Abstract

This paper investigates a highly parallel extension of the single-pixel camera based on a focal plane array. It discusses the practical challenges that arise when implementing such an architecture and demonstrates that system-specific optical effects must be measured and integrated within the system model for accurate image reconstruction. Three different projection lenses were used to evaluate the ability of the system to accommodate varying degrees of optical imperfection. Reconstruction of binary and grayscale objects using system-specific models and Nesterov’s proximal gradient method produced images with higher spatial resolution and lower reconstruction error than using either bicubic interpolation or a theoretical system model that assumes ideal optical behavior. The high-quality images produced using relatively few observations suggest that higher throughput imaging may be achieved with such architectures than with conventional single-pixel cameras. The optical design considerations and quantitative performance metrics proposed here may lead to improved image reconstruction for similar highly parallel systems.

© 2016 Optical Society of America

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References

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  1. R. G. Baraniuk, “Compressive sensing,” IEEE Signal Process. Mag. 24(4), 121–124 (2007).
    [Crossref]
  2. M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. E. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
  5. R. M. Willett, R. F. Marcia, and J. M. Nichols, “Compressed sensing for practical optical imaging systems: a tutorial,” Opt. Eng. 50(7), 072601 (2011).
    [Crossref]
  6. 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]
  7. Y. Wu, P. Ye, I. O. Mirza, G. R. Arce, and D. W. Prather, “Experimental demonstration of an optical-sectioning compressive sensing microscope (CSM),” Opt. Express 18(24), 24565–24578 (2010).
    [Crossref] [PubMed]
  8. 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(26), E1679–E1687 (2012).
    [Crossref] [PubMed]
  9. M. S. Mermelstein, “Synthetic aperture microscopy,” Ph.D. thesis, Massachusetts Institute of Technology, Cambridge, MA, (1999).
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    [Crossref]
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    [Crossref]
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  13. J. Ke and E. Y. Lam, “Object reconstruction in block-based compressive imaging,” Opt. Express 20(20), 22102–22117 (2012).
    [Crossref] [PubMed]
  14. A. Mahalanobis, R. Shilling, R. Murphy, and R. Muise, “Recent results of medium wave infrared compressive sensing,” Appl. Opt. 53(34), 8060–8070 (2014).
    [Crossref] [PubMed]
  15. J. Wang, M. Gupta, and A. C. Sankaranarayanan, “LiSens - A scalable architecture for video compressive sensing,” in Proceedings of IEEE International Conference on Computational Photography (2015), pp. 1–9.
    [Crossref]
  16. M. Elad, “Optimized projections for compressed sensing,” IEEE Trans. Signal Process. 55(12), 5695–5702 (2007).
    [Crossref]
  17. J. Ke, E. Y. Lam, and P. Wei, “Binary sensing matrix design for compressive imaging measurements,” in Signal Recovery and Synthesis (Optical Society of America, 2014), paper SM2F.7.
  18. H. Arguello and G. R. Arce, “Rank minimization code aperture design for spectrally selective compressive imaging,” IEEE Trans. Image Process. 22(3), 941–954 (2013).
    [Crossref] [PubMed]
  19. G. H. Golub and C. F. V. Loan, Matrix Computations (Johns Hopkins University Press, 2013).
  20. M. Rudelson and R. Vershynin, “Non-asymptotic theory of random matrices: extreme singular values,” arXiv 1003.2990 (2010).
  21. M. Rudelson and R. Vershynin, “The Littlewood-Offord problem and invertibility of random matrices,” Adv. Math. 218(2), 600–633 (2008).
    [Crossref]
  22. R. Gu and A. Dogandzic, “A fast proximal gradient algorithm for reconstructing nonnegative signals with sparse transform coefficients”, in Proceedings of Asilomar Conference on Signals, Systems, and Computers (2014), pp. 1662–1667.
    [Crossref]

2014 (3)

G. R. Arce, D. J. Brady, L. Carin, H. Arguello, and D. S. Kittle, “Compressive coded aperture spectral imaging,” IEEE Signal Process. Mag. 31(1), 105–115 (2014).
[Crossref]

R. H. Shepard, C. Fernandez-Cull, R. Raskar, B. Shi, C. Barsi, and H. Zhao, “Optical design and characterization of an advanced computational imaging system,” Proc. SPIE 9216, 92160A (2014).
[Crossref]

A. Mahalanobis, R. Shilling, R. Murphy, and R. Muise, “Recent results of medium wave infrared compressive sensing,” Appl. Opt. 53(34), 8060–8070 (2014).
[Crossref] [PubMed]

2013 (2)

H. Arguello and G. R. Arce, “Rank minimization code aperture design for spectrally selective compressive imaging,” IEEE Trans. Image Process. 22(3), 941–954 (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 (2)

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(26), E1679–E1687 (2012).
[Crossref] [PubMed]

J. Ke and E. Y. Lam, “Object reconstruction in block-based compressive imaging,” Opt. Express 20(20), 22102–22117 (2012).
[Crossref] [PubMed]

2011 (1)

R. M. Willett, R. F. Marcia, and J. M. Nichols, “Compressed sensing for practical optical imaging systems: a tutorial,” Opt. Eng. 50(7), 072601 (2011).
[Crossref]

2010 (1)

2008 (2)

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. E. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
[Crossref]

M. Rudelson and R. Vershynin, “The Littlewood-Offord problem and invertibility of random matrices,” Adv. Math. 218(2), 600–633 (2008).
[Crossref]

2007 (3)

R. G. Baraniuk, “Compressive sensing,” IEEE Signal Process. Mag. 24(4), 121–124 (2007).
[Crossref]

M. Elad, “Optimized projections for compressed sensing,” IEEE Trans. Signal Process. 55(12), 5695–5702 (2007).
[Crossref]

M. A. Neifeld and J. Ke, “Optical architectures for compressive imaging,” Appl. Opt. 46(22), 5293–5303 (2007).
[Crossref] [PubMed]

2006 (1)

J. Ryu, S. S. Hong, B. K. P. Horn, D. M. Freeman, and M. S. Mermelstein, “Multibeam interferometric illumination as the primary source of resolution in optical microscopy,” Appl. Phys. Lett. 88(17), 171112 (2006).
[Crossref]

Arce, G. R.

G. R. Arce, D. J. Brady, L. Carin, H. Arguello, and D. S. Kittle, “Compressive coded aperture spectral imaging,” IEEE Signal Process. Mag. 31(1), 105–115 (2014).
[Crossref]

H. Arguello and G. R. Arce, “Rank minimization code aperture design for spectrally selective compressive imaging,” IEEE Trans. Image Process. 22(3), 941–954 (2013).
[Crossref] [PubMed]

Y. Wu, P. Ye, I. O. Mirza, G. R. Arce, and D. W. Prather, “Experimental demonstration of an optical-sectioning compressive sensing microscope (CSM),” Opt. Express 18(24), 24565–24578 (2010).
[Crossref] [PubMed]

Arguello, H.

G. R. Arce, D. J. Brady, L. Carin, H. Arguello, and D. S. Kittle, “Compressive coded aperture spectral imaging,” IEEE Signal Process. Mag. 31(1), 105–115 (2014).
[Crossref]

H. Arguello and G. R. Arce, “Rank minimization code aperture design for spectrally selective compressive imaging,” IEEE Trans. Image Process. 22(3), 941–954 (2013).
[Crossref] [PubMed]

Baraniuk, R. G.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. E. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
[Crossref]

R. G. Baraniuk, “Compressive sensing,” IEEE Signal Process. Mag. 24(4), 121–124 (2007).
[Crossref]

Barsi, C.

R. H. Shepard, C. Fernandez-Cull, R. Raskar, B. Shi, C. Barsi, and H. Zhao, “Optical design and characterization of an advanced computational imaging system,” Proc. SPIE 9216, 92160A (2014).
[Crossref]

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(26), E1679–E1687 (2012).
[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]

Brady, D. J.

G. R. Arce, D. J. Brady, L. Carin, H. Arguello, and D. S. Kittle, “Compressive coded aperture spectral imaging,” IEEE Signal Process. Mag. 31(1), 105–115 (2014).
[Crossref]

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(26), E1679–E1687 (2012).
[Crossref] [PubMed]

Carin, L.

G. R. Arce, D. J. Brady, L. Carin, H. Arguello, and D. S. Kittle, “Compressive coded aperture spectral imaging,” IEEE Signal Process. Mag. 31(1), 105–115 (2014).
[Crossref]

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(26), E1679–E1687 (2012).
[Crossref] [PubMed]

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(26), E1679–E1687 (2012).
[Crossref] [PubMed]

Davenport, M. A.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. E. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
[Crossref]

Dogandzic, A.

R. Gu and A. Dogandzic, “A fast proximal gradient algorithm for reconstructing nonnegative signals with sparse transform coefficients”, in Proceedings of Asilomar Conference on Signals, Systems, and Computers (2014), pp. 1662–1667.
[Crossref]

Duarte, M. F.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. E. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
[Crossref]

Edgar, M. P.

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]

Elad, M.

M. Elad, “Optimized projections for compressed sensing,” IEEE Trans. Signal Process. 55(12), 5695–5702 (2007).
[Crossref]

Fernandez-Cull, C.

R. H. Shepard, C. Fernandez-Cull, R. Raskar, B. Shi, C. Barsi, and H. Zhao, “Optical design and characterization of an advanced computational imaging system,” Proc. SPIE 9216, 92160A (2014).
[Crossref]

Freeman, D. M.

J. Ryu, S. S. Hong, B. K. P. Horn, D. M. Freeman, and M. S. Mermelstein, “Multibeam interferometric illumination as the primary source of resolution in optical microscopy,” Appl. Phys. Lett. 88(17), 171112 (2006).
[Crossref]

Gu, R.

R. Gu and A. Dogandzic, “A fast proximal gradient algorithm for reconstructing nonnegative signals with sparse transform coefficients”, in Proceedings of Asilomar Conference on Signals, Systems, and Computers (2014), pp. 1662–1667.
[Crossref]

Gupta, M.

J. Wang, M. Gupta, and A. C. Sankaranarayanan, “LiSens - A scalable architecture for video compressive sensing,” in Proceedings of IEEE International Conference on Computational Photography (2015), pp. 1–9.
[Crossref]

Hong, S. S.

J. Ryu, S. S. Hong, B. K. P. Horn, D. M. Freeman, and M. S. Mermelstein, “Multibeam interferometric illumination as the primary source of resolution in optical microscopy,” Appl. Phys. Lett. 88(17), 171112 (2006).
[Crossref]

Horn, B. K. P.

J. Ryu, S. S. Hong, B. K. P. Horn, D. M. Freeman, and M. S. Mermelstein, “Multibeam interferometric illumination as the primary source of resolution in optical microscopy,” Appl. Phys. Lett. 88(17), 171112 (2006).
[Crossref]

Ke, J.

Kelly, K. E.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. E. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
[Crossref]

Kittle, D. S.

G. R. Arce, D. J. Brady, L. Carin, H. Arguello, and D. S. Kittle, “Compressive coded aperture spectral imaging,” IEEE Signal Process. Mag. 31(1), 105–115 (2014).
[Crossref]

Lam, E. Y.

Laska, J. N.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. E. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
[Crossref]

Mahalanobis, A.

Marcia, R. F.

R. M. Willett, R. F. Marcia, and J. M. Nichols, “Compressed sensing for practical optical imaging systems: a tutorial,” Opt. Eng. 50(7), 072601 (2011).
[Crossref]

Mermelstein, M. S.

J. Ryu, S. S. Hong, B. K. P. Horn, D. M. Freeman, and M. S. Mermelstein, “Multibeam interferometric illumination as the primary source of resolution in optical microscopy,” Appl. Phys. Lett. 88(17), 171112 (2006).
[Crossref]

Mirza, I. O.

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(26), E1679–E1687 (2012).
[Crossref] [PubMed]

Muise, R.

Murphy, R.

Neifeld, M. A.

Nichols, J. M.

R. M. Willett, R. F. Marcia, and J. M. Nichols, “Compressed sensing for practical optical imaging systems: a tutorial,” Opt. Eng. 50(7), 072601 (2011).
[Crossref]

Padgett, M. J.

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]

Prather, D. W.

Raskar, R.

R. H. Shepard, C. Fernandez-Cull, R. Raskar, B. Shi, C. Barsi, and H. Zhao, “Optical design and characterization of an advanced computational imaging system,” Proc. SPIE 9216, 92160A (2014).
[Crossref]

Rudelson, M.

M. Rudelson and R. Vershynin, “The Littlewood-Offord problem and invertibility of random matrices,” Adv. Math. 218(2), 600–633 (2008).
[Crossref]

Ryu, J.

J. Ryu, S. S. Hong, B. K. P. Horn, D. M. Freeman, and M. S. Mermelstein, “Multibeam interferometric illumination as the primary source of resolution in optical microscopy,” Appl. Phys. Lett. 88(17), 171112 (2006).
[Crossref]

Sankaranarayanan, A. C.

J. Wang, M. Gupta, and A. C. Sankaranarayanan, “LiSens - A scalable architecture for video compressive sensing,” in Proceedings of IEEE International Conference on Computational Photography (2015), pp. 1–9.
[Crossref]

Shepard, R. H.

R. H. Shepard, C. Fernandez-Cull, R. Raskar, B. Shi, C. Barsi, and H. Zhao, “Optical design and characterization of an advanced computational imaging system,” Proc. SPIE 9216, 92160A (2014).
[Crossref]

Shi, B.

R. H. Shepard, C. Fernandez-Cull, R. Raskar, B. Shi, C. Barsi, and H. Zhao, “Optical design and characterization of an advanced computational imaging system,” Proc. SPIE 9216, 92160A (2014).
[Crossref]

Shilling, R.

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(26), E1679–E1687 (2012).
[Crossref] [PubMed]

Sun, B.

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, T.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. E. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
[Crossref]

Takhar, D.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. E. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
[Crossref]

Vershynin, R.

M. Rudelson and R. Vershynin, “The Littlewood-Offord problem and invertibility of random matrices,” Adv. Math. 218(2), 600–633 (2008).
[Crossref]

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]

Wang, J.

J. Wang, M. Gupta, and A. C. Sankaranarayanan, “LiSens - A scalable architecture for video compressive sensing,” in Proceedings of IEEE International Conference on Computational Photography (2015), pp. 1–9.
[Crossref]

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]

Willett, R. M.

R. M. Willett, R. F. Marcia, and J. M. Nichols, “Compressed sensing for practical optical imaging systems: a tutorial,” Opt. Eng. 50(7), 072601 (2011).
[Crossref]

Wu, Y.

Ye, P.

Zhao, H.

R. H. Shepard, C. Fernandez-Cull, R. Raskar, B. Shi, C. Barsi, and H. Zhao, “Optical design and characterization of an advanced computational imaging system,” Proc. SPIE 9216, 92160A (2014).
[Crossref]

Adv. Math. (1)

M. Rudelson and R. Vershynin, “The Littlewood-Offord problem and invertibility of random matrices,” Adv. Math. 218(2), 600–633 (2008).
[Crossref]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

J. Ryu, S. S. Hong, B. K. P. Horn, D. M. Freeman, and M. S. Mermelstein, “Multibeam interferometric illumination as the primary source of resolution in optical microscopy,” Appl. Phys. Lett. 88(17), 171112 (2006).
[Crossref]

IEEE Signal Process. Mag. (3)

G. R. Arce, D. J. Brady, L. Carin, H. Arguello, and D. S. Kittle, “Compressive coded aperture spectral imaging,” IEEE Signal Process. Mag. 31(1), 105–115 (2014).
[Crossref]

R. G. Baraniuk, “Compressive sensing,” IEEE Signal Process. Mag. 24(4), 121–124 (2007).
[Crossref]

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. E. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
[Crossref]

IEEE Trans. Image Process. (1)

H. Arguello and G. R. Arce, “Rank minimization code aperture design for spectrally selective compressive imaging,” IEEE Trans. Image Process. 22(3), 941–954 (2013).
[Crossref] [PubMed]

IEEE Trans. Signal Process. (1)

M. Elad, “Optimized projections for compressed sensing,” IEEE Trans. Signal Process. 55(12), 5695–5702 (2007).
[Crossref]

Opt. Eng. (1)

R. M. Willett, R. F. Marcia, and J. M. Nichols, “Compressed sensing for practical optical imaging systems: a tutorial,” Opt. Eng. 50(7), 072601 (2011).
[Crossref]

Opt. Express (2)

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(26), E1679–E1687 (2012).
[Crossref] [PubMed]

Proc. SPIE (1)

R. H. Shepard, C. Fernandez-Cull, R. Raskar, B. Shi, C. Barsi, and H. Zhao, “Optical design and characterization of an advanced computational imaging system,” Proc. SPIE 9216, 92160A (2014).
[Crossref]

Science (1)

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]

Other (7)

M. S. Mermelstein, “Synthetic aperture microscopy,” Ph.D. thesis, Massachusetts Institute of Technology, Cambridge, MA, (1999).

R. Kerviche, N. Zhu, and A. Ashok, “Information-optimal scalable compressive imaging system,” in Computational Imaging and Sensing Conference (Optical Society of America, 2014), paper CM2D.2.

J. Wang, M. Gupta, and A. C. Sankaranarayanan, “LiSens - A scalable architecture for video compressive sensing,” in Proceedings of IEEE International Conference on Computational Photography (2015), pp. 1–9.
[Crossref]

J. Ke, E. Y. Lam, and P. Wei, “Binary sensing matrix design for compressive imaging measurements,” in Signal Recovery and Synthesis (Optical Society of America, 2014), paper SM2F.7.

G. H. Golub and C. F. V. Loan, Matrix Computations (Johns Hopkins University Press, 2013).

M. Rudelson and R. Vershynin, “Non-asymptotic theory of random matrices: extreme singular values,” arXiv 1003.2990 (2010).

R. Gu and A. Dogandzic, “A fast proximal gradient algorithm for reconstructing nonnegative signals with sparse transform coefficients”, in Proceedings of Asilomar Conference on Signals, Systems, and Computers (2014), pp. 1662–1667.
[Crossref]

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Figures (8)

Fig. 1
Fig. 1 (a) A single-pixel camera applies a coded mask at an optical plane that lies conjugate to both the object and detector. (b) Multiple sub-masks can be mapped to neighboring detectors in an array-based sensor to generate a highly parallel version of the single-pixel camera. (c) Photograph showing the primary components of our experimental platform.
Fig. 2
Fig. 2 Illustration of IPC-based projection challenges. (a) Under ideal 4 × undersampling, exactly 4 mask elements are imaged onto each sensor pixel. (d, e) Ideally, all light from mask elements labeled 1–4 is then collected by sensor pixel “A”. While element–pixel alignment errors (b) and distortion effects (c) can be minimized, the experimental sensor response (f) still shows some light leaking onto neighboring pixels.
Fig. 3
Fig. 3 Prediction errors for experimentally determined H’s with different values of m for three different projection lenses. Circles indicate the PTA at m associated with the minimum prediction error for each lens. Squares indicate the PTA corresponding to m = 36.
Fig. 4
Fig. 4 MTF data for the three lenses used in our experimental setup. Each projection lens was positioned for 3.55 × demagnification from the coded mask to sensor array with a 9 mm entrance pupil diameter.
Fig. 5
Fig. 5 Images and corresponding line profiles for (a) the object, (b) a single observation without a coded mask, (c) 4 × bicubic interpolation of the uncoded image in (b), (d) NPG-based CS reconstruction using the ideal H, and (e) NPG-based CS reconstruction using the experimentally determined H. CS reconstructions correspond to 10 observations with the microscope objective as the projection lens. Each line profile (f-j) is a vertical slice taken at the left side (depicted by arrow above panel (a)).
Fig. 6
Fig. 6 Data for the grayscale cameraman test pattern. (a) Cameraman test object. (b) A single observation of the object without a coded mask. (c) 4 × bicubic interpolation of (b). NPG-based CS reconstruction using 12 observations with (d) ideal H, (e) experimental H of size 6 × 6, and (f) experimental H of size 14 × 14. (g) Reconstruction error using experimental and ideal H’s for increasing numbers of observations.
Fig. 7
Fig. 7 Image reconstruction for three different projection lenses. NPG-based CS reconstructions of the cameraman test object (Fig. 6(a)) from 12 observations using (a) the plano-convex singlet, (b) achromatic doublet, and (c) microscope objective. (d) Reconstruction error for each lens with increasing numbers of observations using both the ideal H and the experimentally determined H.
Fig. 8
Fig. 8 Experimental platform and results for imaging a 1951 USAF Resolution Target. (a) Photograph showing the modified experimental platform with object illumination and imaging optics added. (b) Target imaged with no mask imposed. (c) Bicubic interpolation on the image shown in (b). CS reconstruction from 30 observations using the ideal H (d) and an experimentally determined H of size 16 (e).

Equations (1)

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y=(DD) T H D C x= A H x

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