Abstract

We demonstrate a photon counting 3D imaging system with short-pulsed structured illumination and a single-pixel photon counting detector. The proposed multiresolution photon counting 3D imaging technique acquires a high-resolution 3D image from a coarse image and details at successfully finer resolution sampled along the wavelet trees and their depth map sparse representations. Both the required measurements and the reconstruction time can be significant reduced, which makes the proposed technique suitable for scenes with high spatial resolution. The experimental results indicate that both the reflectivity and depth map of a scene at resolutions up to 512×512 pixels can be acquired and retrieved with practical times as low as 17.5 seconds. In addition, we demonstrate that this technique has ability to image in presence of partially-transmissive occluders, and to directly acquire novelty images to find changes in a scene.

© 2016 Optical Society of America

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References

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2016 (4)

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

H. D. Dai, G. H. Gu, W. J. He, Q. Chen, and T. Y. Mao, “Adaptive video compressed sampling in the wavelet domain,” Opt. Laser Technol. 81, 90–99 (2016).
[Crossref]

Y. Yan, H. Dai, X. Liu, W. He, Q. Chen, and G. Gu, “Colored adaptive compressed imaging with a single photodiode,” Appl. Opt. 55(14), 3711–3718 (2016).
[Crossref] [PubMed]

D. Shin, F. Xu, F. N. Wong, J. H. Shapiro, and V. K. Goyal, “Computational multi-depth single-photon imaging,” Opt. Express 24(3), 1873–1888 (2016).
[Crossref] [PubMed]

2015 (2)

G. Gariepy, N. Krstajić, R. Henderson, C. Li, R. R. Thomson, G. S. Buller, B. Heshmat, R. Raskar, J. Leach, and D. Faccio, “Single-photon sensitive light-in-fight imaging,” Nat. Commun. 6, 6021 (2015).
[Crossref] [PubMed]

G. Gariepy, F. Tonolini, R. Henderson, J. Leach, and D. Faccio, “Detection and tracking of moving objects hidden from view,” Nat. Photonics 10(1), 23–26 (2015).
[Crossref]

2014 (4)

U. C. Herzfeld, B. W. Mcdonald, B. F. Wallin, T. A. Neumann, T. Markus, A. Brenner, and C. Field, “Algorithm for detection of ground and canopy cover in micropulse photon-counting lidar altimeter data in preparation for the icesat-2 mission,” IEEE Trans. Geosci. Remote Sens. 52(4), 2109–2125 (2014).
[Crossref]

A. Kirmani, D. Venkatraman, D. Shin, A. Colaço, F. N. C. Wong, J. H. Shapiro, and V. K. Goyal, “First-photon imaging,” Science 343(6166), 58–61 (2014).
[Crossref] [PubMed]

W. K. Yu, M. F. Li, X. R. Yao, X. F. Liu, L. A. Wu, and G. J. Zhai, “Adaptive compressive ghost imaging based on wavelet trees and sparse representation,” Opt. Express 22(6), 7133–7144 (2014).
[Crossref] [PubMed]

H. Dai, G. Gu, W. He, F. Liao, J. Zhuang, X. Liu, and Q. Chen, “Adaptive compressed sampling based on extended wavelet trees,” Appl. Opt. 53(29), 6619–6628 (2014).
[Crossref] [PubMed]

2013 (4)

G. A. Howland, D. J. Lum, M. R. Ware, and J. C. Howell, “Photon counting compressive depth mapping,” Opt. Express 21(20), 23822–23837 (2013).
[Crossref] [PubMed]

O. S. Magana-Loaiza, G. A. Howland, M. Malik, J. C. Howell, and R. W. Boyd, “Compressive object tracking using entangled photons,” Appl. Phys. Lett. 102(23), 231104 (2013).
[Crossref]

M. Assmann and M. Bayer, “Compressive adaptive computational ghost imaging,” Sci. Rep. 3, 1545 (2013).
[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]

2012 (1)

A. Averbuch, S. Dekel, and S. Deutsch, “Adaptive compressed image sensing using dictionaries,” SIAM J. Imaging Sci. 5(1), 57–89 (2012).
[Crossref]

2011 (2)

2010 (1)

B. Schwarz, “Mapping the world in 3D,” Nat. Photonics 4(7), 429–430 (2010).
[Crossref]

2009 (1)

2008 (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(2), 83–91 (2008).
[Crossref]

2007 (1)

2006 (3)

D. 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]

E. J. Candes and T. Tao, “Near-optimal signal recovery from random projections: Universal encoding strategies?” IEEE Trans. Inf. Theory 52(12), 5406–5425 (2006).
[Crossref]

2005 (2)

R. M. Marino and W. R. Davis., “Real-time 3d ladar imaging,” Linc. Lab. J. 15, 23–35 (2005).

M. Richard and W. Davis, “Jigsaw: A foliage-penetrating 3D imaging laser radar system,” Linc. Lab. J. 15, 1 (2005).

2004 (1)

W. Becker, A. Bergmann, M. A. Hink, K. König, K. Benndorf, and C. Biskup, “Fluorescence lifetime imaging by time-correlated single-photon counting,” Microsc. Res. Tech. 63(1), 58–66 (2004).
[Crossref] [PubMed]

2000 (1)

C. Christopoulos, A. Skodras, and T. Ebrahimi, “The JPEG2000 still image coding system: an overview,” IEEE Trans. Consum. Electron. 46(4), 1103–1127 (2000).
[Crossref]

1996 (2)

A. Said and W. Pearlman, “A new fast and efficient image codec based on set partitioning in hierarchical trees,” IEEE Trans. Circ. Syst. Video Tech. 6(3), 243–250 (1996).
[Crossref]

W. C. Priedhorsky, R. C. Smith, and C. Ho, “Laser ranging and mapping with a photon-counting detector,” Appl. Opt. 35(3), 441–452 (1996).
[Crossref] [PubMed]

1995 (1)

1993 (1)

J. Shapiro, “Embedded image coding using zerotrees of wavelet coefficients,” IEEE Trans. Signal Process. 41(12), 3445–3462 (1993).
[Crossref]

Anand, P.

Anand, U.

Assmann, M.

M. Assmann and M. Bayer, “Compressive adaptive computational ghost imaging,” Sci. Rep. 3, 1545 (2013).
[Crossref] [PubMed]

Averbuch, A.

A. Averbuch, S. Dekel, and S. Deutsch, “Adaptive compressed image sensing using dictionaries,” SIAM J. Imaging Sci. 5(1), 57–89 (2012).
[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]

M. Wakin, J. Laska, M. Duarte, D. Baron, S. Sarvotham, D. Takhar, K. Kelly, and R. Baraniuk, “An architecture for compressive imaging,” in Proceedings of IEEE Conference on Image Processing, (IEEE, 2006), pp. 1273–1276.

Baron, D.

M. Wakin, J. Laska, M. Duarte, D. Baron, S. Sarvotham, D. Takhar, K. Kelly, and R. Baraniuk, “An architecture for compressive imaging,” in Proceedings of IEEE Conference on Image Processing, (IEEE, 2006), pp. 1273–1276.

Bayer, M.

M. Assmann and M. Bayer, “Compressive adaptive computational ghost imaging,” Sci. Rep. 3, 1545 (2013).
[Crossref] [PubMed]

Becker, W.

W. Becker, A. Bergmann, M. A. Hink, K. König, K. Benndorf, and C. Biskup, “Fluorescence lifetime imaging by time-correlated single-photon counting,” Microsc. Res. Tech. 63(1), 58–66 (2004).
[Crossref] [PubMed]

Benham, C.

Benndorf, K.

W. Becker, A. Bergmann, M. A. Hink, K. König, K. Benndorf, and C. Biskup, “Fluorescence lifetime imaging by time-correlated single-photon counting,” Microsc. Res. Tech. 63(1), 58–66 (2004).
[Crossref] [PubMed]

Benninger, R. K. P.

Bergmann, A.

W. Becker, A. Bergmann, M. A. Hink, K. König, K. Benndorf, and C. Biskup, “Fluorescence lifetime imaging by time-correlated single-photon counting,” Microsc. Res. Tech. 63(1), 58–66 (2004).
[Crossref] [PubMed]

Biskup, C.

W. Becker, A. Bergmann, M. A. Hink, K. König, K. Benndorf, and C. Biskup, “Fluorescence lifetime imaging by time-correlated single-photon counting,” Microsc. Res. Tech. 63(1), 58–66 (2004).
[Crossref] [PubMed]

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]

Boyd, R. W.

O. S. Magana-Loaiza, G. A. Howland, M. Malik, J. C. Howell, and R. W. Boyd, “Compressive object tracking using entangled photons,” Appl. Phys. Lett. 102(23), 231104 (2013).
[Crossref]

Brenner, A.

U. C. Herzfeld, B. W. Mcdonald, B. F. Wallin, T. A. Neumann, T. Markus, A. Brenner, and C. Field, “Algorithm for detection of ground and canopy cover in micropulse photon-counting lidar altimeter data in preparation for the icesat-2 mission,” IEEE Trans. Geosci. Remote Sens. 52(4), 2109–2125 (2014).
[Crossref]

Bucholtz, A.

Buller, G. S.

G. Gariepy, N. Krstajić, R. Henderson, C. Li, R. R. Thomson, G. S. Buller, B. Heshmat, R. Raskar, J. Leach, and D. Faccio, “Single-photon sensitive light-in-fight imaging,” Nat. Commun. 6, 6021 (2015).
[Crossref] [PubMed]

A. McCarthy, R. J. Collins, N. J. Krichel, V. Fernández, A. M. Wallace, and G. S. Buller, “Long-range time-of-flight scanning sensor based on high-speed time-correlated single-photon counting,” Appl. Opt. 48(32), 6241–6251 (2009).
[Crossref] [PubMed]

Candes, E. J.

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]

E. J. Candes and T. Tao, “Near-optimal signal recovery from random projections: Universal encoding strategies?” IEEE Trans. Inf. Theory 52(12), 5406–5425 (2006).
[Crossref]

Chen, Q.

Christopoulos, C.

C. Christopoulos, A. Skodras, and T. Ebrahimi, “The JPEG2000 still image coding system: an overview,” IEEE Trans. Consum. Electron. 46(4), 1103–1127 (2000).
[Crossref]

Colaço, A.

A. Kirmani, D. Venkatraman, D. Shin, A. Colaço, F. N. C. Wong, J. H. Shapiro, and V. K. Goyal, “First-photon imaging,” Science 343(6166), 58–61 (2014).
[Crossref] [PubMed]

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. Express 19(22), 21485–21507 (2011).
[Crossref] [PubMed]

A. Colaço, A. Kirmani, G. A. Howland, J. C. Howell, and V. K. Goyal, “Compressive depth map acquisition using a single photon-counting detector: Parametric signal processing meets sparsity,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, (IEEE, 2012), pp. 96–102.
[Crossref]

Collins, R. J.

Dai, H.

Dai, H. D.

H. D. Dai, G. H. Gu, W. J. He, Q. Chen, and T. Y. Mao, “Adaptive video compressed sampling in the wavelet domain,” Opt. Laser Technol. 81, 90–99 (2016).
[Crossref]

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]

Davis, D. M.

Davis, W.

M. Richard and W. Davis, “Jigsaw: A foliage-penetrating 3D imaging laser radar system,” Linc. Lab. J. 15, 1 (2005).

Davis, W. R.

R. M. Marino and W. R. Davis., “Real-time 3d ladar imaging,” Linc. Lab. J. 15, 23–35 (2005).

De Beule, P. A. A.

Dekel, S.

A. Averbuch, S. Dekel, and S. Deutsch, “Adaptive compressed image sensing using dictionaries,” SIAM J. Imaging Sci. 5(1), 57–89 (2012).
[Crossref]

Delaigle, J. F.

J. F. Delaigle, C. Deveeschouwer, B. Macq, and I. Langendijk, “Human visual system features enabling watermarking,” in Proceeding of IEEE International Conference on Multimedia and Expo, (IEEE, 2002), pp. 489–492.
[Crossref]

Deutsch, S.

A. Averbuch, S. Dekel, and S. Deutsch, “Adaptive compressed image sensing using dictionaries,” SIAM J. Imaging Sci. 5(1), 57–89 (2012).
[Crossref]

Deveeschouwer, C.

J. F. Delaigle, C. Deveeschouwer, B. Macq, and I. Langendijk, “Human visual system features enabling watermarking,” in Proceeding of IEEE International Conference on Multimedia and Expo, (IEEE, 2002), pp. 489–492.
[Crossref]

Dixon, P. B.

Donoho, D.

D. 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]

M. Wakin, J. Laska, M. Duarte, D. Baron, S. Sarvotham, D. Takhar, K. Kelly, and R. Baraniuk, “An architecture for compressive imaging,” in Proceedings of IEEE Conference on Image Processing, (IEEE, 2006), pp. 1273–1276.

Dunsby, C.

Ebrahimi, T.

C. Christopoulos, A. Skodras, and T. Ebrahimi, “The JPEG2000 still image coding system: an overview,” IEEE Trans. Consum. Electron. 46(4), 1103–1127 (2000).
[Crossref]

Edgar, M. P.

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

Faccio, D.

G. Gariepy, N. Krstajić, R. Henderson, C. Li, R. R. Thomson, G. S. Buller, B. Heshmat, R. Raskar, J. Leach, and D. Faccio, “Single-photon sensitive light-in-fight imaging,” Nat. Commun. 6, 6021 (2015).
[Crossref] [PubMed]

G. Gariepy, F. Tonolini, R. Henderson, J. Leach, and D. Faccio, “Detection and tracking of moving objects hidden from view,” Nat. Photonics 10(1), 23–26 (2015).
[Crossref]

Fernández, V.

Field, C.

U. C. Herzfeld, B. W. Mcdonald, B. F. Wallin, T. A. Neumann, T. Markus, A. Brenner, and C. Field, “Algorithm for detection of ground and canopy cover in micropulse photon-counting lidar altimeter data in preparation for the icesat-2 mission,” IEEE Trans. Geosci. Remote Sens. 52(4), 2109–2125 (2014).
[Crossref]

French, P. M. W.

Gariepy, G.

G. Gariepy, F. Tonolini, R. Henderson, J. Leach, and D. Faccio, “Detection and tracking of moving objects hidden from view,” Nat. Photonics 10(1), 23–26 (2015).
[Crossref]

G. Gariepy, N. Krstajić, R. Henderson, C. Li, R. R. Thomson, G. S. Buller, B. Heshmat, R. Raskar, J. Leach, and D. Faccio, “Single-photon sensitive light-in-fight imaging,” Nat. Commun. 6, 6021 (2015).
[Crossref] [PubMed]

Gibson, G. M.

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

Goyal, V. K.

D. Shin, F. Xu, F. N. Wong, J. H. Shapiro, and V. K. Goyal, “Computational multi-depth single-photon imaging,” Opt. Express 24(3), 1873–1888 (2016).
[Crossref] [PubMed]

A. Kirmani, D. Venkatraman, D. Shin, A. Colaço, F. N. C. Wong, J. H. Shapiro, and V. K. Goyal, “First-photon imaging,” Science 343(6166), 58–61 (2014).
[Crossref] [PubMed]

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. Express 19(22), 21485–21507 (2011).
[Crossref] [PubMed]

A. Colaço, A. Kirmani, G. A. Howland, J. C. Howell, and V. K. Goyal, “Compressive depth map acquisition using a single photon-counting detector: Parametric signal processing meets sparsity,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, (IEEE, 2012), pp. 96–102.
[Crossref]

Gu, G.

Gu, G. H.

H. D. Dai, G. H. Gu, W. J. He, Q. Chen, and T. Y. Mao, “Adaptive video compressed sampling in the wavelet domain,” Opt. Laser Technol. 81, 90–99 (2016).
[Crossref]

He, W.

He, W. J.

H. D. Dai, G. H. Gu, W. J. He, Q. Chen, and T. Y. Mao, “Adaptive video compressed sampling in the wavelet domain,” Opt. Laser Technol. 81, 90–99 (2016).
[Crossref]

Henderson, R.

G. Gariepy, N. Krstajić, R. Henderson, C. Li, R. R. Thomson, G. S. Buller, B. Heshmat, R. Raskar, J. Leach, and D. Faccio, “Single-photon sensitive light-in-fight imaging,” Nat. Commun. 6, 6021 (2015).
[Crossref] [PubMed]

G. Gariepy, F. Tonolini, R. Henderson, J. Leach, and D. Faccio, “Detection and tracking of moving objects hidden from view,” Nat. Photonics 10(1), 23–26 (2015).
[Crossref]

Herzfeld, U. C.

U. C. Herzfeld, B. W. Mcdonald, B. F. Wallin, T. A. Neumann, T. Markus, A. Brenner, and C. Field, “Algorithm for detection of ground and canopy cover in micropulse photon-counting lidar altimeter data in preparation for the icesat-2 mission,” IEEE Trans. Geosci. Remote Sens. 52(4), 2109–2125 (2014).
[Crossref]

Heshmat, B.

G. Gariepy, N. Krstajić, R. Henderson, C. Li, R. R. Thomson, G. S. Buller, B. Heshmat, R. Raskar, J. Leach, and D. Faccio, “Single-photon sensitive light-in-fight imaging,” Nat. Commun. 6, 6021 (2015).
[Crossref] [PubMed]

Hink, M. A.

W. Becker, A. Bergmann, M. A. Hink, K. König, K. Benndorf, and C. Biskup, “Fluorescence lifetime imaging by time-correlated single-photon counting,” Microsc. Res. Tech. 63(1), 58–66 (2004).
[Crossref] [PubMed]

Ho, C.

Howell, J. C.

O. S. Magana-Loaiza, G. A. Howland, M. Malik, J. C. Howell, and R. W. Boyd, “Compressive object tracking using entangled photons,” Appl. Phys. Lett. 102(23), 231104 (2013).
[Crossref]

G. A. Howland, D. J. Lum, M. R. Ware, and J. C. Howell, “Photon counting compressive depth mapping,” Opt. Express 21(20), 23822–23837 (2013).
[Crossref] [PubMed]

G. A. Howland, P. B. Dixon, and J. C. Howell, “Photon-counting compressive sensing laser radar for 3D imaging,” Appl. Opt. 50(31), 5917–5920 (2011).
[Crossref] [PubMed]

A. Colaço, A. Kirmani, G. A. Howland, J. C. Howell, and V. K. Goyal, “Compressive depth map acquisition using a single photon-counting detector: Parametric signal processing meets sparsity,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, (IEEE, 2012), pp. 96–102.
[Crossref]

Howland, G. A.

O. S. Magana-Loaiza, G. A. Howland, M. Malik, J. C. Howell, and R. W. Boyd, “Compressive object tracking using entangled photons,” Appl. Phys. Lett. 102(23), 231104 (2013).
[Crossref]

G. A. Howland, D. J. Lum, M. R. Ware, and J. C. Howell, “Photon counting compressive depth mapping,” Opt. Express 21(20), 23822–23837 (2013).
[Crossref] [PubMed]

G. A. Howland, P. B. Dixon, and J. C. Howell, “Photon-counting compressive sensing laser radar for 3D imaging,” Appl. Opt. 50(31), 5917–5920 (2011).
[Crossref] [PubMed]

A. Colaço, A. Kirmani, G. A. Howland, J. C. Howell, and V. K. Goyal, “Compressive depth map acquisition using a single photon-counting detector: Parametric signal processing meets sparsity,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, (IEEE, 2012), pp. 96–102.
[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]

M. Wakin, J. Laska, M. Duarte, D. Baron, S. Sarvotham, D. Takhar, K. Kelly, and R. Baraniuk, “An architecture for compressive imaging,” in Proceedings of IEEE Conference on Image Processing, (IEEE, 2006), pp. 1273–1276.

Kirmani, A.

A. Kirmani, D. Venkatraman, D. Shin, A. Colaço, F. N. C. Wong, J. H. Shapiro, and V. K. Goyal, “First-photon imaging,” Science 343(6166), 58–61 (2014).
[Crossref] [PubMed]

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. Express 19(22), 21485–21507 (2011).
[Crossref] [PubMed]

A. Colaço, A. Kirmani, G. A. Howland, J. C. Howell, and V. K. Goyal, “Compressive depth map acquisition using a single photon-counting detector: Parametric signal processing meets sparsity,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, (IEEE, 2012), pp. 96–102.
[Crossref]

König, K.

W. Becker, A. Bergmann, M. A. Hink, K. König, K. Benndorf, and C. Biskup, “Fluorescence lifetime imaging by time-correlated single-photon counting,” Microsc. Res. Tech. 63(1), 58–66 (2004).
[Crossref] [PubMed]

Krichel, N. J.

Krstajic, N.

G. Gariepy, N. Krstajić, R. Henderson, C. Li, R. R. Thomson, G. S. Buller, B. Heshmat, R. Raskar, J. Leach, and D. Faccio, “Single-photon sensitive light-in-fight imaging,” Nat. Commun. 6, 6021 (2015).
[Crossref] [PubMed]

Kumar, S.

Lamb, R.

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

Langendijk, I.

J. F. Delaigle, C. Deveeschouwer, B. Macq, and I. Langendijk, “Human visual system features enabling watermarking,” in Proceeding of IEEE International Conference on Multimedia and Expo, (IEEE, 2002), pp. 489–492.
[Crossref]

Lanigan, P. M. P.

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]

M. Wakin, J. Laska, M. Duarte, D. Baron, S. Sarvotham, D. Takhar, K. Kelly, and R. Baraniuk, “An architecture for compressive imaging,” in Proceedings of IEEE Conference on Image Processing, (IEEE, 2006), pp. 1273–1276.

Leach, J.

G. Gariepy, F. Tonolini, R. Henderson, J. Leach, and D. Faccio, “Detection and tracking of moving objects hidden from view,” Nat. Photonics 10(1), 23–26 (2015).
[Crossref]

G. Gariepy, N. Krstajić, R. Henderson, C. Li, R. R. Thomson, G. S. Buller, B. Heshmat, R. Raskar, J. Leach, and D. Faccio, “Single-photon sensitive light-in-fight imaging,” Nat. Commun. 6, 6021 (2015).
[Crossref] [PubMed]

Li, C.

G. Gariepy, N. Krstajić, R. Henderson, C. Li, R. R. Thomson, G. S. Buller, B. Heshmat, R. Raskar, J. Leach, and D. Faccio, “Single-photon sensitive light-in-fight imaging,” Nat. Commun. 6, 6021 (2015).
[Crossref] [PubMed]

Li, M. F.

Liao, F.

Liu, X.

Liu, X. F.

Lum, D. J.

Macq, B.

J. F. Delaigle, C. Deveeschouwer, B. Macq, and I. Langendijk, “Human visual system features enabling watermarking,” in Proceeding of IEEE International Conference on Multimedia and Expo, (IEEE, 2002), pp. 489–492.
[Crossref]

Magana-Loaiza, O. S.

O. S. Magana-Loaiza, G. A. Howland, M. Malik, J. C. Howell, and R. W. Boyd, “Compressive object tracking using entangled photons,” Appl. Phys. Lett. 102(23), 231104 (2013).
[Crossref]

Malik, M.

O. S. Magana-Loaiza, G. A. Howland, M. Malik, J. C. Howell, and R. W. Boyd, “Compressive object tracking using entangled photons,” Appl. Phys. Lett. 102(23), 231104 (2013).
[Crossref]

Mao, T. Y.

H. D. Dai, G. H. Gu, W. J. He, Q. Chen, and T. Y. Mao, “Adaptive video compressed sampling in the wavelet domain,” Opt. Laser Technol. 81, 90–99 (2016).
[Crossref]

Marino, R. M.

R. M. Marino and W. R. Davis., “Real-time 3d ladar imaging,” Linc. Lab. J. 15, 23–35 (2005).

Markus, T.

U. C. Herzfeld, B. W. Mcdonald, B. F. Wallin, T. A. Neumann, T. Markus, A. Brenner, and C. Field, “Algorithm for detection of ground and canopy cover in micropulse photon-counting lidar altimeter data in preparation for the icesat-2 mission,” IEEE Trans. Geosci. Remote Sens. 52(4), 2109–2125 (2014).
[Crossref]

McCarthy, A.

Mcdonald, B. W.

U. C. Herzfeld, B. W. Mcdonald, B. F. Wallin, T. A. Neumann, T. Markus, A. Brenner, and C. Field, “Algorithm for detection of ground and canopy cover in micropulse photon-counting lidar altimeter data in preparation for the icesat-2 mission,” IEEE Trans. Geosci. Remote Sens. 52(4), 2109–2125 (2014).
[Crossref]

Naylor, A.

Neil, M. A. A.

Neumann, T. A.

U. C. Herzfeld, B. W. Mcdonald, B. F. Wallin, T. A. Neumann, T. Markus, A. Brenner, and C. Field, “Algorithm for detection of ground and canopy cover in micropulse photon-counting lidar altimeter data in preparation for the icesat-2 mission,” IEEE Trans. Geosci. Remote Sens. 52(4), 2109–2125 (2014).
[Crossref]

Owen, D. M.

Padgett, M. J.

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

Pearlman, W.

A. Said and W. Pearlman, “A new fast and efficient image codec based on set partitioning in hierarchical trees,” IEEE Trans. Circ. Syst. Video Tech. 6(3), 243–250 (1996).
[Crossref]

Priedhorsky, W. C.

Radwell, N.

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

Raskar, R.

G. Gariepy, N. Krstajić, R. Henderson, C. Li, R. R. Thomson, G. S. Buller, B. Heshmat, R. Raskar, J. Leach, and D. Faccio, “Single-photon sensitive light-in-fight imaging,” Nat. Commun. 6, 6021 (2015).
[Crossref] [PubMed]

Richard, M.

M. Richard and W. Davis, “Jigsaw: A foliage-penetrating 3D imaging laser radar system,” Linc. Lab. J. 15, 1 (2005).

Romberg, J.

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]

Said, A.

A. Said and W. Pearlman, “A new fast and efficient image codec based on set partitioning in hierarchical trees,” IEEE Trans. Circ. Syst. Video Tech. 6(3), 243–250 (1996).
[Crossref]

Sarvotham, S.

M. Wakin, J. Laska, M. Duarte, D. Baron, S. Sarvotham, D. Takhar, K. Kelly, and R. Baraniuk, “An architecture for compressive imaging,” in Proceedings of IEEE Conference on Image Processing, (IEEE, 2006), pp. 1273–1276.

Schwarz, B.

B. Schwarz, “Mapping the world in 3D,” Nat. Photonics 4(7), 429–430 (2010).
[Crossref]

Shapiro, J.

J. Shapiro, “Embedded image coding using zerotrees of wavelet coefficients,” IEEE Trans. Signal Process. 41(12), 3445–3462 (1993).
[Crossref]

Shapiro, J. H.

D. Shin, F. Xu, F. N. Wong, J. H. Shapiro, and V. K. Goyal, “Computational multi-depth single-photon imaging,” Opt. Express 24(3), 1873–1888 (2016).
[Crossref] [PubMed]

A. Kirmani, D. Venkatraman, D. Shin, A. Colaço, F. N. C. Wong, J. H. Shapiro, and V. K. Goyal, “First-photon imaging,” Science 343(6166), 58–61 (2014).
[Crossref] [PubMed]

Shin, D.

D. Shin, F. Xu, F. N. Wong, J. H. Shapiro, and V. K. Goyal, “Computational multi-depth single-photon imaging,” Opt. Express 24(3), 1873–1888 (2016).
[Crossref] [PubMed]

A. Kirmani, D. Venkatraman, D. Shin, A. Colaço, F. N. C. Wong, J. H. Shapiro, and V. K. Goyal, “First-photon imaging,” Science 343(6166), 58–61 (2014).
[Crossref] [PubMed]

Skodras, A.

C. Christopoulos, A. Skodras, and T. Ebrahimi, “The JPEG2000 still image coding system: an overview,” IEEE Trans. Consum. Electron. 46(4), 1103–1127 (2000).
[Crossref]

Smith, R. C.

Sun, B.

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

Sun, M.

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

M. Wakin, J. Laska, M. Duarte, D. Baron, S. Sarvotham, D. Takhar, K. Kelly, and R. Baraniuk, “An architecture for compressive imaging,” in Proceedings of IEEE Conference on Image Processing, (IEEE, 2006), pp. 1273–1276.

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]

E. J. Candes and T. Tao, “Near-optimal signal recovery from random projections: Universal encoding strategies?” IEEE Trans. Inf. Theory 52(12), 5406–5425 (2006).
[Crossref]

Thomson, R. R.

G. Gariepy, N. Krstajić, R. Henderson, C. Li, R. R. Thomson, G. S. Buller, B. Heshmat, R. Raskar, J. Leach, and D. Faccio, “Single-photon sensitive light-in-fight imaging,” Nat. Commun. 6, 6021 (2015).
[Crossref] [PubMed]

Tonolini, F.

G. Gariepy, F. Tonolini, R. Henderson, J. Leach, and D. Faccio, “Detection and tracking of moving objects hidden from view,” Nat. Photonics 10(1), 23–26 (2015).
[Crossref]

Venkatraman, D.

A. Kirmani, D. Venkatraman, D. Shin, A. Colaço, F. N. C. Wong, J. H. Shapiro, and V. K. Goyal, “First-photon imaging,” Science 343(6166), 58–61 (2014).
[Crossref] [PubMed]

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.

M. Wakin, J. Laska, M. Duarte, D. Baron, S. Sarvotham, D. Takhar, K. Kelly, and R. Baraniuk, “An architecture for compressive imaging,” in Proceedings of IEEE Conference on Image Processing, (IEEE, 2006), pp. 1273–1276.

Wallace, A. M.

Wallin, B. F.

U. C. Herzfeld, B. W. Mcdonald, B. F. Wallin, T. A. Neumann, T. Markus, A. Brenner, and C. Field, “Algorithm for detection of ground and canopy cover in micropulse photon-counting lidar altimeter data in preparation for the icesat-2 mission,” IEEE Trans. Geosci. Remote Sens. 52(4), 2109–2125 (2014).
[Crossref]

Ware, M. R.

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]

Wong, F. N.

Wong, F. N. C.

A. Kirmani, D. Venkatraman, D. Shin, A. Colaço, F. N. C. Wong, J. H. Shapiro, and V. K. Goyal, “First-photon imaging,” Science 343(6166), 58–61 (2014).
[Crossref] [PubMed]

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. Express 19(22), 21485–21507 (2011).
[Crossref] [PubMed]

Wu, L. A.

Xu, F.

Yan, Y.

Yao, X. R.

Yu, W. K.

Zhai, G. J.

Zhuang, J.

Appl. Opt. (6)

Appl. Phys. Lett. (1)

O. S. Magana-Loaiza, G. A. Howland, M. Malik, J. C. Howell, and R. W. Boyd, “Compressive object tracking using entangled photons,” Appl. Phys. Lett. 102(23), 231104 (2013).
[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(2), 83–91 (2008).
[Crossref]

IEEE Trans. Circ. Syst. Video Tech. (1)

A. Said and W. Pearlman, “A new fast and efficient image codec based on set partitioning in hierarchical trees,” IEEE Trans. Circ. Syst. Video Tech. 6(3), 243–250 (1996).
[Crossref]

IEEE Trans. Consum. Electron. (1)

C. Christopoulos, A. Skodras, and T. Ebrahimi, “The JPEG2000 still image coding system: an overview,” IEEE Trans. Consum. Electron. 46(4), 1103–1127 (2000).
[Crossref]

IEEE Trans. Geosci. Remote Sens. (1)

U. C. Herzfeld, B. W. Mcdonald, B. F. Wallin, T. A. Neumann, T. Markus, A. Brenner, and C. Field, “Algorithm for detection of ground and canopy cover in micropulse photon-counting lidar altimeter data in preparation for the icesat-2 mission,” IEEE Trans. Geosci. Remote Sens. 52(4), 2109–2125 (2014).
[Crossref]

IEEE Trans. Inf. Theory (3)

D. 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]

E. J. Candes and T. Tao, “Near-optimal signal recovery from random projections: Universal encoding strategies?” IEEE Trans. Inf. Theory 52(12), 5406–5425 (2006).
[Crossref]

IEEE Trans. Signal Process. (1)

J. Shapiro, “Embedded image coding using zerotrees of wavelet coefficients,” IEEE Trans. Signal Process. 41(12), 3445–3462 (1993).
[Crossref]

Linc. Lab. J. (2)

R. M. Marino and W. R. Davis., “Real-time 3d ladar imaging,” Linc. Lab. J. 15, 23–35 (2005).

M. Richard and W. Davis, “Jigsaw: A foliage-penetrating 3D imaging laser radar system,” Linc. Lab. J. 15, 1 (2005).

Microsc. Res. Tech. (1)

W. Becker, A. Bergmann, M. A. Hink, K. König, K. Benndorf, and C. Biskup, “Fluorescence lifetime imaging by time-correlated single-photon counting,” Microsc. Res. Tech. 63(1), 58–66 (2004).
[Crossref] [PubMed]

Nat. Commun. (2)

G. Gariepy, N. Krstajić, R. Henderson, C. Li, R. R. Thomson, G. S. Buller, B. Heshmat, R. Raskar, J. Leach, and D. Faccio, “Single-photon sensitive light-in-fight imaging,” Nat. Commun. 6, 6021 (2015).
[Crossref] [PubMed]

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

Nat. Photonics (2)

G. Gariepy, F. Tonolini, R. Henderson, J. Leach, and D. Faccio, “Detection and tracking of moving objects hidden from view,” Nat. Photonics 10(1), 23–26 (2015).
[Crossref]

B. Schwarz, “Mapping the world in 3D,” Nat. Photonics 4(7), 429–430 (2010).
[Crossref]

Opt. Express (5)

Opt. Laser Technol. (1)

H. D. Dai, G. H. Gu, W. J. He, Q. Chen, and T. Y. Mao, “Adaptive video compressed sampling in the wavelet domain,” Opt. Laser Technol. 81, 90–99 (2016).
[Crossref]

Sci. Rep. (1)

M. Assmann and M. Bayer, “Compressive adaptive computational ghost imaging,” Sci. Rep. 3, 1545 (2013).
[Crossref] [PubMed]

Science (2)

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]

A. Kirmani, D. Venkatraman, D. Shin, A. Colaço, F. N. C. Wong, J. H. Shapiro, and V. K. Goyal, “First-photon imaging,” Science 343(6166), 58–61 (2014).
[Crossref] [PubMed]

SIAM J. Imaging Sci. (1)

A. Averbuch, S. Dekel, and S. Deutsch, “Adaptive compressed image sensing using dictionaries,” SIAM J. Imaging Sci. 5(1), 57–89 (2012).
[Crossref]

Other (8)

A. Colaço, A. Kirmani, G. A. Howland, J. C. Howell, and V. K. Goyal, “Compressive depth map acquisition using a single photon-counting detector: Parametric signal processing meets sparsity,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, (IEEE, 2012), pp. 96–102.
[Crossref]

R. Lamb and G. Buller, “Single-pixel imaging using 3d scanning time-of-flight photon counting,” SPIE Newsroom (2010).

M. Wakin, J. Laska, M. Duarte, D. Baron, S. Sarvotham, D. Takhar, K. Kelly, and R. Baraniuk, “An architecture for compressive imaging,” in Proceedings of IEEE Conference on Image Processing, (IEEE, 2006), pp. 1273–1276.

Princeton Lightwave, “Falcon 128x32 Geiger-Mode Flash 3-D LIDAR Camera,” http://www.princetonlightwave.com/wp-content/uploads/2016/09/PLI-Falcon.pdf .

S. Mallat, A Wavelet Tour of Signal Processing: The Sparse Way (Academic, 2008).

C. Li, W. Yin, and Y. Zhang, “Users guide for TVAL3: TV minimization by augmented lagrangian and alternating direction algorithms,” CAAM Report (2009).

K. G. Beauchamp, Applications of Walsh and Related Functions (Academic, 1984).

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[Crossref]

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Figures (9)

Fig. 1
Fig. 1 Comparison of the sparsity of scene reflectivity and depth map in the wavelet domain. The target scene is a house with resolutions of 512×512 pixels, whose reflectivity and depth map are presented in (a) and (b), together with their three-level wavelet representation shown in (c) and (d). (e) presents curves where the coefficients shown in (c) and (d) sorted by magnitude.
Fig. 2
Fig. 2 Experimental setup. The combination of a pulsed laser and a DMD is implemented to provide structured illumination onto a scene, and the back-scattered photons are detected by a photomultiplier tube module (photon counting type). The timing histograms computed by a TCSPC module are used to reconstruct both reflectivity and depth maps.
Fig. 3
Fig. 3 Overview of the 3D imaging technique at the s-th stage. The combination of a pulsed laser and DMD patterns at the s-th stage (a) is implemented to provide structured illumination to a scene. The back-scattered photons (b) are time-correlated with the transmitting pluses to compute the photon counting histograms (c). A wavelet coefficient cube (d) (the intensity of coefficients is enhanced for better illustration) is obtained by combining the results of wavelet coefficients computation and the low-resolution coefficients perviously sampled, which is converted to real space via an inverse wavelet transform to obtain an image cube (e). Then histograms recording the TOF of photons reaching different transverse pixels (f) are be obtained, from which the depth map (g) and reflectivity (h) can be estimated. At last, the patterns to be displayed at the next stage are generated by significant regions estimation based on the wavelet trees and depth map sparse representation. The acquisition and data processing carry on until the expected resolution is reaching.
Fig. 4
Fig. 4 Imaging with a simple scene. (a) is the photograph of the scene consisting of cardboard cutouts of the letters “NJ”, “U”, “ST”. The depth maps and the reflectivity are both acquired with resolution of 512×512 pixel and compression ratios of 5%, 10% and 20%, shown in (b)-(d) and (e)-(g) respectively.
Fig. 5
Fig. 5 Imaging with a natural scene. (a) is the photograph of the scene consisting of a magic cube and a porcelain cup. The reflectivity and depth maps are both acquired at a resolution of 512×512 pixel and compression ratios of 5%, 10% and 20%, shown in (b)-(d) and (e)-(g) respectively.
Fig. 6
Fig. 6 A natural scene imaged by the method proposed in [21] and [24]. (a)-(c) and (d)-(f) are the reflectivity and depth maps acquired by the method proposed in [21] at a resolution of 512×512 pixel and compression ratios of 5%, 10%, and, 20%. (g)-(i) and (j)-(l) are those acquired by the method proposed in [24].
Fig. 7
Fig. 7 3D imaging through a partially-transmissive occluder. (a) Illustration of scene containing cardboard cutouts and a netting used as a partially-transmissive occluder. The reflectivity and depth map obtained without temporal gating are presented in (b) and (c), while (d) and (e) are the results reconstructed with temporal gating.
Fig. 8
Fig. 8 3D novelty imaging. (a) and (b) present the photographs of the current scene and the reference scene, where the letter “U” has changed positions (both transversely and longitudinally). (c) and (d) present the reflectivity and depth map of the current scene reconstructed at compression ratio of 20%. (e) and (f) show the corresponding difference reflectivity and depth map obtained at compression ratio of 5%, where the negative values in the difference images denote the object’s former location.
Fig. 9
Fig. 9 Curves describe (a) the number of measurements and (b) the compression ratios to reaching PSNRs of 30 dB, 35 dB, and 40 dB with increasing of resolution.

Equations (3)

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w j,k 1 = f, ψ j,k 1 = 2 j [ 2 j k 1 2 j ( k 1 +1 ) 2 j k 2 2 j ( k 2 +1/2 ) f( x 1 , x 2 )d x 1 d x 2 2 j k 1 2 j ( k 1 +1 ) 2 j ( k 2 +1/2 ) 2 j ( k 2 +1 ) f( x 1 , x 2 )d x 1 d x 2 ],
PSNR=10log 255 2 MSE ,
MSE= 1 ab p,q=1 a,b [ T 0 ( p,q ) T r ( p,q ) ] 2 .

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