Abstract

We propose an original concept of compressive sensing (CS) polarimetric imaging based on a digital micromirror (DMD) array and two single-pixel detectors, without using any polarizer. The polarimetric sensitivity of the proposed setup is due to the tiny difference in Fresnel’s coefficients of reflecting mirrors, which is exploited here to form an original reconstruction problem including a CS problem and a source-separation task. We show that a two-step approach, tackling each problem successively, is outperformed by a dedicated combined reconstruction method, which is demonstrated in this paper and preferably implemented through a reweighted fast iterative shrinkage-thresholding algorithm. The combined reconstruction approach is then further improved by including physical constraints specific to the polarimetric imaging context considered, which are implemented in an original constrained generalized forward–backward algorithm. Numerical simulations demonstrate the efficiency of the two-pixel CS polarimetric imaging setup at retrieving polarimetric contrast data with significant compression rate and good reconstruction quality. The influence of experimental imperfections of the DMD is also analyzed through numerical simulations, and 2D polarimetric imaging reconstruction results are finally presented.

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

Full Article  |  PDF Article
OSA Recommended Articles
Active illumination single-pixel camera based on compressive sensing

Filipe Magalhães, Francisco M. Araújo, Miguel V. Correia, Mehrdad Abolbashari, and Faramarz Farahi
Appl. Opt. 50(4) 405-414 (2011)

Recent results of medium wave infrared compressive sensing

A. Mahalanobis, R. Shilling, R. Murphy, and R. Muise
Appl. Opt. 53(34) 8060-8070 (2014)

Compressive sensing spectroscopy with a single pixel camera

David J. Starling, Ian Storer, and Gregory A. Howland
Appl. Opt. 55(19) 5198-5202 (2016)

References

  • View by:
  • |
  • |
  • |

  1. W. Groner, J. W. Winkelman, A. G. Harris, C. Ince, G. J. Bouma, K. Messmer, and R. G. Nadeau, “Orthogonal polarization spectral imaging: a new method for study of the microcirculation,” Nat. Med. 5, 1209–1212 (1999).
    [Crossref]
  2. F. Boulvert, B. Boulbry, G. Le Brun, B. Le Jeune, S. Rivet, and J. Cariou, “Analysis of the depolarizing properties of irradiated pig skin,” J. Opt. A 7, 21–28 (2005).
    [Crossref]
  3. M. Anastasiadou, A. D. Martino, D. Clement, F. Liège, B. Laude-Boulesteix, N. Quang, J. Dreyfuss, B. Huynh, A. Nazac, L. Schwartz, and H. Cohen, “Polarimetric imaging for the diagnosis of cervical cancer,” Phys. Stat. Solidi C 5, 1423–1426 (2008).
    [Crossref]
  4. S. Breugnot and P. Clémenceau, “Modeling and performances of a polarization active imager at lambda = 806  nm,” Proc. SPIE 3707, 449–460 (1999).
    [Crossref]
  5. M. Alouini, F. Goudail, A. Grisard, J. Bourderionnet, D. Dolfi, A. Bénière, I. Baarstad, T. Løke, P. Kaspersen, X. Normandin, and G. Berginc, “Near-infrared active polarimetric and multispectral laboratory demonstrator for target detection,” Appl. Opt. 48, 1610–1618 (2009).
    [Crossref]
  6. J. Fade, S. Panigrahi, A. Carré, L. Frein, C. Hamel, F. Bretenaker, H. Ramachandran, and M. Alouini, “Long-range polarimetric imaging through fog,” Appl. Opt. 53, 3854–3865 (2014).
    [Crossref]
  7. F. Snik, J. Craven-Jones, M. Escuti, S. Fineschi, D. Harrington, A. De Martino, D. Mawet, J. Riedi, and J. S. Tyo, “An overview of polarimetric sensing techniques and technology with applications to different research fields,” Proc. SPIE 9099, 90990B (2014).
    [Crossref]
  8. C. Brosseau, Fundamentals of Polarized Light—A Statistical Optics Approach (Wiley, 1998).
  9. N. Gupta, R. Dahmani, and S. Choy, “Acousto-optic tunable filter based visible- to near-infrared spectropolarimetric imager,” Opt. Eng. 41, 1033–1038 (2002).
    [Crossref]
  10. G. Anna, H. Sauer, F. Goudail, and D. Dolfi, “Fully tunable active polarization imager for contrast enhancement and partial polarimetry,” Appl. Opt. 51, 5302–5309 (2012).
    [Crossref]
  11. A. Bénière, M. Alouini, F. Goudail, and D. Dolfi, “Design and experimental validation of a snapshot polarization contrast imager,” Appl. Opt. 48, 5764–5773 (2009).
    [Crossref]
  12. F. Goudail and P. Réfrégier, Statistical Image Processing Techniques for Noisy Images: an Application Oriented Approach (Kluwer, 2004).
  13. R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
    [Crossref]
  14. W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93, 121105 (2008).
    [Crossref]
  15. A. Wagadarikar, R. John, R. Willett, and D. Brady, “Single disperser design for coded aperture snapshot spectral imaging,” Appl. Opt. 47, B44–B51 (2008).
    [Crossref]
  16. A. Asensio Ramos and A. López Ariste, “Compressive sensing for spectroscopy and polarimetry,” arXiv:0909.4439 (2009).
  17. V. Studer, J. Bobin, M. Chahid, H. S. Mousavi, E. Candes, and M. Dahan, “Compressive fluorescence microscopy for biological and hyperspectral imaging,” Proc. Natl. Acad. Sci. U.S.A. 109, E1679–E1687 (2012).
    [Crossref]
  18. Y. August and A. Stern, “Compressive sensing spectrometry based on liquid crystal devices,” Opt. Lett. 38, 4996–4999 (2013).
    [Crossref]
  19. A. Liutkus, D. Martina, S. Popoff, G. Chardon, O. Katz, G. Lerosey, S. Gigan, L. Daudet, and I. Carron, “Imaging with nature: a universal analog compressive imager using a multiply scattering medium,” arXiv:1309.0425 (2013).
  20. V. Durán, P. Clemente, M. Fernández-Alonso, E. Tajahuerce, and J. Lancis, “Single-pixel polarimetric imaging,” Opt. Lett. 37, 824–826 (2012).
    [Crossref]
  21. F. Soldevila, E. Irles, V. Durán, P. Clemente, M. Fernández-Alonso, E. Tajahuerce, and J. Lancis, “Single-pixel polarimetric imaging spectrometer by compressive sensing,” Appl. Phys. B 113, 551–558 (2013).
    [Crossref]
  22. S. S. Welsh, M. P. Edgar, R. Bowman, B. Sun, and M. J. Padgett, “Near video-rate linear stokes imaging with single-pixel detectors,” J. Opt. 17, 025705 (2015).
    [Crossref]
  23. C. Fu, H. Arguello, B. M. Sadler, and G. R. Arce, “Compressive spectral polarization imaging by a pixelized polarizer and colored patterned detector,” J. Opt. Soc. Am. A 32, 2178–2188 (2015).
    [Crossref]
  24. F. Soldevila, P. Clemente, E. Tajahuerce, N. Uribe-Patarroyo, P. Andrés, and J. Lancis, “Computational imaging with a balanced detector,” Sci. Rep. 6, 29181 (2016).
    [Crossref]
  25. J. Liang, C. Ma, L. Zhu, Y. Chen, L. Gao, and L. V. Wang, “Single-shot real-time video recording of a photonic mach cone induced by a scattered light pulse,” Sci. Adv. 3, e1601814 (2017).
    [Crossref]
  26. N. A. Riza, J. P. La Torre, and M. J. Amin, “CAOS–CMOS camera,” Opt. Express 24, 13444–13458 (2016).
    [Crossref]
  27. Y. C. Eldar and G. Kutyniok, Compressed Sensing: Theory and Applications (Cambridge University, 2012).
  28. Texas Instruments, “DLP6500-0.65-1080p datasheet,” Rev. B (2016).
  29. I. N. Flamarique, C. W. Hawryshyn, and F. I. Hárosi, “Double-cone internal reflection as a basis for polarization detection in fish,” J. Opt. Soc. Am. A 15, 349–358 (1998).
    [Crossref]
  30. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999), pp. 752–754.
  31. A. D. Rakić, A. B. Djurišić, J. M. Elazar, and M. L. Majewski, “Optical properties of metallic films for vertical-cavity optoelectronic devices,” Appl. Opt. 37, 5271–5283 (1998).
    [Crossref]
  32. E. Candès and M. Wakin, “People hearing without listening: an introduction to compressive sampling,” IEEE Signal Process. Mag. 25(2), 21–30 (2008).
    [Crossref]
  33. E. Candès, “Compressive sampling,” in International Congress of Mathematics, Madrid, Spain (2006).
  34. H. Raguet, J. Fadili, and G. Peyre, “A generalized forward-backward splitting,” SIAM J. Imaging Sci. 6, 1199–1226 (2013).
    [Crossref]
  35. J.-L. Starck, J. Fadili, and F. Murtagh, “The undecimated wavelet decomposition and its reconstruction,” IEEE Trans. Image Process. 16, 297–309 (2007).
    [Crossref]
  36. E. J. Candes, M. B. Wakin, and S. P. Boyd, “Enhancing sparsity by reweighted L1 minimization,” J. Fourier Anal. Appl. 14, 877–905 (2008).
    [Crossref]
  37. N. Parikh and S. Boyd, “Proximal algorithms,” Found. Trends Optim. 1, 123–231 (2014).
  38. P. L. Combettes and V. R. Wajs, “Signal recovery by proximal forward-backward splitting,” Multiscale Model. Simul. 4, 1168–1200 (2005).
    [Crossref]
  39. A. Beck and M. Teboulle, “Fast iterative shrinkage-thresholding algorithm for linear inverse problems,” SIAM J. Imaging Sci. 2, 183–202 (2009).
    [Crossref]

2017 (1)

J. Liang, C. Ma, L. Zhu, Y. Chen, L. Gao, and L. V. Wang, “Single-shot real-time video recording of a photonic mach cone induced by a scattered light pulse,” Sci. Adv. 3, e1601814 (2017).
[Crossref]

2016 (2)

F. Soldevila, P. Clemente, E. Tajahuerce, N. Uribe-Patarroyo, P. Andrés, and J. Lancis, “Computational imaging with a balanced detector,” Sci. Rep. 6, 29181 (2016).
[Crossref]

N. A. Riza, J. P. La Torre, and M. J. Amin, “CAOS–CMOS camera,” Opt. Express 24, 13444–13458 (2016).
[Crossref]

2015 (2)

C. Fu, H. Arguello, B. M. Sadler, and G. R. Arce, “Compressive spectral polarization imaging by a pixelized polarizer and colored patterned detector,” J. Opt. Soc. Am. A 32, 2178–2188 (2015).
[Crossref]

S. S. Welsh, M. P. Edgar, R. Bowman, B. Sun, and M. J. Padgett, “Near video-rate linear stokes imaging with single-pixel detectors,” J. Opt. 17, 025705 (2015).
[Crossref]

2014 (3)

F. Snik, J. Craven-Jones, M. Escuti, S. Fineschi, D. Harrington, A. De Martino, D. Mawet, J. Riedi, and J. S. Tyo, “An overview of polarimetric sensing techniques and technology with applications to different research fields,” Proc. SPIE 9099, 90990B (2014).
[Crossref]

J. Fade, S. Panigrahi, A. Carré, L. Frein, C. Hamel, F. Bretenaker, H. Ramachandran, and M. Alouini, “Long-range polarimetric imaging through fog,” Appl. Opt. 53, 3854–3865 (2014).
[Crossref]

N. Parikh and S. Boyd, “Proximal algorithms,” Found. Trends Optim. 1, 123–231 (2014).

2013 (3)

Y. August and A. Stern, “Compressive sensing spectrometry based on liquid crystal devices,” Opt. Lett. 38, 4996–4999 (2013).
[Crossref]

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

H. Raguet, J. Fadili, and G. Peyre, “A generalized forward-backward splitting,” SIAM J. Imaging Sci. 6, 1199–1226 (2013).
[Crossref]

2012 (3)

2009 (3)

2008 (6)

E. J. Candes, M. B. Wakin, and S. P. Boyd, “Enhancing sparsity by reweighted L1 minimization,” J. Fourier Anal. Appl. 14, 877–905 (2008).
[Crossref]

A. Wagadarikar, R. John, R. Willett, and D. Brady, “Single disperser design for coded aperture snapshot spectral imaging,” Appl. Opt. 47, B44–B51 (2008).
[Crossref]

E. Candès and M. Wakin, “People hearing without listening: an introduction to compressive sampling,” IEEE Signal Process. Mag. 25(2), 21–30 (2008).
[Crossref]

R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
[Crossref]

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93, 121105 (2008).
[Crossref]

M. Anastasiadou, A. D. Martino, D. Clement, F. Liège, B. Laude-Boulesteix, N. Quang, J. Dreyfuss, B. Huynh, A. Nazac, L. Schwartz, and H. Cohen, “Polarimetric imaging for the diagnosis of cervical cancer,” Phys. Stat. Solidi C 5, 1423–1426 (2008).
[Crossref]

2007 (1)

J.-L. Starck, J. Fadili, and F. Murtagh, “The undecimated wavelet decomposition and its reconstruction,” IEEE Trans. Image Process. 16, 297–309 (2007).
[Crossref]

2005 (2)

F. Boulvert, B. Boulbry, G. Le Brun, B. Le Jeune, S. Rivet, and J. Cariou, “Analysis of the depolarizing properties of irradiated pig skin,” J. Opt. A 7, 21–28 (2005).
[Crossref]

P. L. Combettes and V. R. Wajs, “Signal recovery by proximal forward-backward splitting,” Multiscale Model. Simul. 4, 1168–1200 (2005).
[Crossref]

2002 (1)

N. Gupta, R. Dahmani, and S. Choy, “Acousto-optic tunable filter based visible- to near-infrared spectropolarimetric imager,” Opt. Eng. 41, 1033–1038 (2002).
[Crossref]

1999 (2)

W. Groner, J. W. Winkelman, A. G. Harris, C. Ince, G. J. Bouma, K. Messmer, and R. G. Nadeau, “Orthogonal polarization spectral imaging: a new method for study of the microcirculation,” Nat. Med. 5, 1209–1212 (1999).
[Crossref]

S. Breugnot and P. Clémenceau, “Modeling and performances of a polarization active imager at lambda = 806  nm,” Proc. SPIE 3707, 449–460 (1999).
[Crossref]

1998 (2)

Alouini, M.

Amin, M. J.

Anastasiadou, M.

M. Anastasiadou, A. D. Martino, D. Clement, F. Liège, B. Laude-Boulesteix, N. Quang, J. Dreyfuss, B. Huynh, A. Nazac, L. Schwartz, and H. Cohen, “Polarimetric imaging for the diagnosis of cervical cancer,” Phys. Stat. Solidi C 5, 1423–1426 (2008).
[Crossref]

Andrés, P.

F. Soldevila, P. Clemente, E. Tajahuerce, N. Uribe-Patarroyo, P. Andrés, and J. Lancis, “Computational imaging with a balanced detector,” Sci. Rep. 6, 29181 (2016).
[Crossref]

Anna, G.

Arce, G. R.

Arguello, H.

Asensio Ramos, A.

A. Asensio Ramos and A. López Ariste, “Compressive sensing for spectroscopy and polarimetry,” arXiv:0909.4439 (2009).

August, Y.

Baarstad, I.

Baraniuk, R. G.

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93, 121105 (2008).
[Crossref]

R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
[Crossref]

Beck, A.

A. Beck and M. Teboulle, “Fast iterative shrinkage-thresholding algorithm for linear inverse problems,” SIAM J. Imaging Sci. 2, 183–202 (2009).
[Crossref]

Bénière, A.

Berginc, G.

Bobin, J.

V. Studer, J. Bobin, M. Chahid, H. S. Mousavi, E. Candes, and M. Dahan, “Compressive fluorescence microscopy for biological and hyperspectral imaging,” Proc. Natl. Acad. Sci. U.S.A. 109, E1679–E1687 (2012).
[Crossref]

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999), pp. 752–754.

Boulbry, B.

F. Boulvert, B. Boulbry, G. Le Brun, B. Le Jeune, S. Rivet, and J. Cariou, “Analysis of the depolarizing properties of irradiated pig skin,” J. Opt. A 7, 21–28 (2005).
[Crossref]

Boulvert, F.

F. Boulvert, B. Boulbry, G. Le Brun, B. Le Jeune, S. Rivet, and J. Cariou, “Analysis of the depolarizing properties of irradiated pig skin,” J. Opt. A 7, 21–28 (2005).
[Crossref]

Bouma, G. J.

W. Groner, J. W. Winkelman, A. G. Harris, C. Ince, G. J. Bouma, K. Messmer, and R. G. Nadeau, “Orthogonal polarization spectral imaging: a new method for study of the microcirculation,” Nat. Med. 5, 1209–1212 (1999).
[Crossref]

Bourderionnet, J.

Bowman, R.

S. S. Welsh, M. P. Edgar, R. Bowman, B. Sun, and M. J. Padgett, “Near video-rate linear stokes imaging with single-pixel detectors,” J. Opt. 17, 025705 (2015).
[Crossref]

Boyd, S.

N. Parikh and S. Boyd, “Proximal algorithms,” Found. Trends Optim. 1, 123–231 (2014).

Boyd, S. P.

E. J. Candes, M. B. Wakin, and S. P. Boyd, “Enhancing sparsity by reweighted L1 minimization,” J. Fourier Anal. Appl. 14, 877–905 (2008).
[Crossref]

Brady, D.

Bretenaker, F.

Breugnot, S.

S. Breugnot and P. Clémenceau, “Modeling and performances of a polarization active imager at lambda = 806  nm,” Proc. SPIE 3707, 449–460 (1999).
[Crossref]

Brosseau, C.

C. Brosseau, Fundamentals of Polarized Light—A Statistical Optics Approach (Wiley, 1998).

Candes, E.

V. Studer, J. Bobin, M. Chahid, H. S. Mousavi, E. Candes, and M. Dahan, “Compressive fluorescence microscopy for biological and hyperspectral imaging,” Proc. Natl. Acad. Sci. U.S.A. 109, E1679–E1687 (2012).
[Crossref]

Candes, E. J.

E. J. Candes, M. B. Wakin, and S. P. Boyd, “Enhancing sparsity by reweighted L1 minimization,” J. Fourier Anal. Appl. 14, 877–905 (2008).
[Crossref]

Candès, E.

E. Candès and M. Wakin, “People hearing without listening: an introduction to compressive sampling,” IEEE Signal Process. Mag. 25(2), 21–30 (2008).
[Crossref]

E. Candès, “Compressive sampling,” in International Congress of Mathematics, Madrid, Spain (2006).

Cariou, J.

F. Boulvert, B. Boulbry, G. Le Brun, B. Le Jeune, S. Rivet, and J. Cariou, “Analysis of the depolarizing properties of irradiated pig skin,” J. Opt. A 7, 21–28 (2005).
[Crossref]

Carré, A.

Carron, I.

A. Liutkus, D. Martina, S. Popoff, G. Chardon, O. Katz, G. Lerosey, S. Gigan, L. Daudet, and I. Carron, “Imaging with nature: a universal analog compressive imager using a multiply scattering medium,” arXiv:1309.0425 (2013).

Chahid, M.

V. Studer, J. Bobin, M. Chahid, H. S. Mousavi, E. Candes, and M. Dahan, “Compressive fluorescence microscopy for biological and hyperspectral imaging,” Proc. Natl. Acad. Sci. U.S.A. 109, E1679–E1687 (2012).
[Crossref]

Chan, W. L.

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93, 121105 (2008).
[Crossref]

Charan, K.

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93, 121105 (2008).
[Crossref]

Chardon, G.

A. Liutkus, D. Martina, S. Popoff, G. Chardon, O. Katz, G. Lerosey, S. Gigan, L. Daudet, and I. Carron, “Imaging with nature: a universal analog compressive imager using a multiply scattering medium,” arXiv:1309.0425 (2013).

Chen, Y.

J. Liang, C. Ma, L. Zhu, Y. Chen, L. Gao, and L. V. Wang, “Single-shot real-time video recording of a photonic mach cone induced by a scattered light pulse,” Sci. Adv. 3, e1601814 (2017).
[Crossref]

Choy, S.

N. Gupta, R. Dahmani, and S. Choy, “Acousto-optic tunable filter based visible- to near-infrared spectropolarimetric imager,” Opt. Eng. 41, 1033–1038 (2002).
[Crossref]

Clémenceau, P.

S. Breugnot and P. Clémenceau, “Modeling and performances of a polarization active imager at lambda = 806  nm,” Proc. SPIE 3707, 449–460 (1999).
[Crossref]

Clement, D.

M. Anastasiadou, A. D. Martino, D. Clement, F. Liège, B. Laude-Boulesteix, N. Quang, J. Dreyfuss, B. Huynh, A. Nazac, L. Schwartz, and H. Cohen, “Polarimetric imaging for the diagnosis of cervical cancer,” Phys. Stat. Solidi C 5, 1423–1426 (2008).
[Crossref]

Clemente, P.

F. Soldevila, P. Clemente, E. Tajahuerce, N. Uribe-Patarroyo, P. Andrés, and J. Lancis, “Computational imaging with a balanced detector,” Sci. Rep. 6, 29181 (2016).
[Crossref]

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

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

Cohen, H.

M. Anastasiadou, A. D. Martino, D. Clement, F. Liège, B. Laude-Boulesteix, N. Quang, J. Dreyfuss, B. Huynh, A. Nazac, L. Schwartz, and H. Cohen, “Polarimetric imaging for the diagnosis of cervical cancer,” Phys. Stat. Solidi C 5, 1423–1426 (2008).
[Crossref]

Combettes, P. L.

P. L. Combettes and V. R. Wajs, “Signal recovery by proximal forward-backward splitting,” Multiscale Model. Simul. 4, 1168–1200 (2005).
[Crossref]

Craven-Jones, J.

F. Snik, J. Craven-Jones, M. Escuti, S. Fineschi, D. Harrington, A. De Martino, D. Mawet, J. Riedi, and J. S. Tyo, “An overview of polarimetric sensing techniques and technology with applications to different research fields,” Proc. SPIE 9099, 90990B (2014).
[Crossref]

Dahan, M.

V. Studer, J. Bobin, M. Chahid, H. S. Mousavi, E. Candes, and M. Dahan, “Compressive fluorescence microscopy for biological and hyperspectral imaging,” Proc. Natl. Acad. Sci. U.S.A. 109, E1679–E1687 (2012).
[Crossref]

Dahmani, R.

N. Gupta, R. Dahmani, and S. Choy, “Acousto-optic tunable filter based visible- to near-infrared spectropolarimetric imager,” Opt. Eng. 41, 1033–1038 (2002).
[Crossref]

Daudet, L.

A. Liutkus, D. Martina, S. Popoff, G. Chardon, O. Katz, G. Lerosey, S. Gigan, L. Daudet, and I. Carron, “Imaging with nature: a universal analog compressive imager using a multiply scattering medium,” arXiv:1309.0425 (2013).

De Martino, A.

F. Snik, J. Craven-Jones, M. Escuti, S. Fineschi, D. Harrington, A. De Martino, D. Mawet, J. Riedi, and J. S. Tyo, “An overview of polarimetric sensing techniques and technology with applications to different research fields,” Proc. SPIE 9099, 90990B (2014).
[Crossref]

Djurišic, A. B.

Dolfi, D.

Dreyfuss, J.

M. Anastasiadou, A. D. Martino, D. Clement, F. Liège, B. Laude-Boulesteix, N. Quang, J. Dreyfuss, B. Huynh, A. Nazac, L. Schwartz, and H. Cohen, “Polarimetric imaging for the diagnosis of cervical cancer,” Phys. Stat. Solidi C 5, 1423–1426 (2008).
[Crossref]

Durán, V.

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

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

Edgar, M. P.

S. S. Welsh, M. P. Edgar, R. Bowman, B. Sun, and M. J. Padgett, “Near video-rate linear stokes imaging with single-pixel detectors,” J. Opt. 17, 025705 (2015).
[Crossref]

Elazar, J. M.

Eldar, Y. C.

Y. C. Eldar and G. Kutyniok, Compressed Sensing: Theory and Applications (Cambridge University, 2012).

Escuti, M.

F. Snik, J. Craven-Jones, M. Escuti, S. Fineschi, D. Harrington, A. De Martino, D. Mawet, J. Riedi, and J. S. Tyo, “An overview of polarimetric sensing techniques and technology with applications to different research fields,” Proc. SPIE 9099, 90990B (2014).
[Crossref]

Fade, J.

Fadili, J.

H. Raguet, J. Fadili, and G. Peyre, “A generalized forward-backward splitting,” SIAM J. Imaging Sci. 6, 1199–1226 (2013).
[Crossref]

J.-L. Starck, J. Fadili, and F. Murtagh, “The undecimated wavelet decomposition and its reconstruction,” IEEE Trans. Image Process. 16, 297–309 (2007).
[Crossref]

Fernández-Alonso, M.

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

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

Fineschi, S.

F. Snik, J. Craven-Jones, M. Escuti, S. Fineschi, D. Harrington, A. De Martino, D. Mawet, J. Riedi, and J. S. Tyo, “An overview of polarimetric sensing techniques and technology with applications to different research fields,” Proc. SPIE 9099, 90990B (2014).
[Crossref]

Flamarique, I. N.

Frein, L.

Fu, C.

Gao, L.

J. Liang, C. Ma, L. Zhu, Y. Chen, L. Gao, and L. V. Wang, “Single-shot real-time video recording of a photonic mach cone induced by a scattered light pulse,” Sci. Adv. 3, e1601814 (2017).
[Crossref]

Gigan, S.

A. Liutkus, D. Martina, S. Popoff, G. Chardon, O. Katz, G. Lerosey, S. Gigan, L. Daudet, and I. Carron, “Imaging with nature: a universal analog compressive imager using a multiply scattering medium,” arXiv:1309.0425 (2013).

Goudail, F.

Grisard, A.

Groner, W.

W. Groner, J. W. Winkelman, A. G. Harris, C. Ince, G. J. Bouma, K. Messmer, and R. G. Nadeau, “Orthogonal polarization spectral imaging: a new method for study of the microcirculation,” Nat. Med. 5, 1209–1212 (1999).
[Crossref]

Gupta, N.

N. Gupta, R. Dahmani, and S. Choy, “Acousto-optic tunable filter based visible- to near-infrared spectropolarimetric imager,” Opt. Eng. 41, 1033–1038 (2002).
[Crossref]

Hamel, C.

Hárosi, F. I.

Harrington, D.

F. Snik, J. Craven-Jones, M. Escuti, S. Fineschi, D. Harrington, A. De Martino, D. Mawet, J. Riedi, and J. S. Tyo, “An overview of polarimetric sensing techniques and technology with applications to different research fields,” Proc. SPIE 9099, 90990B (2014).
[Crossref]

Harris, A. G.

W. Groner, J. W. Winkelman, A. G. Harris, C. Ince, G. J. Bouma, K. Messmer, and R. G. Nadeau, “Orthogonal polarization spectral imaging: a new method for study of the microcirculation,” Nat. Med. 5, 1209–1212 (1999).
[Crossref]

Hawryshyn, C. W.

Huynh, B.

M. Anastasiadou, A. D. Martino, D. Clement, F. Liège, B. Laude-Boulesteix, N. Quang, J. Dreyfuss, B. Huynh, A. Nazac, L. Schwartz, and H. Cohen, “Polarimetric imaging for the diagnosis of cervical cancer,” Phys. Stat. Solidi C 5, 1423–1426 (2008).
[Crossref]

Ince, C.

W. Groner, J. W. Winkelman, A. G. Harris, C. Ince, G. J. Bouma, K. Messmer, and R. G. Nadeau, “Orthogonal polarization spectral imaging: a new method for study of the microcirculation,” Nat. Med. 5, 1209–1212 (1999).
[Crossref]

Irles, E.

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

John, R.

Kaspersen, P.

Katz, O.

A. Liutkus, D. Martina, S. Popoff, G. Chardon, O. Katz, G. Lerosey, S. Gigan, L. Daudet, and I. Carron, “Imaging with nature: a universal analog compressive imager using a multiply scattering medium,” arXiv:1309.0425 (2013).

Kelly, K. F.

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93, 121105 (2008).
[Crossref]

Kutyniok, G.

Y. C. Eldar and G. Kutyniok, Compressed Sensing: Theory and Applications (Cambridge University, 2012).

La Torre, J. P.

Lancis, J.

F. Soldevila, P. Clemente, E. Tajahuerce, N. Uribe-Patarroyo, P. Andrés, and J. Lancis, “Computational imaging with a balanced detector,” Sci. Rep. 6, 29181 (2016).
[Crossref]

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

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

Laude-Boulesteix, B.

M. Anastasiadou, A. D. Martino, D. Clement, F. Liège, B. Laude-Boulesteix, N. Quang, J. Dreyfuss, B. Huynh, A. Nazac, L. Schwartz, and H. Cohen, “Polarimetric imaging for the diagnosis of cervical cancer,” Phys. Stat. Solidi C 5, 1423–1426 (2008).
[Crossref]

Le Brun, G.

F. Boulvert, B. Boulbry, G. Le Brun, B. Le Jeune, S. Rivet, and J. Cariou, “Analysis of the depolarizing properties of irradiated pig skin,” J. Opt. A 7, 21–28 (2005).
[Crossref]

Le Jeune, B.

F. Boulvert, B. Boulbry, G. Le Brun, B. Le Jeune, S. Rivet, and J. Cariou, “Analysis of the depolarizing properties of irradiated pig skin,” J. Opt. A 7, 21–28 (2005).
[Crossref]

Lerosey, G.

A. Liutkus, D. Martina, S. Popoff, G. Chardon, O. Katz, G. Lerosey, S. Gigan, L. Daudet, and I. Carron, “Imaging with nature: a universal analog compressive imager using a multiply scattering medium,” arXiv:1309.0425 (2013).

Liang, J.

J. Liang, C. Ma, L. Zhu, Y. Chen, L. Gao, and L. V. Wang, “Single-shot real-time video recording of a photonic mach cone induced by a scattered light pulse,” Sci. Adv. 3, e1601814 (2017).
[Crossref]

Liège, F.

M. Anastasiadou, A. D. Martino, D. Clement, F. Liège, B. Laude-Boulesteix, N. Quang, J. Dreyfuss, B. Huynh, A. Nazac, L. Schwartz, and H. Cohen, “Polarimetric imaging for the diagnosis of cervical cancer,” Phys. Stat. Solidi C 5, 1423–1426 (2008).
[Crossref]

Liutkus, A.

A. Liutkus, D. Martina, S. Popoff, G. Chardon, O. Katz, G. Lerosey, S. Gigan, L. Daudet, and I. Carron, “Imaging with nature: a universal analog compressive imager using a multiply scattering medium,” arXiv:1309.0425 (2013).

Løke, T.

López Ariste, A.

A. Asensio Ramos and A. López Ariste, “Compressive sensing for spectroscopy and polarimetry,” arXiv:0909.4439 (2009).

Ma, C.

J. Liang, C. Ma, L. Zhu, Y. Chen, L. Gao, and L. V. Wang, “Single-shot real-time video recording of a photonic mach cone induced by a scattered light pulse,” Sci. Adv. 3, e1601814 (2017).
[Crossref]

Majewski, M. L.

Martina, D.

A. Liutkus, D. Martina, S. Popoff, G. Chardon, O. Katz, G. Lerosey, S. Gigan, L. Daudet, and I. Carron, “Imaging with nature: a universal analog compressive imager using a multiply scattering medium,” arXiv:1309.0425 (2013).

Martino, A. D.

M. Anastasiadou, A. D. Martino, D. Clement, F. Liège, B. Laude-Boulesteix, N. Quang, J. Dreyfuss, B. Huynh, A. Nazac, L. Schwartz, and H. Cohen, “Polarimetric imaging for the diagnosis of cervical cancer,” Phys. Stat. Solidi C 5, 1423–1426 (2008).
[Crossref]

Mawet, D.

F. Snik, J. Craven-Jones, M. Escuti, S. Fineschi, D. Harrington, A. De Martino, D. Mawet, J. Riedi, and J. S. Tyo, “An overview of polarimetric sensing techniques and technology with applications to different research fields,” Proc. SPIE 9099, 90990B (2014).
[Crossref]

Messmer, K.

W. Groner, J. W. Winkelman, A. G. Harris, C. Ince, G. J. Bouma, K. Messmer, and R. G. Nadeau, “Orthogonal polarization spectral imaging: a new method for study of the microcirculation,” Nat. Med. 5, 1209–1212 (1999).
[Crossref]

Mittleman, D. M.

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93, 121105 (2008).
[Crossref]

Mousavi, H. S.

V. Studer, J. Bobin, M. Chahid, H. S. Mousavi, E. Candes, and M. Dahan, “Compressive fluorescence microscopy for biological and hyperspectral imaging,” Proc. Natl. Acad. Sci. U.S.A. 109, E1679–E1687 (2012).
[Crossref]

Murtagh, F.

J.-L. Starck, J. Fadili, and F. Murtagh, “The undecimated wavelet decomposition and its reconstruction,” IEEE Trans. Image Process. 16, 297–309 (2007).
[Crossref]

Nadeau, R. G.

W. Groner, J. W. Winkelman, A. G. Harris, C. Ince, G. J. Bouma, K. Messmer, and R. G. Nadeau, “Orthogonal polarization spectral imaging: a new method for study of the microcirculation,” Nat. Med. 5, 1209–1212 (1999).
[Crossref]

Nazac, A.

M. Anastasiadou, A. D. Martino, D. Clement, F. Liège, B. Laude-Boulesteix, N. Quang, J. Dreyfuss, B. Huynh, A. Nazac, L. Schwartz, and H. Cohen, “Polarimetric imaging for the diagnosis of cervical cancer,” Phys. Stat. Solidi C 5, 1423–1426 (2008).
[Crossref]

Normandin, X.

Padgett, M. J.

S. S. Welsh, M. P. Edgar, R. Bowman, B. Sun, and M. J. Padgett, “Near video-rate linear stokes imaging with single-pixel detectors,” J. Opt. 17, 025705 (2015).
[Crossref]

Panigrahi, S.

Parikh, N.

N. Parikh and S. Boyd, “Proximal algorithms,” Found. Trends Optim. 1, 123–231 (2014).

Peyre, G.

H. Raguet, J. Fadili, and G. Peyre, “A generalized forward-backward splitting,” SIAM J. Imaging Sci. 6, 1199–1226 (2013).
[Crossref]

Popoff, S.

A. Liutkus, D. Martina, S. Popoff, G. Chardon, O. Katz, G. Lerosey, S. Gigan, L. Daudet, and I. Carron, “Imaging with nature: a universal analog compressive imager using a multiply scattering medium,” arXiv:1309.0425 (2013).

Quang, N.

M. Anastasiadou, A. D. Martino, D. Clement, F. Liège, B. Laude-Boulesteix, N. Quang, J. Dreyfuss, B. Huynh, A. Nazac, L. Schwartz, and H. Cohen, “Polarimetric imaging for the diagnosis of cervical cancer,” Phys. Stat. Solidi C 5, 1423–1426 (2008).
[Crossref]

Raguet, H.

H. Raguet, J. Fadili, and G. Peyre, “A generalized forward-backward splitting,” SIAM J. Imaging Sci. 6, 1199–1226 (2013).
[Crossref]

Rakic, A. D.

Ramachandran, H.

Réfrégier, P.

F. Goudail and P. Réfrégier, Statistical Image Processing Techniques for Noisy Images: an Application Oriented Approach (Kluwer, 2004).

Riedi, J.

F. Snik, J. Craven-Jones, M. Escuti, S. Fineschi, D. Harrington, A. De Martino, D. Mawet, J. Riedi, and J. S. Tyo, “An overview of polarimetric sensing techniques and technology with applications to different research fields,” Proc. SPIE 9099, 90990B (2014).
[Crossref]

Rivet, S.

F. Boulvert, B. Boulbry, G. Le Brun, B. Le Jeune, S. Rivet, and J. Cariou, “Analysis of the depolarizing properties of irradiated pig skin,” J. Opt. A 7, 21–28 (2005).
[Crossref]

Riza, N. A.

Sadler, B. M.

Sauer, H.

Schwartz, L.

M. Anastasiadou, A. D. Martino, D. Clement, F. Liège, B. Laude-Boulesteix, N. Quang, J. Dreyfuss, B. Huynh, A. Nazac, L. Schwartz, and H. Cohen, “Polarimetric imaging for the diagnosis of cervical cancer,” Phys. Stat. Solidi C 5, 1423–1426 (2008).
[Crossref]

Snik, F.

F. Snik, J. Craven-Jones, M. Escuti, S. Fineschi, D. Harrington, A. De Martino, D. Mawet, J. Riedi, and J. S. Tyo, “An overview of polarimetric sensing techniques and technology with applications to different research fields,” Proc. SPIE 9099, 90990B (2014).
[Crossref]

Soldevila, F.

F. Soldevila, P. Clemente, E. Tajahuerce, N. Uribe-Patarroyo, P. Andrés, and J. Lancis, “Computational imaging with a balanced detector,” Sci. Rep. 6, 29181 (2016).
[Crossref]

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

Starck, J.-L.

J.-L. Starck, J. Fadili, and F. Murtagh, “The undecimated wavelet decomposition and its reconstruction,” IEEE Trans. Image Process. 16, 297–309 (2007).
[Crossref]

Stern, A.

Studer, V.

V. Studer, J. Bobin, M. Chahid, H. S. Mousavi, E. Candes, and M. Dahan, “Compressive fluorescence microscopy for biological and hyperspectral imaging,” Proc. Natl. Acad. Sci. U.S.A. 109, E1679–E1687 (2012).
[Crossref]

Sun, B.

S. S. Welsh, M. P. Edgar, R. Bowman, B. Sun, and M. J. Padgett, “Near video-rate linear stokes imaging with single-pixel detectors,” J. Opt. 17, 025705 (2015).
[Crossref]

Tajahuerce, E.

F. Soldevila, P. Clemente, E. Tajahuerce, N. Uribe-Patarroyo, P. Andrés, and J. Lancis, “Computational imaging with a balanced detector,” Sci. Rep. 6, 29181 (2016).
[Crossref]

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

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

Takhar, D.

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93, 121105 (2008).
[Crossref]

Teboulle, M.

A. Beck and M. Teboulle, “Fast iterative shrinkage-thresholding algorithm for linear inverse problems,” SIAM J. Imaging Sci. 2, 183–202 (2009).
[Crossref]

Tyo, J. S.

F. Snik, J. Craven-Jones, M. Escuti, S. Fineschi, D. Harrington, A. De Martino, D. Mawet, J. Riedi, and J. S. Tyo, “An overview of polarimetric sensing techniques and technology with applications to different research fields,” Proc. SPIE 9099, 90990B (2014).
[Crossref]

Uribe-Patarroyo, N.

F. Soldevila, P. Clemente, E. Tajahuerce, N. Uribe-Patarroyo, P. Andrés, and J. Lancis, “Computational imaging with a balanced detector,” Sci. Rep. 6, 29181 (2016).
[Crossref]

Wagadarikar, A.

Wajs, V. R.

P. L. Combettes and V. R. Wajs, “Signal recovery by proximal forward-backward splitting,” Multiscale Model. Simul. 4, 1168–1200 (2005).
[Crossref]

Wakin, M.

E. Candès and M. Wakin, “People hearing without listening: an introduction to compressive sampling,” IEEE Signal Process. Mag. 25(2), 21–30 (2008).
[Crossref]

Wakin, M. B.

E. J. Candes, M. B. Wakin, and S. P. Boyd, “Enhancing sparsity by reweighted L1 minimization,” J. Fourier Anal. Appl. 14, 877–905 (2008).
[Crossref]

Wang, L. V.

J. Liang, C. Ma, L. Zhu, Y. Chen, L. Gao, and L. V. Wang, “Single-shot real-time video recording of a photonic mach cone induced by a scattered light pulse,” Sci. Adv. 3, e1601814 (2017).
[Crossref]

Welsh, S. S.

S. S. Welsh, M. P. Edgar, R. Bowman, B. Sun, and M. J. Padgett, “Near video-rate linear stokes imaging with single-pixel detectors,” J. Opt. 17, 025705 (2015).
[Crossref]

Willett, R.

Winkelman, J. W.

W. Groner, J. W. Winkelman, A. G. Harris, C. Ince, G. J. Bouma, K. Messmer, and R. G. Nadeau, “Orthogonal polarization spectral imaging: a new method for study of the microcirculation,” Nat. Med. 5, 1209–1212 (1999).
[Crossref]

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999), pp. 752–754.

Zhu, L.

J. Liang, C. Ma, L. Zhu, Y. Chen, L. Gao, and L. V. Wang, “Single-shot real-time video recording of a photonic mach cone induced by a scattered light pulse,” Sci. Adv. 3, e1601814 (2017).
[Crossref]

Appl. Opt. (6)

Appl. Phys. B (1)

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

Appl. Phys. Lett. (1)

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93, 121105 (2008).
[Crossref]

Found. Trends Optim. (1)

N. Parikh and S. Boyd, “Proximal algorithms,” Found. Trends Optim. 1, 123–231 (2014).

IEEE Signal Process. Mag. (2)

E. Candès and M. Wakin, “People hearing without listening: an introduction to compressive sampling,” IEEE Signal Process. Mag. 25(2), 21–30 (2008).
[Crossref]

R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
[Crossref]

IEEE Trans. Image Process. (1)

J.-L. Starck, J. Fadili, and F. Murtagh, “The undecimated wavelet decomposition and its reconstruction,” IEEE Trans. Image Process. 16, 297–309 (2007).
[Crossref]

J. Fourier Anal. Appl. (1)

E. J. Candes, M. B. Wakin, and S. P. Boyd, “Enhancing sparsity by reweighted L1 minimization,” J. Fourier Anal. Appl. 14, 877–905 (2008).
[Crossref]

J. Opt. (1)

S. S. Welsh, M. P. Edgar, R. Bowman, B. Sun, and M. J. Padgett, “Near video-rate linear stokes imaging with single-pixel detectors,” J. Opt. 17, 025705 (2015).
[Crossref]

J. Opt. A (1)

F. Boulvert, B. Boulbry, G. Le Brun, B. Le Jeune, S. Rivet, and J. Cariou, “Analysis of the depolarizing properties of irradiated pig skin,” J. Opt. A 7, 21–28 (2005).
[Crossref]

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

Multiscale Model. Simul. (1)

P. L. Combettes and V. R. Wajs, “Signal recovery by proximal forward-backward splitting,” Multiscale Model. Simul. 4, 1168–1200 (2005).
[Crossref]

Nat. Med. (1)

W. Groner, J. W. Winkelman, A. G. Harris, C. Ince, G. J. Bouma, K. Messmer, and R. G. Nadeau, “Orthogonal polarization spectral imaging: a new method for study of the microcirculation,” Nat. Med. 5, 1209–1212 (1999).
[Crossref]

Opt. Eng. (1)

N. Gupta, R. Dahmani, and S. Choy, “Acousto-optic tunable filter based visible- to near-infrared spectropolarimetric imager,” Opt. Eng. 41, 1033–1038 (2002).
[Crossref]

Opt. Express (1)

Opt. Lett. (2)

Phys. Stat. Solidi C (1)

M. Anastasiadou, A. D. Martino, D. Clement, F. Liège, B. Laude-Boulesteix, N. Quang, J. Dreyfuss, B. Huynh, A. Nazac, L. Schwartz, and H. Cohen, “Polarimetric imaging for the diagnosis of cervical cancer,” Phys. Stat. Solidi C 5, 1423–1426 (2008).
[Crossref]

Proc. Natl. Acad. Sci. U.S.A. (1)

V. Studer, J. Bobin, M. Chahid, H. S. Mousavi, E. Candes, and M. Dahan, “Compressive fluorescence microscopy for biological and hyperspectral imaging,” Proc. Natl. Acad. Sci. U.S.A. 109, E1679–E1687 (2012).
[Crossref]

Proc. SPIE (2)

S. Breugnot and P. Clémenceau, “Modeling and performances of a polarization active imager at lambda = 806  nm,” Proc. SPIE 3707, 449–460 (1999).
[Crossref]

F. Snik, J. Craven-Jones, M. Escuti, S. Fineschi, D. Harrington, A. De Martino, D. Mawet, J. Riedi, and J. S. Tyo, “An overview of polarimetric sensing techniques and technology with applications to different research fields,” Proc. SPIE 9099, 90990B (2014).
[Crossref]

Sci. Adv. (1)

J. Liang, C. Ma, L. Zhu, Y. Chen, L. Gao, and L. V. Wang, “Single-shot real-time video recording of a photonic mach cone induced by a scattered light pulse,” Sci. Adv. 3, e1601814 (2017).
[Crossref]

Sci. Rep. (1)

F. Soldevila, P. Clemente, E. Tajahuerce, N. Uribe-Patarroyo, P. Andrés, and J. Lancis, “Computational imaging with a balanced detector,” Sci. Rep. 6, 29181 (2016).
[Crossref]

SIAM J. Imaging Sci. (2)

A. Beck and M. Teboulle, “Fast iterative shrinkage-thresholding algorithm for linear inverse problems,” SIAM J. Imaging Sci. 2, 183–202 (2009).
[Crossref]

H. Raguet, J. Fadili, and G. Peyre, “A generalized forward-backward splitting,” SIAM J. Imaging Sci. 6, 1199–1226 (2013).
[Crossref]

Other (8)

E. Candès, “Compressive sampling,” in International Congress of Mathematics, Madrid, Spain (2006).

Y. C. Eldar and G. Kutyniok, Compressed Sensing: Theory and Applications (Cambridge University, 2012).

Texas Instruments, “DLP6500-0.65-1080p datasheet,” Rev. B (2016).

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999), pp. 752–754.

A. Liutkus, D. Martina, S. Popoff, G. Chardon, O. Katz, G. Lerosey, S. Gigan, L. Daudet, and I. Carron, “Imaging with nature: a universal analog compressive imager using a multiply scattering medium,” arXiv:1309.0425 (2013).

A. Asensio Ramos and A. López Ariste, “Compressive sensing for spectroscopy and polarimetry,” arXiv:0909.4439 (2009).

C. Brosseau, Fundamentals of Polarized Light—A Statistical Optics Approach (Wiley, 1998).

F. Goudail and P. Réfrégier, Statistical Image Processing Techniques for Noisy Images: an Application Oriented Approach (Kluwer, 2004).

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 (9)

Fig. 1.
Fig. 1. Sketch of the proposed two-pixel CS polarimetric imaging setup. It is inspired from the concept of SPC, where the image is first spatially sampled by a DMD which reflects light in two directions, and where the total photon flux is detected on a single photodetector in each direction. The illuminating light source can be either polarized (as represented) or not.
Fig. 2.
Fig. 2. (a) Evolution of the reflection coefficients in intensity for two tilt directions and two polarimetric components S and P , as a function of incidence angle θ on the DMD surface at wavelength 780 nm. (b) Evolution of the condition number κ ( A ) of matrix A as a function of θ at 780 nm. (c) Contour plot of κ ( A ) as a function of θ and wavelength. The black cross indicates the physical situation addressed in the numerical experiments.
Fig. 3.
Fig. 3. Inset (a): synthetic 1D polarimetric test signal used to assess reconstruction algorithm performance. An example of reconstructed signal is also given (see text for details). Inset (b): example of measured intensities on photodetectors P 1 and P 2 for M = 306 (compression 40%) different binary patterns (Hadamard) applied on the DMD. Main figure: plot of intensity y 2 as a function of y 1 , revealing strong anticorrelation between the two detected signals.
Fig. 4.
Fig. 4. Evolution of the PSNR of the signal X ^ reconstructed with the four compared algorithms as a function of detected signal SNR for a compression rate of 40%. The symbols represent the mean PSNR over 30 realizations, with error bars indicating the interquartile range. The lines are guides for the eyes.
Fig. 5.
Fig. 5. 2D map of the PSNR (averaged over 10 realizations) of X ^ reconstructed with the combined-reweighting FISTA, as a function of incidence angle θ and compression rate. The corresponding condition number κ ( A ) is indicated as a function of θ .
Fig. 6.
Fig. 6. Influence of the bias on incidence angle θ in the reconstruction quality (PSNR) for 0% compression (solid lines). PSNR of the reconstructed signal in the presence of bias and random tilt error on individual micromirrors (dashed line).
Fig. 7.
Fig. 7. Simulated polarimetric imaging scenario containing two objects over constant background. First row: total intensity image x T (true), x ^ T (reconstruction), and reconstruction error map. The two objects are indistinguishable in the total intensity image. Second row: true and reconstructed OSC image, and reconstruction error map.
Fig. 8.
Fig. 8. (a) Reconstructed OSC image and (b) reconstruction error map for various values of the OSC of the second object. (c) Evolution of the reconstruction PSNR of X when the OSC of the second object is varied between 0 and 1.
Fig. 9.
Fig. 9. Example of numerical polarimetric imaging experiment on realistic 512 × 512 pixel image data. First row: total intensity image x T , reconstruction x ^ T , and error map with 60% compression rate. The total intensity image is the standard cameraman test image, where the four hidden objects are totally hidden. Second row: true OSC image, reconstructed OSC image, and error map. The four hidden objects are revealed by their polarimetric contrast over depolarizing background on the OSC images.

Tables (2)

Tables Icon

Algorithm 1 Combined GFB

Tables Icon

Algorithm 2 Reweighted FISTA

Equations (23)

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

Y ˜ ° = [ y ˜ 1 ° y ˜ 2 ° ] = [ r 1 S r 1 P r 2 S r 2 P ] [ x S x P ] = A ˜ X .
Y ˜ = [ y ˜ 1 ° ϕ y ˜ 2 ° ϕ ¯ ] ,
Y = 1 2 [ y ˜ 1 ° ϕ y ˜ 2 ° ϕ ] = Q Y ˜ ° ϕ 2 , with    Q = [ 1 0 0 1 ] .
Y = AX ϕ + b , with    A = Q A ˜ 2 = 1 2 [ r 1 S r 1 P r 2 S r 2 P ] .
X ^ = Argmin X P ( X ) + 1 2 Y AX ϕ F 2 ,
Y ° ^ = Argmin Y ° Λ ( Y ° Ψ T ) 1 + 1 2 Y Y ° ϕ F 2 ,
X ^ = Argmin X Y ° ^ AX F 2 .
X ^ = Argmin X Λ ( X Ψ T ) 1 + 1 2 Y AX ϕ F 2 ,
Argmin X Λ ( X Ψ T ) 1 + i X 0 ( X ) + i DX 0 ( X ) + 1 2 Y AX ϕ F 2 ,
   i { 1 , 2 } ; λ i = τ · mad ( [ G Ψ T ] i ) ,
   i , j ; w i j = ε ε + | [ X ^ Ψ T ] i j | X ^ Ψ T ,
min X P ( X ) + L ( X ) ,
X ( t + 1 ) = prox γ P ( X ( t ) γ L ( X ( t ) ) ) ,
prox γ P ( z ) = Argmin X γ P ( X ) + 1 2 z X F 2 .
P ( X ) = Λ ( X Ψ T ) 1 ,
prox Λ ( . Ψ T ) 1 ( Z ) = Ψ S Λ ( Z Ψ T ) ,
i , j ; S Λ ( Z i j ) = { Z i j Λ i j sign ( Z i j ) if    | Z i j | > Λ i j 0 otherwise .
i , j ; prox i X 0 ( · ) ( Z i j ) = { Z i j if    Z i j > 0 0 otherwise .
prox i D · 0 ( Z ) = Argmin DX 0 1 2 Z X F 2 .
prox i D · 0 ( Z ) = Argmin X DX , π + 1 2 Z X F 2 .
DZ 2 π 0 .
j ; π j = { 1 2 [ DZ ] j if    [ DZ ] j < 0 0 otherwise .
prox i D · 0 ( Z ) = Z D T π .

Metrics