Abstract

Target images recorded with range-gated laser imaging systems and conventional passive imaging systems through rapidly changing turbid mediums inevitably suffer from inhomogeneous degradations. Consequently, this makes the images partly or entirely different from their true targets and eventually has adverse effects on target identification. To date, the inhomogeneous degradations are still not finely eliminable despite utilizing adaptive optical methods and pure mathematical signal improvement techniques. Herein, we demonstrate an image restoration method involving intrinsic physical evolution of light beams based on the backscattering images of a turbid medium. The corresponding mathematical signal processing algorithms are applied for restoring the true target images in the presence of rapidly changing inhomogeneous degradations. This technique would benefit target imaging through moving cloud/mist in air and flowing muddy masses under water.

© 2017 Optical Society of America

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References

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2016 (1)

2015 (2)

S. Kang, S. Jeong, W. Choi, H. Ko, T. D. Yang, J. H. Joo, J. S. Lee, Y. S. Lim, Q. H. Park, and W. Choi, “Imaging deep within a scattering medium using collective accumulation of single-scattered waves,” Nat. Photonics 9, 253–258 (2015).

K. Wu, Q. Cheng, Y. Shi, H. Wang, and G. P. Wang, “Hiding scattering layers for noninvasive imaging of hidden objects,” Sci. Rep. 5, 8375 (2015).
[Crossref] [PubMed]

2014 (1)

O. Katz, P. Heidmann, M. Fink, and S. Gigan, “Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations,” Nat. Photonics 8(10), 784–790 (2014).
[Crossref]

2012 (2)

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491(7423), 232–234 (2012).
[Crossref] [PubMed]

P. F. McManamon, “Review of ladar: a historic, yet emerging, sensor technology with rich phenomenology,” Opt. Eng. 51(6), 060901 (2012).
[Crossref]

2011 (2)

Z. M. Jin and X. P. Yang, “A variational model to remove the multiplicative noise in ultrasound images,” J. Math. Imaging Vis. 39(1), 62–74 (2011).
[Crossref]

O. Katz, E. Small, Y. Bromberg, and Y. Silberberg, “Focusing and compression of ultrashort pulses through scattering media,” Nat. Photonics 5(6), 372–377 (2011).
[Crossref]

2009 (2)

J. F. Yang, Y. Zhang, and W. T. Yin, “An efficient TVL1 algorithm for deblurring multichannel images corrupted by impulsive noise,” SIAM J. Sci. Comput. 31(4), 2842–2865 (2009).
[Crossref]

M. Laurenzis, F. Christnacher, N. Metzger, E. Bacher, and I. Zielenski, “3d range-gated imaging at infrared wavelengths with super-resolution depth mapping,” Proc. SPIE 7298, 729833 (2009).
[Crossref]

2007 (2)

2006 (3)

P. Andersson, “Long-range three dimensional imaging using range-gated laser radar images,” Opt. Eng. 45(3), 034301 (2006).
[Crossref]

M. Martin-Fernandez, E. Munoz-Moreno, and C. Alberola-Lopez, “A speckle removal filter based on anisotropic Wiener filtering and the Rice distribution,” Proc. IEEE Ultrason. Symp. 7(3), 1694–1697 (2006).
[Crossref]

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photonics 6(5), 283–292 (2006).
[Crossref]

2005 (4)

T. F. Chan and S. Esedoglu, “Aspects of total variation regularized L1 function approximation,” SIAM J. Appl. Math. 65(5), 1817–1837 (2005).
[Crossref]

A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50(4), R1–R43 (2005).
[Crossref] [PubMed]

C. S. Tan, G. Seet, A. Sluzek, and D. M. He, “A novel application of range-gated underwater laser imaging system (ULIS) in near-target turbid medium,” Opt. Lasers Eng. 43(9), 995–1009 (2005).
[Crossref]

J. Busck, “Underwater 3-D optical imaging with a gated viewing laser radar,” Opt. Eng. 44(11), 116001 (2005).
[Crossref]

2004 (1)

A. Chambolle, “An algorithm for total variation minimization and applications,” J. Math. Imaging Vis. 20(1/2), 89–97 (2004).
[Crossref]

2003 (1)

R. G. Driggers, R. H. Vollmerhausen, N. Devitt, C. Halfort, and K. J. Barnard, “Impact of speckle on laser range-gated shortwave infrared imaging system target identification performance,” Opt. Eng. 42(3), 738–746 (2003).
[Crossref]

2002 (1)

R. S. Bennink, S. J. Bentley, and R. W. Boyd, “‘Two-Photon’ coincidence imaging with a classical source,” Phys. Rev. Lett. 89(11), 113601 (2002).
[Crossref] [PubMed]

1996 (1)

D. G. Lainiotis, P. Papaparaskeva, and K. Plataniotis, “Nonlinear filtering for LIDAR signal processing,” Math. Probl. Eng. 2(5), 367–392 (1996).
[Crossref]

1995 (2)

E. A. McLean, H. R. Burris, and M. P. Strand, “Short-pulse range-gated optical imaging in turbid water,” Appl. Opt. 34(21), 4343–4351 (1995).
[Crossref] [PubMed]

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, “Observation of two-photon “ghost” interference and diffraction,” Phys. Rev. Lett. 74(18), 3600–3603 (1995).
[Crossref] [PubMed]

1993 (1)

G. R. Fournier, D. Bonnier, J. L. Forand, and P. W. Pace, “Range-gated underwater laser imaging system,” Opt. Eng. 32(9), 2185–2190 (1993).
[Crossref]

1992 (1)

L. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica D 60(1-4), 259–268 (1992).
[Crossref]

1990 (1)

I. Freund, “Looking through walls and around corners,” Physica A 168(1), 49–65 (1990).
[Crossref]

1984 (1)

1966 (1)

Alberola-Lopez, C.

M. Martin-Fernandez, E. Munoz-Moreno, and C. Alberola-Lopez, “A speckle removal filter based on anisotropic Wiener filtering and the Rice distribution,” Proc. IEEE Ultrason. Symp. 7(3), 1694–1697 (2006).
[Crossref]

Andersson, P.

P. Andersson, “Long-range three dimensional imaging using range-gated laser radar images,” Opt. Eng. 45(3), 034301 (2006).
[Crossref]

Arridge, S. R.

A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50(4), R1–R43 (2005).
[Crossref] [PubMed]

Bacher, E.

M. Laurenzis, F. Christnacher, N. Metzger, E. Bacher, and I. Zielenski, “3d range-gated imaging at infrared wavelengths with super-resolution depth mapping,” Proc. SPIE 7298, 729833 (2009).
[Crossref]

Barnard, K. J.

R. G. Driggers, R. H. Vollmerhausen, N. Devitt, C. Halfort, and K. J. Barnard, “Impact of speckle on laser range-gated shortwave infrared imaging system target identification performance,” Opt. Eng. 42(3), 738–746 (2003).
[Crossref]

Bennink, R. S.

R. S. Bennink, S. J. Bentley, and R. W. Boyd, “‘Two-Photon’ coincidence imaging with a classical source,” Phys. Rev. Lett. 89(11), 113601 (2002).
[Crossref] [PubMed]

Bentley, S. J.

R. S. Bennink, S. J. Bentley, and R. W. Boyd, “‘Two-Photon’ coincidence imaging with a classical source,” Phys. Rev. Lett. 89(11), 113601 (2002).
[Crossref] [PubMed]

Bertolotti, J.

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491(7423), 232–234 (2012).
[Crossref] [PubMed]

Blum, C.

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491(7423), 232–234 (2012).
[Crossref] [PubMed]

Bonnier, D.

G. R. Fournier, D. Bonnier, J. L. Forand, and P. W. Pace, “Range-gated underwater laser imaging system,” Opt. Eng. 32(9), 2185–2190 (1993).
[Crossref]

Boyd, R. W.

R. S. Bennink, S. J. Bentley, and R. W. Boyd, “‘Two-Photon’ coincidence imaging with a classical source,” Phys. Rev. Lett. 89(11), 113601 (2002).
[Crossref] [PubMed]

Bromberg, Y.

O. Katz, E. Small, Y. Bromberg, and Y. Silberberg, “Focusing and compression of ultrashort pulses through scattering media,” Nat. Photonics 5(6), 372–377 (2011).
[Crossref]

Burris, H. R.

Busck, J.

J. Busck, “Underwater 3-D optical imaging with a gated viewing laser radar,” Opt. Eng. 44(11), 116001 (2005).
[Crossref]

Chambolle, A.

A. Chambolle, “An algorithm for total variation minimization and applications,” J. Math. Imaging Vis. 20(1/2), 89–97 (2004).
[Crossref]

Chan, T. F.

T. F. Chan and S. Esedoglu, “Aspects of total variation regularized L1 function approximation,” SIAM J. Appl. Math. 65(5), 1817–1837 (2005).
[Crossref]

Cheng, Q.

K. Wu, Q. Cheng, Y. Shi, H. Wang, and G. P. Wang, “Hiding scattering layers for noninvasive imaging of hidden objects,” Sci. Rep. 5, 8375 (2015).
[Crossref] [PubMed]

Choi, W.

S. Kang, S. Jeong, W. Choi, H. Ko, T. D. Yang, J. H. Joo, J. S. Lee, Y. S. Lim, Q. H. Park, and W. Choi, “Imaging deep within a scattering medium using collective accumulation of single-scattered waves,” Nat. Photonics 9, 253–258 (2015).

S. Kang, S. Jeong, W. Choi, H. Ko, T. D. Yang, J. H. Joo, J. S. Lee, Y. S. Lim, Q. H. Park, and W. Choi, “Imaging deep within a scattering medium using collective accumulation of single-scattered waves,” Nat. Photonics 9, 253–258 (2015).

Christnacher, F.

M. Laurenzis, F. Christnacher, N. Metzger, E. Bacher, and I. Zielenski, “3d range-gated imaging at infrared wavelengths with super-resolution depth mapping,” Proc. SPIE 7298, 729833 (2009).
[Crossref]

M. Laurenzis, F. Christnacher, and D. Monnin, “Long-range three-dimensional active imaging with superresolution depth mapping,” Opt. Lett. 32(21), 3146–3148 (2007).
[Crossref] [PubMed]

Devitt, N.

R. G. Driggers, R. H. Vollmerhausen, N. Devitt, C. Halfort, and K. J. Barnard, “Impact of speckle on laser range-gated shortwave infrared imaging system target identification performance,” Opt. Eng. 42(3), 738–746 (2003).
[Crossref]

Driggers, R. G.

R. G. Driggers, R. H. Vollmerhausen, N. Devitt, C. Halfort, and K. J. Barnard, “Impact of speckle on laser range-gated shortwave infrared imaging system target identification performance,” Opt. Eng. 42(3), 738–746 (2003).
[Crossref]

Esedoglu, S.

T. F. Chan and S. Esedoglu, “Aspects of total variation regularized L1 function approximation,” SIAM J. Appl. Math. 65(5), 1817–1837 (2005).
[Crossref]

Espinola, R. L.

Fatemi, E.

L. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica D 60(1-4), 259–268 (1992).
[Crossref]

Fernald, F. G.

Fink, M.

O. Katz, P. Heidmann, M. Fink, and S. Gigan, “Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations,” Nat. Photonics 8(10), 784–790 (2014).
[Crossref]

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photonics 6(5), 283–292 (2006).
[Crossref]

Forand, J. L.

G. R. Fournier, D. Bonnier, J. L. Forand, and P. W. Pace, “Range-gated underwater laser imaging system,” Opt. Eng. 32(9), 2185–2190 (1993).
[Crossref]

Fournier, G. R.

G. R. Fournier, D. Bonnier, J. L. Forand, and P. W. Pace, “Range-gated underwater laser imaging system,” Opt. Eng. 32(9), 2185–2190 (1993).
[Crossref]

Freund, I.

I. Freund, “Looking through walls and around corners,” Physica A 168(1), 49–65 (1990).
[Crossref]

Gibson, A. P.

A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50(4), R1–R43 (2005).
[Crossref] [PubMed]

Gigan, S.

O. Katz, P. Heidmann, M. Fink, and S. Gigan, “Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations,” Nat. Photonics 8(10), 784–790 (2014).
[Crossref]

Gillespie, L. F.

Halford, C. E.

Halfort, C.

R. G. Driggers, R. H. Vollmerhausen, N. Devitt, C. Halfort, and K. J. Barnard, “Impact of speckle on laser range-gated shortwave infrared imaging system target identification performance,” Opt. Eng. 42(3), 738–746 (2003).
[Crossref]

He, D. M.

C. S. Tan, G. Seet, A. Sluzek, and D. M. He, “A novel application of range-gated underwater laser imaging system (ULIS) in near-target turbid medium,” Opt. Lasers Eng. 43(9), 995–1009 (2005).
[Crossref]

Hebden, J. C.

A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50(4), R1–R43 (2005).
[Crossref] [PubMed]

Heidmann, P.

O. Katz, P. Heidmann, M. Fink, and S. Gigan, “Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations,” Nat. Photonics 8(10), 784–790 (2014).
[Crossref]

Hu, W.

Jacobs, E. L.

Jeong, S.

S. Kang, S. Jeong, W. Choi, H. Ko, T. D. Yang, J. H. Joo, J. S. Lee, Y. S. Lim, Q. H. Park, and W. Choi, “Imaging deep within a scattering medium using collective accumulation of single-scattered waves,” Nat. Photonics 9, 253–258 (2015).

Jin, Z. M.

Z. M. Jin and X. P. Yang, “A variational model to remove the multiplicative noise in ultrasound images,” J. Math. Imaging Vis. 39(1), 62–74 (2011).
[Crossref]

Joo, J. H.

S. Kang, S. Jeong, W. Choi, H. Ko, T. D. Yang, J. H. Joo, J. S. Lee, Y. S. Lim, Q. H. Park, and W. Choi, “Imaging deep within a scattering medium using collective accumulation of single-scattered waves,” Nat. Photonics 9, 253–258 (2015).

Kang, S.

S. Kang, S. Jeong, W. Choi, H. Ko, T. D. Yang, J. H. Joo, J. S. Lee, Y. S. Lim, Q. H. Park, and W. Choi, “Imaging deep within a scattering medium using collective accumulation of single-scattered waves,” Nat. Photonics 9, 253–258 (2015).

Katz, O.

O. Katz, P. Heidmann, M. Fink, and S. Gigan, “Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations,” Nat. Photonics 8(10), 784–790 (2014).
[Crossref]

O. Katz, E. Small, Y. Bromberg, and Y. Silberberg, “Focusing and compression of ultrashort pulses through scattering media,” Nat. Photonics 5(6), 372–377 (2011).
[Crossref]

Klyshko, D. N.

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, “Observation of two-photon “ghost” interference and diffraction,” Phys. Rev. Lett. 74(18), 3600–3603 (1995).
[Crossref] [PubMed]

Ko, H.

S. Kang, S. Jeong, W. Choi, H. Ko, T. D. Yang, J. H. Joo, J. S. Lee, Y. S. Lim, Q. H. Park, and W. Choi, “Imaging deep within a scattering medium using collective accumulation of single-scattered waves,” Nat. Photonics 9, 253–258 (2015).

Lagendijk, A.

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491(7423), 232–234 (2012).
[Crossref] [PubMed]

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photonics 6(5), 283–292 (2006).
[Crossref]

Lainiotis, D. G.

D. G. Lainiotis, P. Papaparaskeva, and K. Plataniotis, “Nonlinear filtering for LIDAR signal processing,” Math. Probl. Eng. 2(5), 367–392 (1996).
[Crossref]

Laurenzis, M.

M. Laurenzis, F. Christnacher, N. Metzger, E. Bacher, and I. Zielenski, “3d range-gated imaging at infrared wavelengths with super-resolution depth mapping,” Proc. SPIE 7298, 729833 (2009).
[Crossref]

M. Laurenzis, F. Christnacher, and D. Monnin, “Long-range three-dimensional active imaging with superresolution depth mapping,” Opt. Lett. 32(21), 3146–3148 (2007).
[Crossref] [PubMed]

Lee, J. S.

S. Kang, S. Jeong, W. Choi, H. Ko, T. D. Yang, J. H. Joo, J. S. Lee, Y. S. Lim, Q. H. Park, and W. Choi, “Imaging deep within a scattering medium using collective accumulation of single-scattered waves,” Nat. Photonics 9, 253–258 (2015).

Lerosey, G.

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photonics 6(5), 283–292 (2006).
[Crossref]

Li, X. J.

Lim, Y. S.

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C. Tomasi and R. Manduchi, “Bilateral filtering for gray and color images,” in Proceedings of IEEE International Conference on Computer Vision (IEEE, 1998), pp. 839–846.
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M. Martin-Fernandez, E. Munoz-Moreno, and C. Alberola-Lopez, “A speckle removal filter based on anisotropic Wiener filtering and the Rice distribution,” Proc. IEEE Ultrason. Symp. 7(3), 1694–1697 (2006).
[Crossref]

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McManamon, P. F.

P. F. McManamon, “Review of ladar: a historic, yet emerging, sensor technology with rich phenomenology,” Opt. Eng. 51(6), 060901 (2012).
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Metzger, N.

M. Laurenzis, F. Christnacher, N. Metzger, E. Bacher, and I. Zielenski, “3d range-gated imaging at infrared wavelengths with super-resolution depth mapping,” Proc. SPIE 7298, 729833 (2009).
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Monnin, D.

Mosk, A. P.

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491(7423), 232–234 (2012).
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A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photonics 6(5), 283–292 (2006).
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Munoz-Moreno, E.

M. Martin-Fernandez, E. Munoz-Moreno, and C. Alberola-Lopez, “A speckle removal filter based on anisotropic Wiener filtering and the Rice distribution,” Proc. IEEE Ultrason. Symp. 7(3), 1694–1697 (2006).
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G. R. Fournier, D. Bonnier, J. L. Forand, and P. W. Pace, “Range-gated underwater laser imaging system,” Opt. Eng. 32(9), 2185–2190 (1993).
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Papaparaskeva, P.

D. G. Lainiotis, P. Papaparaskeva, and K. Plataniotis, “Nonlinear filtering for LIDAR signal processing,” Math. Probl. Eng. 2(5), 367–392 (1996).
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S. Kang, S. Jeong, W. Choi, H. Ko, T. D. Yang, J. H. Joo, J. S. Lee, Y. S. Lim, Q. H. Park, and W. Choi, “Imaging deep within a scattering medium using collective accumulation of single-scattered waves,” Nat. Photonics 9, 253–258 (2015).

Plataniotis, K.

D. G. Lainiotis, P. Papaparaskeva, and K. Plataniotis, “Nonlinear filtering for LIDAR signal processing,” Math. Probl. Eng. 2(5), 367–392 (1996).
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L. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica D 60(1-4), 259–268 (1992).
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C. S. Tan, G. Seet, A. Sluzek, and D. M. He, “A novel application of range-gated underwater laser imaging system (ULIS) in near-target turbid medium,” Opt. Lasers Eng. 43(9), 995–1009 (2005).
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D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, “Observation of two-photon “ghost” interference and diffraction,” Phys. Rev. Lett. 74(18), 3600–3603 (1995).
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D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, “Observation of two-photon “ghost” interference and diffraction,” Phys. Rev. Lett. 74(18), 3600–3603 (1995).
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C. S. Tan, G. Seet, A. Sluzek, and D. M. He, “A novel application of range-gated underwater laser imaging system (ULIS) in near-target turbid medium,” Opt. Lasers Eng. 43(9), 995–1009 (2005).
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O. Katz, E. Small, Y. Bromberg, and Y. Silberberg, “Focusing and compression of ultrashort pulses through scattering media,” Nat. Photonics 5(6), 372–377 (2011).
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Strekalov, D. V.

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, “Observation of two-photon “ghost” interference and diffraction,” Phys. Rev. Lett. 74(18), 3600–3603 (1995).
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C. S. Tan, G. Seet, A. Sluzek, and D. M. He, “A novel application of range-gated underwater laser imaging system (ULIS) in near-target turbid medium,” Opt. Lasers Eng. 43(9), 995–1009 (2005).
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J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491(7423), 232–234 (2012).
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Vollmerhausen, R. H.

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K. Wu, Q. Cheng, Y. Shi, H. Wang, and G. P. Wang, “Hiding scattering layers for noninvasive imaging of hidden objects,” Sci. Rep. 5, 8375 (2015).
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K. Wu, Q. Cheng, Y. Shi, H. Wang, and G. P. Wang, “Hiding scattering layers for noninvasive imaging of hidden objects,” Sci. Rep. 5, 8375 (2015).
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Wang, P.

Wu, K.

K. Wu, Q. Cheng, Y. Shi, H. Wang, and G. P. Wang, “Hiding scattering layers for noninvasive imaging of hidden objects,” Sci. Rep. 5, 8375 (2015).
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Yang, J. F.

J. F. Yang, Y. Zhang, and W. T. Yin, “An efficient TVL1 algorithm for deblurring multichannel images corrupted by impulsive noise,” SIAM J. Sci. Comput. 31(4), 2842–2865 (2009).
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S. Kang, S. Jeong, W. Choi, H. Ko, T. D. Yang, J. H. Joo, J. S. Lee, Y. S. Lim, Q. H. Park, and W. Choi, “Imaging deep within a scattering medium using collective accumulation of single-scattered waves,” Nat. Photonics 9, 253–258 (2015).

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Yin, W. T.

J. F. Yang, Y. Zhang, and W. T. Yin, “An efficient TVL1 algorithm for deblurring multichannel images corrupted by impulsive noise,” SIAM J. Sci. Comput. 31(4), 2842–2865 (2009).
[Crossref]

Zhang, Y.

J. F. Yang, Y. Zhang, and W. T. Yin, “An efficient TVL1 algorithm for deblurring multichannel images corrupted by impulsive noise,” SIAM J. Sci. Comput. 31(4), 2842–2865 (2009).
[Crossref]

Zielenski, I.

M. Laurenzis, F. Christnacher, N. Metzger, E. Bacher, and I. Zielenski, “3d range-gated imaging at infrared wavelengths with super-resolution depth mapping,” Proc. SPIE 7298, 729833 (2009).
[Crossref]

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J. Math. Imaging Vis. (2)

A. Chambolle, “An algorithm for total variation minimization and applications,” J. Math. Imaging Vis. 20(1/2), 89–97 (2004).
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Z. M. Jin and X. P. Yang, “A variational model to remove the multiplicative noise in ultrasound images,” J. Math. Imaging Vis. 39(1), 62–74 (2011).
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Math. Probl. Eng. (1)

D. G. Lainiotis, P. Papaparaskeva, and K. Plataniotis, “Nonlinear filtering for LIDAR signal processing,” Math. Probl. Eng. 2(5), 367–392 (1996).
[Crossref]

Nat. Photonics (4)

O. Katz, P. Heidmann, M. Fink, and S. Gigan, “Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations,” Nat. Photonics 8(10), 784–790 (2014).
[Crossref]

S. Kang, S. Jeong, W. Choi, H. Ko, T. D. Yang, J. H. Joo, J. S. Lee, Y. S. Lim, Q. H. Park, and W. Choi, “Imaging deep within a scattering medium using collective accumulation of single-scattered waves,” Nat. Photonics 9, 253–258 (2015).

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photonics 6(5), 283–292 (2006).
[Crossref]

O. Katz, E. Small, Y. Bromberg, and Y. Silberberg, “Focusing and compression of ultrashort pulses through scattering media,” Nat. Photonics 5(6), 372–377 (2011).
[Crossref]

Nature (1)

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491(7423), 232–234 (2012).
[Crossref] [PubMed]

Opt. Eng. (5)

G. R. Fournier, D. Bonnier, J. L. Forand, and P. W. Pace, “Range-gated underwater laser imaging system,” Opt. Eng. 32(9), 2185–2190 (1993).
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J. Busck, “Underwater 3-D optical imaging with a gated viewing laser radar,” Opt. Eng. 44(11), 116001 (2005).
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P. Andersson, “Long-range three dimensional imaging using range-gated laser radar images,” Opt. Eng. 45(3), 034301 (2006).
[Crossref]

P. F. McManamon, “Review of ladar: a historic, yet emerging, sensor technology with rich phenomenology,” Opt. Eng. 51(6), 060901 (2012).
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Opt. Lasers Eng. (1)

C. S. Tan, G. Seet, A. Sluzek, and D. M. He, “A novel application of range-gated underwater laser imaging system (ULIS) in near-target turbid medium,” Opt. Lasers Eng. 43(9), 995–1009 (2005).
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D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, “Observation of two-photon “ghost” interference and diffraction,” Phys. Rev. Lett. 74(18), 3600–3603 (1995).
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Proc. IEEE Ultrason. Symp. (1)

M. Martin-Fernandez, E. Munoz-Moreno, and C. Alberola-Lopez, “A speckle removal filter based on anisotropic Wiener filtering and the Rice distribution,” Proc. IEEE Ultrason. Symp. 7(3), 1694–1697 (2006).
[Crossref]

Proc. SPIE (1)

M. Laurenzis, F. Christnacher, N. Metzger, E. Bacher, and I. Zielenski, “3d range-gated imaging at infrared wavelengths with super-resolution depth mapping,” Proc. SPIE 7298, 729833 (2009).
[Crossref]

Sci. Rep. (1)

K. Wu, Q. Cheng, Y. Shi, H. Wang, and G. P. Wang, “Hiding scattering layers for noninvasive imaging of hidden objects,” Sci. Rep. 5, 8375 (2015).
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Supplementary Material (1)

NameDescription
» Visualization 1: MP4 (3090 KB)      Schematic of the method

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Figures (6)

Fig. 1
Fig. 1 Schematic diagram of the longitudinal laser tomography experimental set up. The gate delay satisfies τ n =n τ 1 , where τ 1 is the gate step and n=1,2,3 . For clarity, yellow and blue are used to indicate the backscattering pulse and the target reflecting pulse, respectively, although their wavelengths are the same as the incident pulse. See Visualization 1 for details.
Fig. 2
Fig. 2 Coordinate system of longitudinal laser tomography set up.
Fig. 3
Fig. 3 Flowchart of the restoration method.
Fig. 4
Fig. 4 Recovery process of the first experimental image group. K S is the calibration parameter extracted from the target image and the medium image, while V ˜ represents the estimated degradation matrix.
Fig. 5
Fig. 5 Recovery process of the second experimental image group.
Fig. 6
Fig. 6 Recovery results for the exponential factor K S with various relative errors.

Equations (10)

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u 0 =Vu+n.
I tar (i,j)= E t D 2 d pix 2 ρ t ( X t , Y t , Z t ) θ 2 f 2 Z t 2 exp[2 0 Z t K e (x,y,z)dz ].
I ideal (i,j)= E t D 2 d pix 2 ρ t ( X t , Y t , Z t ) θ 2 f 2 Z t 2 .
V(i,j)= I tar (i,j) I ideal (i,j) =exp[2 0 Z t K e (x,y,z)dz ].
V(i,j)=exp[2S ρ S (x,y)].
V(i,j)=exp[2S Z S 2 C E S I S (i,j)]exp[2 K S I S (i,j)].
K S = ln( I tar / I ideal ) 2 I S .
K S = ln( W ¯ 1 / W 0 ¯ ) 2 W S ¯ .
V (i,j)=exp[2 Z 2 S Z S 2 E S 2 E 2 S K S I S (i,j)],
min u Σ [ | u |+γ| u 0 v ˜ u| ] ,

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