marino, J. Drover, R. Hatch, D. Schue, R. Freehart, G. Rowe, J. Mooney, C. Hart, B. Stanley, J. McLaughlin, E. I. Lee, J. Berenholtz, B. Aull, J. Zayhowski, A. Vasile, P. Ramaswami, K. Ingersoll, T. Amoruso, I. Khan, W. Davis, and R. Heinrichs, “Jigsaw phase III: a miniaturized airborne 3-D imaging laser radar with photon-counting sensitivity for foliage penetration,” Proc. SPIE6550, 65500N (2007).
[CrossRef]

Wang, X.

Willett, R. F.

Z. T. Harmony, R. F. Marcia, and R. F. Willett, “Sparse poisson intensity reconstruction algorithms” in Proceedings of the IEEE/SP 15th Workshop on Statistical Signal Processing (IEEE2009), pp 634–637.

Wong, F. N. C.

Wright, S. J.

M. A. T. Figueiredo, R. D. Nowak, and S. J. Wright, “Gradient Projection for Sparse Reconstruction: Application to Compressed Sensing and Other Inverse Problems,” IEEE J. Sel. Topics Signal Process.1, 586–597 (2007).
[CrossRef]

Wu, L.

Zalud, P. F.

M. A. Itzler, M. Entwistle, M. Owens, K. Patel, X. Jiang, K. Slomkowski, S. Rangwala, P. F. Zalud, T. Senko, J. Tower, and J. Ferraro, “Comparison of 32 × 128 and 32 × 32 geiger-mode APD FPAS for single photon 3D ladar imaging,” Proc. SPIE8033, 80330G (2011).
[CrossRef]

Zayhowski, J.

M. Vaidyanathan, S. Blask, T. Higgins, W. Clifton, D. Davidsohn, R. Carson, V. Reynolds, J. Pfannenstiel, R. Cannata, R. Marino, J. Drover, R. Hatch, D. Schue, R. Freehart, G. Rowe, J. Mooney, C. Hart, B. Stanley, J. McLaughlin, E. I. Lee, J. Berenholtz, B. Aull, J. Zayhowski, A. Vasile, P. Ramaswami, K. Ingersoll, T. Amoruso, I. Khan, W. Davis, and R. Heinrichs, “Jigsaw phase III: a miniaturized airborne 3-D imaging laser radar with photon-counting sensitivity for foliage penetration,” Proc. SPIE6550, 65500N (2007).
[CrossRef]

Zwiller, V.

Appl. Opt. (2)

Appl. Phys. Lett. (1)

O. S. Magaña-Loaiza, G. A. Howland, M. Malik, J. C. Howell, and R. W. Boyd, “Compressive object tracking using entangled photons,” Appl. Phys. Lett.102, 231104 (2013).
[CrossRef]

IEEE J. Sel. Topics Signal Process. (2)

M. A. T. Figueiredo, R. D. Nowak, and S. J. Wright, “Gradient Projection for Sparse Reconstruction: Application to Compressed Sensing and Other Inverse Problems,” IEEE J. Sel. Topics Signal Process.1, 586–597 (2007).
[CrossRef]

J. Bobin, J.-L. Starck, and R. Ottensamer, “Compressed sensing in astronomy,” IEEE J. Sel. Topics Signal Process.2, 718–726 (2008).
[CrossRef]

IEEE Sensors J. (1)

S. Foix, G. Alenya, and C. Torras, “Lock-in time-of-flight (TOF) cameras: A survey,” IEEE Sensors J.11, 1917–1926 (2011).
[CrossRef]

IEEE Signal Process. Mag. (1)

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, 83–91 (2008).
[CrossRef]

IEEE Trans. Inf. Theory (2)

D. L. Donoho, “Compressed Sensing,” IEEE Trans. Inf. Theory52, 1289–1306 (2006).
[CrossRef]

D. L. Donoho, A. Maleki, and A. Montanari, “The Noise- Sensitivity Phase Transition in Compressed Sensing”, IEEE Trans. Inf. Theory57, 6920 (2011).
[CrossRef]

IEEE Trans. Instrum. Meas. (1)

S. Hussmann and T. Liepert, “Three-dimensional TOF robot vision system,” IEEE Trans. Instrum. Meas.58, 141–146 (2009).
[CrossRef]

Inverse Probl. (1)

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

ISPRS Journal of Photogrammetry and Remote Sensing (1)

C. Mallet and F. Bretar, “Full-waveform topographic lidar: State-of-the-art,” ISPRS Journal of Photogrammetry and Remote Sensing64, 1–16 (2009).
[CrossRef]

Lincoln Laboratory Journal (1)

M. Richard and W. Davis, “Jigsaw: A foliage-penetrating 3D imaging laser radar system,” Lincoln Laboratory Journal15, 1 (2005).

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. Med58, 1182–1195 (2007).
[CrossRef] [PubMed]

Nat. Photonics (1)

B. Schwarz, “Mapping the world in 3D,” Nat. Photonics4, 429–430 (2010).
[CrossRef]

New J. Phys. (1)

S. T. Flammia, D. Gross, Y.-K. Liu, and J. Eisert, “Quantum tomography via compressed sensing: error bounds, sample complexity and efficient estimators,” New J. Phys.14, 095022 (2012).
[CrossRef]

Opt. Eng. (1)

M. C. Amann, T. Bosch, M. Lescure, R. Myllyla, and M. Rioux, “Laser ranging: a critical review of usual techniques for distance measurement,” Opt. Eng.40, 10–19 (2001).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. X (1)

G. A. Howland and J. C. Howell, “Efficient high-dimensional entanglement imaging with a compressive-sensing double-pixel camera,” Phys. Rev. X3, 011013 (2013).
[CrossRef]

Proc. SPIE (3)

M. Vaidyanathan, S. Blask, T. Higgins, W. Clifton, D. Davidsohn, R. Carson, V. Reynolds, J. Pfannenstiel, R. Cannata, R. Marino, J. Drover, R. Hatch, D. Schue, R. Freehart, G. Rowe, J. Mooney, C. Hart, B. Stanley, J. McLaughlin, E. I. Lee, J. Berenholtz, B. Aull, J. Zayhowski, A. Vasile, P. Ramaswami, K. Ingersoll, T. Amoruso, I. Khan, W. Davis, and R. Heinrichs, “Jigsaw phase III: a miniaturized airborne 3-D imaging laser radar with photon-counting sensitivity for foliage penetration,” Proc. SPIE6550, 65500N (2007).
[CrossRef]

M. Entwistle, M. A. Itzler, J. Chen, M. Owens, K. Patel, X. Jiang, K. Slomkowski, and S. Rangwala, “Geiger-mode APD camera system for single-photon 3D ladar imaging,” Proc. SPIE8375, 83750D (2012).

M. A. Itzler, M. Entwistle, M. Owens, K. Patel, X. Jiang, K. Slomkowski, S. Rangwala, P. F. Zalud, T. Senko, J. Tower, and J. Ferraro, “Comparison of 32 × 128 and 32 × 32 geiger-mode APD FPAS for single photon 3D ladar imaging,” Proc. SPIE8033, 80330G (2011).
[CrossRef]

Other (5)

M. Sarkis and K. Diepold, “Depth map compression via compressed sensing,” in Proceedings of 16th IEEE International Conference on Image Processing, (IEEE, 2009), pp. 737–740.

V. Cevher, A. Sankaranarayanan, M. F. Duarte, D. Reddy, R. G. Baraniuk, and R. Chellappa, “Compressive sensing for background subtraction,” in Computer Vision - ECCV 2008 Lecture Notes in Computer Science (Springer, 2008) pp. 155–168.
[CrossRef]

D. Donoho and I. Johnstone, “Threshold selection for wavelet shrinkage of noisy data,” in Proceedings of the 16th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, (IEEE1994), 1A24–A25

C. Li, W. Yin, and Y. Zhang, “TVAL3: TV minimization by augmented lagrangian and alternating direction algorithms,” http://www.caam.rice.edu/~optimization/L1/TVAL3/ .

Z. T. Harmony, R. F. Marcia, and R. F. Willett, “Sparse poisson intensity reconstruction algorithms” in Proceedings of the IEEE/SP 15th Workshop on Statistical Signal Processing (IEEE2009), pp 634–637.

Supplementary Material (1)

» Media 1: AVI (1142 KB)     

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1
Fig. 1

Experimental Setup A 780 nm, 10 Mhz, 2 ns pulsed laser diode flood illuminates a scene containing targets at different depths. Returning pulses are imaged onto a DMD array with resolution up to 256 × 256 pixels. A polarizer prevents flares from specular reflection. Light reflecting off DMD “on” pixels is directed through a narrow-band filter to a single-photon sensitive PMT module that produces TTL pulses. Typical count rates are about 2 million photons per second. A TCSPC module time-correlates photon arrivals with the outgoing pulse train to determine a TOF for each detected photon. A series of psuedorandom, binary patterns consisting of randomly permuted, zero-shifted Hadamard patterns are placed on the DMD with per-pattern dwell times as short as 1/1440 sec. These implement an incoherent sensing matrix. For each pattern, the number of photon arrivals and their total TOF is recorded. Our protocol is then used to reconstruct the intensity image and the depth map.

Fig. 2
Fig. 2

Long Exposure A scene consisting of cardboard cutouts (a) is imaged at n = 256 × 256 resolution from m = 0.2n random projections with a 6.07 minute exposure time. The protocol recovers a high quality intensity map (b) and intensity × DOF map (c). Their ratio is the depth map (d).

Fig. 3
Fig. 3

Short Exposure Scene from Fig. 2 acquired with rapid acquisition times. The intensity and depth maps in (a) and (b) were acquired in 23 seconds while (c) and (d) were acquired in only 3 seconds. At these exposure times, the intensity map regularly contains less than one photon per significant pixel, so it is impossible to raster scan.

Fig. 4
Fig. 4

Natural Scene A scene consisting of a cactus, shoe, and microscope is imaged at n = 256 × 256 pixel resolution with m = 0.3n and a per-pattern dwell time tp = 50/1440 seconds.

Fig. 5
Fig. 5

Depth Calibration Depth maps of a rectangular cardboard cutout (a) are acquired at n = 32 × 32 pixel resolution with a typical reconstruction given in (b). The cutouts to-target distance was increased in increments of 15.52 cm (c) and 2.54 cm (d). Depths can accurately recovered to less than 2.54 cm for this scene.

Fig. 6
Fig. 6

Novelty Filtering (a) and (b) give photographs of two instances of a scene, where the ‘R’ has changed positions (including depth). (c) and (d) show high quality, long 6.07 minute exposure depth map reconstructions for the full current scene and difference image respectively. (e) and (f) show corresponding short 37 second exposure depth map reconstructions. Negative values in the difference image indicate the object’s former location.

Fig. 7
Fig. 7

Movie Frames from a depth-map movie ( Media 1), of a three-dimensional pendulum consisting of a baseball suspended by a 170 cm rope swinging through a 25 degree solid angle. The transverse resolution is 32×32 pixels with a frame rate of 14 frames per second.

Fig. 8
Fig. 8

Object Tracking The expected values for transverse (x,y) and range (z) coordinates are given in (a), (b), and (c) as a function of frame number. Blue circles show expected values obtained from reconstructed depth maps, while green lines give sinusoidal fits. (d) shows a 3D parametric plot of the pendulum’s trajectory.

Tables (1)

Tables Icon

Table 1 System Specifications

Equations (6)

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

Y = A X + Γ ,
min X 1 2 Y A X 2 2 + τ g ( X ) ,
Y Q = A X Q = { C j = 1 N A i j η j T j } for i = 1 to m ,
X D = Nz ( X I ) . X Q . / | X I |
Δ Y = Y ( c ) Y ( r )
Δ Y = A Δ X .

Metrics