Abstract

Modern imaging techniques have proved to be very efficient to recover a scene with high dynamic range (HDR) values. However, this high dynamic range can introduce star-burst patterns around highlights arising from the diffraction of the camera aperture. The spatial extent of this effect can be very wide and alters pixels values, which, in a measurement context, are not reliable anymore. To address this problem, we introduce a novel algorithm that, utilizing a closed-form PSF, predicts where the diffraction will affect the pixels of an HDR image, making it possible to discard them from the measurement. Our approach gives better results than common deconvolution techniques and the uncertainty values (convolution kernel and noise) of the algorithm output are recovered.

© 2017 Optical Society of America

Full Article  |  PDF Article
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References

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  1. E. Reinhard, High Dynamic Range Imaging: Acquisition, Display, and Image-Based Lighting (Morgan Kaufmann/Elsevier, 2010).
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    [Crossref]
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    [Crossref]
  7. Y. Biraud, “Les méthodes de déconvolution et leurs limitations fondamentales,” Revue de Physique Appliquée 11, 203–214 (1976).
    [Crossref]
  8. G. Thomas, “An improvement of the Van-Cittert’s method,” in “ICASSP ’81. IEEE International Conference on Acoustics, Speech, and Signal Processing,”, vol. 6 (Institute of Electrical and Electronics Engineers), vol. 6, pp. 47–49.
  9. P. L. Combettes and H. J. Trussell, “Deconvolution with bounded uncertainty,” International Journal of Adaptive Control and Signal Processing 9, 3–17 (1995).
    [Crossref]
  10. S. Vajda, K. R. Godfrey, and P. Valko, “Numerical deconvolution using system identification methods,” Journal of Pharmacokinetics and Biopharmaceutics 16, 85–107 (1988).
    [Crossref] [PubMed]
  11. D. Verotta, “Two constrained deconvolution methods using spline functions,” Journal of Pharmacokinetics and Biopharmaceutics 21, 609–636 (1993).
    [Crossref] [PubMed]
  12. S. Pommé and B. Caro Marroyo, “Improved peak shape fitting in alpha spectra,” Applied Radiation and Isotopes 96, 148–153 (2015).
    [Crossref]
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    [Crossref] [PubMed]
  14. J. Skilling and R. K. Bryan, “Maximum entropy image reconstruction: general algorithm,” Monthly Notices of the Royal Astronomical Society 211, 111–124 (1984).
    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
  18. W. H. Richardson, “Bayesian-Based Iterative Method of Image Restoration*,” Journal of the Optical Society of America 62, 55 (1972).
    [Crossref]
  19. P. J. Verveer and T. M. Jovin, “Acceleration of the ICTM image restoration algorithm,” Journal of Microscopy 188, 191–195 (1997).
    [Crossref]
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    [Crossref] [PubMed]
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  25. G. van Kempen, H. van der Voort, J. Bauman, and K. Strasters, “Comparing maximum likelihood estimation and constrained Tikhonov-Miller restoration,” IEEE Engineering in Medicine and Biology Magazine 15, 76–83 (1996).
    [Crossref]
  26. O. K. Ersoy, Diffraction, Fourier Optics and Imaging (John Wiley2006).
  27. Shung-Wu Lee and R. Mittra, “Fourier transform of a polygonal shape function and its application in electromagnetics,” IEEE Transactions on Antennas and Propagation 31, 99–103 (1983).
    [Crossref]
  28. G. Durgin, “The Practical Behavior of Various Edge-Diffraction Formulas,” IEEE Antennas and Propagation Magazine 51, 24–35 (2009).
    [Crossref]
  29. M. Granados, B. Ajdin, M. Wand, C. Theobalt, H.P. Seidel, and H. Lensch, 2010. “Optimal HDR reconstruction with linear digital cameras,” Computer Vision and Pattern Recognition (CVPR), 2010 IEEE Conference on, IEEE, 215–222.

2015 (1)

S. Pommé and B. Caro Marroyo, “Improved peak shape fitting in alpha spectra,” Applied Radiation and Isotopes 96, 148–153 (2015).
[Crossref]

2009 (1)

G. Durgin, “The Practical Behavior of Various Edge-Diffraction Formulas,” IEEE Antennas and Propagation Magazine 51, 24–35 (2009).
[Crossref]

2006 (1)

E. García-Toraño, “Current status of alpha-particle spectrometry,” Applied Radiation and Isotopes 64, 1273–1280 (2006).
[Crossref] [PubMed]

2005 (1)

Y. Eldar, “Robust Deconvolution of Deterministic and Random Signals,” IEEE Transactions on Information Theory 51, 2921–2929 (2005).
[Crossref]

1997 (2)

P. J. Verveer and T. M. Jovin, “Acceleration of the ICTM image restoration algorithm,” Journal of Microscopy 188, 191–195 (1997).
[Crossref]

J. Aldrich, “R.A. Fisher and the making of maximum likelihood 1912–1922,” Statistical Science 12, 162–176 (1997).
[Crossref]

1996 (2)

G. van Kempen, H. van der Voort, J. Bauman, and K. Strasters, “Comparing maximum likelihood estimation and constrained Tikhonov-Miller restoration,” IEEE Engineering in Medicine and Biology Magazine 15, 76–83 (1996).
[Crossref]

F. N. Madden, K. R. Godfrey, M. J. Chappell, R. Hovorka, and R. A. Bates, “A comparison of six deconvolution techniques,” Journal of Pharmacokinetics and Biopharmaceutics 24, 283–299 (1996).
[Crossref] [PubMed]

1995 (2)

V. Krishnamurthi, Y.-H. Liu, S. Bhattacharyya, J. N. Turner, and T. J. Holmes, “Blind deconvolution of fluorescence micrographs by maximum-likelihood estimation,” Appl. Opt. 34, 6633 (1995).
[Crossref] [PubMed]

P. L. Combettes and H. J. Trussell, “Deconvolution with bounded uncertainty,” International Journal of Adaptive Control and Signal Processing 9, 3–17 (1995).
[Crossref]

1993 (1)

D. Verotta, “Two constrained deconvolution methods using spline functions,” Journal of Pharmacokinetics and Biopharmaceutics 21, 609–636 (1993).
[Crossref] [PubMed]

1992 (1)

1988 (1)

S. Vajda, K. R. Godfrey, and P. Valko, “Numerical deconvolution using system identification methods,” Journal of Pharmacokinetics and Biopharmaceutics 16, 85–107 (1988).
[Crossref] [PubMed]

1987 (1)

M. K. Charter and S. F. Gull, “Maximum entropy and its application to the calculation of drug absorption rates,” Journal of Pharmacokinetics and Biopharmaceutics 15, 645–655 (1987).
[Crossref] [PubMed]

1984 (1)

J. Skilling and R. K. Bryan, “Maximum entropy image reconstruction: general algorithm,” Monthly Notices of the Royal Astronomical Society 211, 111–124 (1984).
[Crossref]

1983 (1)

Shung-Wu Lee and R. Mittra, “Fourier transform of a polygonal shape function and its application in electromagnetics,” IEEE Transactions on Antennas and Propagation 31, 99–103 (1983).
[Crossref]

1976 (1)

Y. Biraud, “Les méthodes de déconvolution et leurs limitations fondamentales,” Revue de Physique Appliquée 11, 203–214 (1976).
[Crossref]

1972 (1)

W. H. Richardson, “Bayesian-Based Iterative Method of Image Restoration*,” Journal of the Optical Society of America 62, 55 (1972).
[Crossref]

1969 (1)

D. D. Dixon, W. N. Johnson, J. D. Kurfess, R. K. Pina, R. C. Puetter, W. R. Purcell, T. O. Tuemer, W. A. Wheaton, and A. D. Zych, “Astronomy and astrophysics,” Astronomy and Astrophysics Supplement, v.120, p.683–686  120, 683–686 (1969).

Ajdin, B.

M. Granados, B. Ajdin, M. Wand, C. Theobalt, H.P. Seidel, and H. Lensch, 2010. “Optimal HDR reconstruction with linear digital cameras,” Computer Vision and Pattern Recognition (CVPR), 2010 IEEE Conference on, IEEE, 215–222.

Aldrich, J.

J. Aldrich, “R.A. Fisher and the making of maximum likelihood 1912–1922,” Statistical Science 12, 162–176 (1997).
[Crossref]

Arsenin, V. I. V. I.

A. N. A. N. Tikhonov and V. I. V. I. Arsenin, Solutions of Ill-Posed Problems (Winston, 1977).

Bates, R. A.

F. N. Madden, K. R. Godfrey, M. J. Chappell, R. Hovorka, and R. A. Bates, “A comparison of six deconvolution techniques,” Journal of Pharmacokinetics and Biopharmaceutics 24, 283–299 (1996).
[Crossref] [PubMed]

Bauman, J.

G. van Kempen, H. van der Voort, J. Bauman, and K. Strasters, “Comparing maximum likelihood estimation and constrained Tikhonov-Miller restoration,” IEEE Engineering in Medicine and Biology Magazine 15, 76–83 (1996).
[Crossref]

Bhattacharyya, S.

Biraud, Y.

Y. Biraud, “Les méthodes de déconvolution et leurs limitations fondamentales,” Revue de Physique Appliquée 11, 203–214 (1976).
[Crossref]

Bryan, R. K.

J. Skilling and R. K. Bryan, “Maximum entropy image reconstruction: general algorithm,” Monthly Notices of the Royal Astronomical Society 211, 111–124 (1984).
[Crossref]

Caro Marroyo, B.

S. Pommé and B. Caro Marroyo, “Improved peak shape fitting in alpha spectra,” Applied Radiation and Isotopes 96, 148–153 (2015).
[Crossref]

Chappell, M. J.

F. N. Madden, K. R. Godfrey, M. J. Chappell, R. Hovorka, and R. A. Bates, “A comparison of six deconvolution techniques,” Journal of Pharmacokinetics and Biopharmaceutics 24, 283–299 (1996).
[Crossref] [PubMed]

Charter, M. K.

M. K. Charter and S. F. Gull, “Maximum entropy and its application to the calculation of drug absorption rates,” Journal of Pharmacokinetics and Biopharmaceutics 15, 645–655 (1987).
[Crossref] [PubMed]

Combettes, P. L.

P. L. Combettes and H. J. Trussell, “Deconvolution with bounded uncertainty,” International Journal of Adaptive Control and Signal Processing 9, 3–17 (1995).
[Crossref]

Dixon, D. D.

D. D. Dixon, W. N. Johnson, J. D. Kurfess, R. K. Pina, R. C. Puetter, W. R. Purcell, T. O. Tuemer, W. A. Wheaton, and A. D. Zych, “Astronomy and astrophysics,” Astronomy and Astrophysics Supplement, v.120, p.683–686  120, 683–686 (1969).

Durgin, G.

G. Durgin, “The Practical Behavior of Various Edge-Diffraction Formulas,” IEEE Antennas and Propagation Magazine 51, 24–35 (2009).
[Crossref]

Eldar, Y.

Y. Eldar, “Robust Deconvolution of Deterministic and Random Signals,” IEEE Transactions on Information Theory 51, 2921–2929 (2005).
[Crossref]

Ersoy, O. K.

O. K. Ersoy, Diffraction, Fourier Optics and Imaging (John Wiley2006).

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing (Cambridge University Press, 1992).

Gadella, T. W. J. T. W. J.

J. Rietdorf and T. W. J. T. W. J. Gadella, Microscopy Techniques (Springer, 2005).
[Crossref]

García-Toraño, E.

E. García-Toraño, “Current status of alpha-particle spectrometry,” Applied Radiation and Isotopes 64, 1273–1280 (2006).
[Crossref] [PubMed]

Godfrey, K. R.

F. N. Madden, K. R. Godfrey, M. J. Chappell, R. Hovorka, and R. A. Bates, “A comparison of six deconvolution techniques,” Journal of Pharmacokinetics and Biopharmaceutics 24, 283–299 (1996).
[Crossref] [PubMed]

S. Vajda, K. R. Godfrey, and P. Valko, “Numerical deconvolution using system identification methods,” Journal of Pharmacokinetics and Biopharmaceutics 16, 85–107 (1988).
[Crossref] [PubMed]

Granados, M.

M. Granados, B. Ajdin, M. Wand, C. Theobalt, H.P. Seidel, and H. Lensch, 2010. “Optimal HDR reconstruction with linear digital cameras,” Computer Vision and Pattern Recognition (CVPR), 2010 IEEE Conference on, IEEE, 215–222.

Gull, S. F.

M. K. Charter and S. F. Gull, “Maximum entropy and its application to the calculation of drug absorption rates,” Journal of Pharmacokinetics and Biopharmaceutics 15, 645–655 (1987).
[Crossref] [PubMed]

Holmes, T. J.

Hovorka, R.

F. N. Madden, K. R. Godfrey, M. J. Chappell, R. Hovorka, and R. A. Bates, “A comparison of six deconvolution techniques,” Journal of Pharmacokinetics and Biopharmaceutics 24, 283–299 (1996).
[Crossref] [PubMed]

Ja, J.

J. A. European Southern Observatory. J. Ja, Astronomy and astrophysics., vol. 15 (EDP Sciences [etc.], 1969).

Johnson, W. N.

D. D. Dixon, W. N. Johnson, J. D. Kurfess, R. K. Pina, R. C. Puetter, W. R. Purcell, T. O. Tuemer, W. A. Wheaton, and A. D. Zych, “Astronomy and astrophysics,” Astronomy and Astrophysics Supplement, v.120, p.683–686  120, 683–686 (1969).

Jovin, T. M.

P. J. Verveer and T. M. Jovin, “Acceleration of the ICTM image restoration algorithm,” Journal of Microscopy 188, 191–195 (1997).
[Crossref]

Kotera, J.

J. Kotera, F. Šroubek, and P. Milanfar, “Blind Deconvolution Using Alternating Maximum a Posteriori Estimation with Heavy-Tailed Priors,” (Springer, Berlin, Heidelberg, 2013), pp. 59–66.

Krishnamurthi, V.

Kurfess, J. D.

D. D. Dixon, W. N. Johnson, J. D. Kurfess, R. K. Pina, R. C. Puetter, W. R. Purcell, T. O. Tuemer, W. A. Wheaton, and A. D. Zych, “Astronomy and astrophysics,” Astronomy and Astrophysics Supplement, v.120, p.683–686  120, 683–686 (1969).

Lee, Shung-Wu

Shung-Wu Lee and R. Mittra, “Fourier transform of a polygonal shape function and its application in electromagnetics,” IEEE Transactions on Antennas and Propagation 31, 99–103 (1983).
[Crossref]

Lensch, H.

M. Granados, B. Ajdin, M. Wand, C. Theobalt, H.P. Seidel, and H. Lensch, 2010. “Optimal HDR reconstruction with linear digital cameras,” Computer Vision and Pattern Recognition (CVPR), 2010 IEEE Conference on, IEEE, 215–222.

Liu, Y.-H.

Madden, F. N.

F. N. Madden, K. R. Godfrey, M. J. Chappell, R. Hovorka, and R. A. Bates, “A comparison of six deconvolution techniques,” Journal of Pharmacokinetics and Biopharmaceutics 24, 283–299 (1996).
[Crossref] [PubMed]

Milanfar, P.

J. Kotera, F. Šroubek, and P. Milanfar, “Blind Deconvolution Using Alternating Maximum a Posteriori Estimation with Heavy-Tailed Priors,” (Springer, Berlin, Heidelberg, 2013), pp. 59–66.

Mittra, R.

Shung-Wu Lee and R. Mittra, “Fourier transform of a polygonal shape function and its application in electromagnetics,” IEEE Transactions on Antennas and Propagation 31, 99–103 (1983).
[Crossref]

Pina, R. K.

D. D. Dixon, W. N. Johnson, J. D. Kurfess, R. K. Pina, R. C. Puetter, W. R. Purcell, T. O. Tuemer, W. A. Wheaton, and A. D. Zych, “Astronomy and astrophysics,” Astronomy and Astrophysics Supplement, v.120, p.683–686  120, 683–686 (1969).

Pommé, S.

S. Pommé and B. Caro Marroyo, “Improved peak shape fitting in alpha spectra,” Applied Radiation and Isotopes 96, 148–153 (2015).
[Crossref]

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing (Cambridge University Press, 1992).

Puetter, R. C.

D. D. Dixon, W. N. Johnson, J. D. Kurfess, R. K. Pina, R. C. Puetter, W. R. Purcell, T. O. Tuemer, W. A. Wheaton, and A. D. Zych, “Astronomy and astrophysics,” Astronomy and Astrophysics Supplement, v.120, p.683–686  120, 683–686 (1969).

Purcell, W. R.

D. D. Dixon, W. N. Johnson, J. D. Kurfess, R. K. Pina, R. C. Puetter, W. R. Purcell, T. O. Tuemer, W. A. Wheaton, and A. D. Zych, “Astronomy and astrophysics,” Astronomy and Astrophysics Supplement, v.120, p.683–686  120, 683–686 (1969).

Reinhard, E.

E. Reinhard, High Dynamic Range Imaging: Acquisition, Display, and Image-Based Lighting (Morgan Kaufmann/Elsevier, 2010).

Richardson, W. H.

W. H. Richardson, “Bayesian-Based Iterative Method of Image Restoration*,” Journal of the Optical Society of America 62, 55 (1972).
[Crossref]

Rietdorf, J.

J. Rietdorf and T. W. J. T. W. J. Gadella, Microscopy Techniques (Springer, 2005).
[Crossref]

Seidel, H.P.

M. Granados, B. Ajdin, M. Wand, C. Theobalt, H.P. Seidel, and H. Lensch, 2010. “Optimal HDR reconstruction with linear digital cameras,” Computer Vision and Pattern Recognition (CVPR), 2010 IEEE Conference on, IEEE, 215–222.

Skilling, J.

J. Skilling and R. K. Bryan, “Maximum entropy image reconstruction: general algorithm,” Monthly Notices of the Royal Astronomical Society 211, 111–124 (1984).
[Crossref]

Šroubek, F.

J. Kotera, F. Šroubek, and P. Milanfar, “Blind Deconvolution Using Alternating Maximum a Posteriori Estimation with Heavy-Tailed Priors,” (Springer, Berlin, Heidelberg, 2013), pp. 59–66.

Strasters, K.

G. van Kempen, H. van der Voort, J. Bauman, and K. Strasters, “Comparing maximum likelihood estimation and constrained Tikhonov-Miller restoration,” IEEE Engineering in Medicine and Biology Magazine 15, 76–83 (1996).
[Crossref]

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing (Cambridge University Press, 1992).

Theobalt, C.

M. Granados, B. Ajdin, M. Wand, C. Theobalt, H.P. Seidel, and H. Lensch, 2010. “Optimal HDR reconstruction with linear digital cameras,” Computer Vision and Pattern Recognition (CVPR), 2010 IEEE Conference on, IEEE, 215–222.

Thomas, G.

G. Thomas, “An improvement of the Van-Cittert’s method,” in “ICASSP ’81. IEEE International Conference on Acoustics, Speech, and Signal Processing,”, vol. 6 (Institute of Electrical and Electronics Engineers), vol. 6, pp. 47–49.

Tikhonov, A. N. A. N.

A. N. A. N. Tikhonov and V. I. V. I. Arsenin, Solutions of Ill-Posed Problems (Winston, 1977).

Trussell, H. J.

P. L. Combettes and H. J. Trussell, “Deconvolution with bounded uncertainty,” International Journal of Adaptive Control and Signal Processing 9, 3–17 (1995).
[Crossref]

Tuemer, T. O.

D. D. Dixon, W. N. Johnson, J. D. Kurfess, R. K. Pina, R. C. Puetter, W. R. Purcell, T. O. Tuemer, W. A. Wheaton, and A. D. Zych, “Astronomy and astrophysics,” Astronomy and Astrophysics Supplement, v.120, p.683–686  120, 683–686 (1969).

Turner, J. N.

Vajda, S.

S. Vajda, K. R. Godfrey, and P. Valko, “Numerical deconvolution using system identification methods,” Journal of Pharmacokinetics and Biopharmaceutics 16, 85–107 (1988).
[Crossref] [PubMed]

Valko, P.

S. Vajda, K. R. Godfrey, and P. Valko, “Numerical deconvolution using system identification methods,” Journal of Pharmacokinetics and Biopharmaceutics 16, 85–107 (1988).
[Crossref] [PubMed]

van der Voort, H.

G. van Kempen, H. van der Voort, J. Bauman, and K. Strasters, “Comparing maximum likelihood estimation and constrained Tikhonov-Miller restoration,” IEEE Engineering in Medicine and Biology Magazine 15, 76–83 (1996).
[Crossref]

van Kempen, G.

G. van Kempen, H. van der Voort, J. Bauman, and K. Strasters, “Comparing maximum likelihood estimation and constrained Tikhonov-Miller restoration,” IEEE Engineering in Medicine and Biology Magazine 15, 76–83 (1996).
[Crossref]

Verotta, D.

D. Verotta, “Two constrained deconvolution methods using spline functions,” Journal of Pharmacokinetics and Biopharmaceutics 21, 609–636 (1993).
[Crossref] [PubMed]

Verveer, P. J.

P. J. Verveer and T. M. Jovin, “Acceleration of the ICTM image restoration algorithm,” Journal of Microscopy 188, 191–195 (1997).
[Crossref]

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing (Cambridge University Press, 1992).

Wand, M.

M. Granados, B. Ajdin, M. Wand, C. Theobalt, H.P. Seidel, and H. Lensch, 2010. “Optimal HDR reconstruction with linear digital cameras,” Computer Vision and Pattern Recognition (CVPR), 2010 IEEE Conference on, IEEE, 215–222.

Wheaton, W. A.

D. D. Dixon, W. N. Johnson, J. D. Kurfess, R. K. Pina, R. C. Puetter, W. R. Purcell, T. O. Tuemer, W. A. Wheaton, and A. D. Zych, “Astronomy and astrophysics,” Astronomy and Astrophysics Supplement, v.120, p.683–686  120, 683–686 (1969).

Wiener, N.

N. Wiener, Extrapolation, Interpolation, and Smoothing of Stationary Time Series with Engineering Applications (Technology Press of the Massachusetts Institute of Technology, 1964).

Zych, A. D.

D. D. Dixon, W. N. Johnson, J. D. Kurfess, R. K. Pina, R. C. Puetter, W. R. Purcell, T. O. Tuemer, W. A. Wheaton, and A. D. Zych, “Astronomy and astrophysics,” Astronomy and Astrophysics Supplement, v.120, p.683–686  120, 683–686 (1969).

Appl. Opt. (1)

Applied Radiation and Isotopes (2)

S. Pommé and B. Caro Marroyo, “Improved peak shape fitting in alpha spectra,” Applied Radiation and Isotopes 96, 148–153 (2015).
[Crossref]

E. García-Toraño, “Current status of alpha-particle spectrometry,” Applied Radiation and Isotopes 64, 1273–1280 (2006).
[Crossref] [PubMed]

Astronomy and Astrophysics (1)

D. D. Dixon, W. N. Johnson, J. D. Kurfess, R. K. Pina, R. C. Puetter, W. R. Purcell, T. O. Tuemer, W. A. Wheaton, and A. D. Zych, “Astronomy and astrophysics,” Astronomy and Astrophysics Supplement, v.120, p.683–686  120, 683–686 (1969).

IEEE Antennas and Propagation Magazine (1)

G. Durgin, “The Practical Behavior of Various Edge-Diffraction Formulas,” IEEE Antennas and Propagation Magazine 51, 24–35 (2009).
[Crossref]

IEEE Engineering in Medicine and Biology Magazine (1)

G. van Kempen, H. van der Voort, J. Bauman, and K. Strasters, “Comparing maximum likelihood estimation and constrained Tikhonov-Miller restoration,” IEEE Engineering in Medicine and Biology Magazine 15, 76–83 (1996).
[Crossref]

IEEE Transactions on Antennas and Propagation (1)

Shung-Wu Lee and R. Mittra, “Fourier transform of a polygonal shape function and its application in electromagnetics,” IEEE Transactions on Antennas and Propagation 31, 99–103 (1983).
[Crossref]

IEEE Transactions on Information Theory (1)

Y. Eldar, “Robust Deconvolution of Deterministic and Random Signals,” IEEE Transactions on Information Theory 51, 2921–2929 (2005).
[Crossref]

International Journal of Adaptive Control and Signal Processing (1)

P. L. Combettes and H. J. Trussell, “Deconvolution with bounded uncertainty,” International Journal of Adaptive Control and Signal Processing 9, 3–17 (1995).
[Crossref]

J. Opt. Soc. Am. A (1)

Journal of Microscopy (1)

P. J. Verveer and T. M. Jovin, “Acceleration of the ICTM image restoration algorithm,” Journal of Microscopy 188, 191–195 (1997).
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Figures (10)

Fig. 1
Fig. 1 Left: Principle of diffraction through a thin-lens camera, composed of a finite aperture lens and a camera sensor separated by a distance D. Even if the object point at d were in the focal plane at d*, the image of the sensor would not be a point as expected, but a pattern due to light behaving as a wave. Right: Mathematical model of a standard n-bladed camera aperture. The full pattern can be divided into similar geometries, themselves sub-divided into two elementary parts : a triangle OAB (blue), and a section of parabola whose axis of symmetry passes through the middle point M (red).
Fig. 2
Fig. 2 Calibration method of the thin-lens camera parameters. Step 1 (resp. 2) aims to set the front ring (resp. diaphragm) of the lens in focus, giving the l1 (resp. l2) distance between the front ring and the mirror. These measurements then allow us to retrieve the focal plane distance d, the shift Δ between the aperture and the front of the camera, and the diaphragm parameters with a picture taken at Step 2.
Fig. 3
Fig. 3 Left: Principle of a picture of a scene with a higher dynamic range than the camera. The level of exposure of the camera sets a band of well-exposed values within the whole scene dynamic range. The under- and over-exposed pixels are discarded from the measurement. Center: HDR imaging principle of a scene. In order to increase the dynamic range of a single picture, multiple pictures can be merged to cover the whole intensity distribution of the scene. Right: Cut of the HDR image values into separate non-overlapping bands of value bk such that the whole image dynamic range is covered.
Fig. 4
Fig. 4 Left: Within-band influence effect. In this worst-case scenario, pixels within a band can be linked through diffraction, while we assume this is not the case. Thus, the effect of diffraction can be removed up to a residual convolution kernel ��wb. Right: Bottom-up influence effect. In this worst-case scenario, pixels from the lower bands should never be able to diffract more than ρ % of the pixel values in the current band. Therefore, a band is strongly interdependent with lower bands by a residual kernel ��bu.
Fig. 5
Fig. 5 Fitting of our diaphragm model for various real diaphragms. The second row shows a fit with straight edges (orange) and with curved edges (green). These examples demonstrate the importance of being able to represent irregular polygonal shapes (high f-number), but also curved shapes (low f-number).
Fig. 6
Fig. 6 Comparison of the PSF resulting from the fitted diaphragm against a real HDR photograph of a quasi-point light source. Some slight differences can be observed in the repartition of light within the widened star branches of the PSF, which is explained by the random variations along the diaphragm edges that we do not take into account.
Fig. 7
Fig. 7 Results of the algorithm applied on real HDR images (tonemapped with Drago et al. [1]) for various camera configurations, with input parameters ��b = 10 and ρ = 5%. The wavelengths used for each color channel are [λR, λG, λB] = [600 nm, 540 nm, 470 nm]. The segmentation images show the discarded pixels (red), the valid pixels (green), and the under-exposed ones (black). If the HDR images exhibits obvious star shaped patterns, the algorithm detects it, and they are finally removed. Such result is qualitative in nature, because there is no reference HDR image without diffraction. False predictions are present in the first two cases (l), where the diffraction prediction seems rotated from the real one. This problem emerges from the misfit of the lens diaphragm, as discussed in subsection 7.7.1.
Fig. 8
Fig. 8 Histograms of the error of magnitude against a virtual reference of the remaining valid pixels for various methods and three different SNRs. The PSF function used is given by our Linos 50mm lens at f/11. The max factor measures the maximum error remaining after applying our method (red curve). The resulting histogram is much more concentrated towards smaller errors than compared to all deconvolution algorithms (blue curves). Of course, the quality of the original image (green curve) is not reached because of the residual kernel contribution, but our output error matches very well with the achieved output (brown curve) prediction.
Fig. 9
Fig. 9 Variation of the residual kernel range ��radius (in pixels) depending on the input parameters. According to its definition, the residual kernel size arises from two contributions which are easily separable (green curve): when one effect is dominant, the other effect does not interfere with it.
Fig. 10
Fig. 10 The output dependencies of the algorithm on the input parameters. The generated input HDR image is a well-distributed HDR image with a dynamic range of 1010 and a speckle size of 20 pixels. In the region of minimal maximum error (dashed green square), the extent of the residual kernel and the percentage of discarded pixels go in opposite trends.

Tables (2)

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Algorithm 1 Diffraction detection algorithm

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Algorithm 2 Residual kernel removal

Equations (28)

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PSF ( x , y ) = 1 λ 2 D 2 S pup | [ P ] ( x λ D , y λ D ) | 2
π 64 1 f # 4 f 4 λ d 3 1
| | d * min ( 1 , 8 f # 2 λ d * f 2 )
I = I * PSF
x ( y ) = 1 2 𝒞 ( y z M ) 2 + [ r A B + 1 8 𝒞 ( z A z B ) 2 ] .
[ P tri ] ( ν x , ν y ) = P tri ( x , y ) e 2 i π ( ν x x + ν y y ) d x d y = γ tri [ e i η A sinc ( η A ) e i η B sinc ( η B ) ]
[ P par ] ( ν x , ν y ) = P par ( x , y ) e 2 i π ( ν x x + ν y y ) d x d y = γ par [ 2 i sin ( π ν y L ) e ξ 2 π Δ e Δ 2 ( erfi ( Δ + ξ ) erfi ( Δ ξ ) ) ]
γ par = exp ( 2 i π [ ν x ( r A B + h ) + ν y z M ] ) / ( 4 π 2 ν x ν y ) , Δ = i π ν y L / ( 2 ξ ) , ξ = 2 i π ν x h .
[ P ] ( ν x , ν y ) = k = 1 n ( [ P tri k ] + [ P par k ] ) ( ( α k ) [ ν x ν y ] )
S pup = k = 1 n [ 1 2 r A B k L k + 1 12 𝒞 L k 3 ] .
Δ = 2 ( l 1 l 2 ) and d = 4 l 1 2 l 2
f # ˜ = f π 2 S pup .
𝒟 I = max ( I ) min ( I ) .
I hdr = I hdr * PSF + .
k [ 1 , 𝒩 ] , b k = ] 𝒟 b k , 𝒟 b 1 k ] with 𝒩 = ceil ( log ( 𝒟 hdr ) log ( 𝒟 b ) ) .
[ I hdr PSF ] × 𝟙 k = [ ( I 1 k 1 + I k + I k + 1 𝒩 ) PSF ] × 𝟙 k = [ I 1 k 1 PSF ] × 𝟙 k + [ I k PSF ] × 𝟙 k + [ I k + 1 𝒩 PSF ] × 𝟙 k .
[ I hdr P S F ] × 𝟙 k [ I 1 k 1 P S F ] × 𝟙 k + [ I k P S F ] × 𝟙 k .
PSF = ( PSF δ 0 max ( PSF ) ) 0 + δ 0 max ( PSF ) norm . δ 0
[ I hdr P S F ] × 𝟙 k [ I 1 k 1 P S F ] × 𝟙 k + I k .
[ I 1 k 1 P S F ] × 𝟙 k > ρ I k .
𝒦 ( x , y ) = { PSF ( x , y ) if 𝒦 w b ( x , y ) = 1 OR 𝒦 b u ( x , y ) = 1 0 otherwise
[ I 1 k 1 PSF ˜ ] × 𝟙 k > ρ I k
I output = I hdr * 𝒦 + .
𝒦 w b ( x , y ) = [ PSF ( x , y ) max ( PSF ) 𝒟 b ]
( 2 PSF ) max ( PSF ) < ρ .
s * = argmin s ( ρ PSF * ( PSF < s ) 2 ) .
𝒦 b u ( x , y ) = [ PSF ( x , y ) s * ]
= | log 10 ( I output ) log 10 ( I * ) | .

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