Abstract

Photon shot noise is the main noise source of optical microscopy images and can be modeled by a Poisson process. Several discrete wavelet transform based methods have been proposed in the literature for denoising images corrupted by Poisson noise. However, the discrete wavelet transform (DWT) has disadvantages such as shift variance, aliasing, and lack of directional selectivity. To overcome these problems, a dual tree complex wavelet transform is used in our proposed denoising algorithm. Our denoising algorithm is based on the assumption that for the Poisson noise case threshold values for wavelet coefficients can be estimated from the approximation coefficients. Our proposed method was compared with one of the state of the art denoising algorithms. Better results were obtained by using the proposed algorithm in terms of image quality metrics. Furthermore, the contrast enhancement effect of the proposed method on collagen fıber images is examined. Our method allows fast and efficient enhancement of images obtained under low light intensity conditions.

© 2012 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. S. Delpretti, F. Luisier, S. Ramani, T. Blu, and M. Unser, “Multiframe sure-let denoising of timelapse fluorescence microscopy images,” in 5th IEEE International Symposium on Biomedical Imaging: from Nano to Macro, 2008. ISBI 2008 (IEEE, 2008), pp. 149–152.
  2. C. Vonesch, F. Aguet, J. L. Vonesch, and M. Unser, “The colored revolution of bioimaging,” IEEE Signal Process. Mag.23(3), 20–31 (2006).
    [CrossRef]
  3. Q. Wu, F. A. Merchant, and K. R. Castleman, Microscope Image Processing (Academic, Amsterdam, 2008).
  4. F. Luisier, T. Blu, and M. Unser, “Image denoising in mixed Poisson-Gaussian noise,” IEEE Trans. Image Process.20(3), 696–708 (2011).
    [CrossRef] [PubMed]
  5. F. J. Anscombe, “The transformation of Poisson, binomial and negative-binomial data,” Biometrika35, 246–254 (1948).
  6. D. L. Donoho, “Nonlinear wavelet methods for recovery of signals, densities, and spectra from indirect and noisy data,” in Proceedings of Symposia in Applied Mathematics. Vol 47. Different Perspectives on Wavelets, I. Daubechies, ed. (American Mathematical Society, 1993).
  7. D. Donoho, “De-noising by soft-thresholding,” IEEE Trans. Inf. Theory41(3), 613–627 (1995).
    [CrossRef]
  8. P. Fryzlewicz and G. P. Nason, “A Haar-Fisz algorithm for Poisson intensity estimation,” J. Comput. Graph. Statist.13(3), 621–638 (2004).
    [CrossRef]
  9. F. Luisier, C. Vonesch, T. Blu, and M. Unser, “Fast interscale wavelet denoising of Poisson-corrupted images,” Signal Process.90(2), 415–427 (2010).
    [CrossRef]
  10. I. W. Selesnick, R. G. Baraniuk, and N. C. Kingsbury, “The dual-tree complex wavelet transform,” IEEE Signal Process. Mag.22(6), 123–151 (2005).
    [CrossRef]
  11. N. Kingsbury, “The dual-tree complex wavelet transform: a new efficient tool for image restoration and enhancement,” in Proceedings of the 9th European Signal Processing Conference (EUSIPCO 98), (Typorama, 1998), pp. 319–322.
  12. F. Daniels, “Quantification of collagen orientation in 3D engineered tissue,” in Biomedical Engineering (Eindhoven University of Technology, Eindhoven, 2006).
  13. N. Kingsbury, “The dual-tree complex wavelet transform: a new technique for shift invariance and directional filters,” in Proceedings of the 8th IEEE DSP Workshop, Utah (IEEE, 1998), Vol. 8, p. 86
  14. V. Musoko, “Biomedical signal and image processing,” in Computing and Control Engineering (Institute of Chemical Technology, Prague, 2005).
  15. A. Salih Husain and S. Aymen Dawood, “Image compression based on 2D dual tree complex wavelet transform,” Eng. Technol. J.28, 1290–1305 (2010).
  16. H. M. Salinas and D. C. Fernández, “Comparison of PDE-based nonlinear diffusion approaches for image enhancement and denoising in optical coherence tomography,” IEEE Trans. Med. Imaging26(6), 761–771 (2007).
    [CrossRef] [PubMed]

2011 (1)

F. Luisier, T. Blu, and M. Unser, “Image denoising in mixed Poisson-Gaussian noise,” IEEE Trans. Image Process.20(3), 696–708 (2011).
[CrossRef] [PubMed]

2010 (2)

F. Luisier, C. Vonesch, T. Blu, and M. Unser, “Fast interscale wavelet denoising of Poisson-corrupted images,” Signal Process.90(2), 415–427 (2010).
[CrossRef]

A. Salih Husain and S. Aymen Dawood, “Image compression based on 2D dual tree complex wavelet transform,” Eng. Technol. J.28, 1290–1305 (2010).

2007 (1)

H. M. Salinas and D. C. Fernández, “Comparison of PDE-based nonlinear diffusion approaches for image enhancement and denoising in optical coherence tomography,” IEEE Trans. Med. Imaging26(6), 761–771 (2007).
[CrossRef] [PubMed]

2006 (1)

C. Vonesch, F. Aguet, J. L. Vonesch, and M. Unser, “The colored revolution of bioimaging,” IEEE Signal Process. Mag.23(3), 20–31 (2006).
[CrossRef]

2005 (1)

I. W. Selesnick, R. G. Baraniuk, and N. C. Kingsbury, “The dual-tree complex wavelet transform,” IEEE Signal Process. Mag.22(6), 123–151 (2005).
[CrossRef]

2004 (1)

P. Fryzlewicz and G. P. Nason, “A Haar-Fisz algorithm for Poisson intensity estimation,” J. Comput. Graph. Statist.13(3), 621–638 (2004).
[CrossRef]

1995 (1)

D. Donoho, “De-noising by soft-thresholding,” IEEE Trans. Inf. Theory41(3), 613–627 (1995).
[CrossRef]

1948 (1)

F. J. Anscombe, “The transformation of Poisson, binomial and negative-binomial data,” Biometrika35, 246–254 (1948).

Aguet, F.

C. Vonesch, F. Aguet, J. L. Vonesch, and M. Unser, “The colored revolution of bioimaging,” IEEE Signal Process. Mag.23(3), 20–31 (2006).
[CrossRef]

Anscombe, F. J.

F. J. Anscombe, “The transformation of Poisson, binomial and negative-binomial data,” Biometrika35, 246–254 (1948).

Aymen Dawood, S.

A. Salih Husain and S. Aymen Dawood, “Image compression based on 2D dual tree complex wavelet transform,” Eng. Technol. J.28, 1290–1305 (2010).

Baraniuk, R. G.

I. W. Selesnick, R. G. Baraniuk, and N. C. Kingsbury, “The dual-tree complex wavelet transform,” IEEE Signal Process. Mag.22(6), 123–151 (2005).
[CrossRef]

Blu, T.

F. Luisier, T. Blu, and M. Unser, “Image denoising in mixed Poisson-Gaussian noise,” IEEE Trans. Image Process.20(3), 696–708 (2011).
[CrossRef] [PubMed]

F. Luisier, C. Vonesch, T. Blu, and M. Unser, “Fast interscale wavelet denoising of Poisson-corrupted images,” Signal Process.90(2), 415–427 (2010).
[CrossRef]

Donoho, D.

D. Donoho, “De-noising by soft-thresholding,” IEEE Trans. Inf. Theory41(3), 613–627 (1995).
[CrossRef]

Fernández, D. C.

H. M. Salinas and D. C. Fernández, “Comparison of PDE-based nonlinear diffusion approaches for image enhancement and denoising in optical coherence tomography,” IEEE Trans. Med. Imaging26(6), 761–771 (2007).
[CrossRef] [PubMed]

Fryzlewicz, P.

P. Fryzlewicz and G. P. Nason, “A Haar-Fisz algorithm for Poisson intensity estimation,” J. Comput. Graph. Statist.13(3), 621–638 (2004).
[CrossRef]

Kingsbury, N. C.

I. W. Selesnick, R. G. Baraniuk, and N. C. Kingsbury, “The dual-tree complex wavelet transform,” IEEE Signal Process. Mag.22(6), 123–151 (2005).
[CrossRef]

Luisier, F.

F. Luisier, T. Blu, and M. Unser, “Image denoising in mixed Poisson-Gaussian noise,” IEEE Trans. Image Process.20(3), 696–708 (2011).
[CrossRef] [PubMed]

F. Luisier, C. Vonesch, T. Blu, and M. Unser, “Fast interscale wavelet denoising of Poisson-corrupted images,” Signal Process.90(2), 415–427 (2010).
[CrossRef]

Nason, G. P.

P. Fryzlewicz and G. P. Nason, “A Haar-Fisz algorithm for Poisson intensity estimation,” J. Comput. Graph. Statist.13(3), 621–638 (2004).
[CrossRef]

Salih Husain, A.

A. Salih Husain and S. Aymen Dawood, “Image compression based on 2D dual tree complex wavelet transform,” Eng. Technol. J.28, 1290–1305 (2010).

Salinas, H. M.

H. M. Salinas and D. C. Fernández, “Comparison of PDE-based nonlinear diffusion approaches for image enhancement and denoising in optical coherence tomography,” IEEE Trans. Med. Imaging26(6), 761–771 (2007).
[CrossRef] [PubMed]

Selesnick, I. W.

I. W. Selesnick, R. G. Baraniuk, and N. C. Kingsbury, “The dual-tree complex wavelet transform,” IEEE Signal Process. Mag.22(6), 123–151 (2005).
[CrossRef]

Unser, M.

F. Luisier, T. Blu, and M. Unser, “Image denoising in mixed Poisson-Gaussian noise,” IEEE Trans. Image Process.20(3), 696–708 (2011).
[CrossRef] [PubMed]

F. Luisier, C. Vonesch, T. Blu, and M. Unser, “Fast interscale wavelet denoising of Poisson-corrupted images,” Signal Process.90(2), 415–427 (2010).
[CrossRef]

C. Vonesch, F. Aguet, J. L. Vonesch, and M. Unser, “The colored revolution of bioimaging,” IEEE Signal Process. Mag.23(3), 20–31 (2006).
[CrossRef]

Vonesch, C.

F. Luisier, C. Vonesch, T. Blu, and M. Unser, “Fast interscale wavelet denoising of Poisson-corrupted images,” Signal Process.90(2), 415–427 (2010).
[CrossRef]

C. Vonesch, F. Aguet, J. L. Vonesch, and M. Unser, “The colored revolution of bioimaging,” IEEE Signal Process. Mag.23(3), 20–31 (2006).
[CrossRef]

Vonesch, J. L.

C. Vonesch, F. Aguet, J. L. Vonesch, and M. Unser, “The colored revolution of bioimaging,” IEEE Signal Process. Mag.23(3), 20–31 (2006).
[CrossRef]

Biometrika (1)

F. J. Anscombe, “The transformation of Poisson, binomial and negative-binomial data,” Biometrika35, 246–254 (1948).

Eng. Technol. J. (1)

A. Salih Husain and S. Aymen Dawood, “Image compression based on 2D dual tree complex wavelet transform,” Eng. Technol. J.28, 1290–1305 (2010).

IEEE Signal Process. Mag. (2)

I. W. Selesnick, R. G. Baraniuk, and N. C. Kingsbury, “The dual-tree complex wavelet transform,” IEEE Signal Process. Mag.22(6), 123–151 (2005).
[CrossRef]

C. Vonesch, F. Aguet, J. L. Vonesch, and M. Unser, “The colored revolution of bioimaging,” IEEE Signal Process. Mag.23(3), 20–31 (2006).
[CrossRef]

IEEE Trans. Image Process. (1)

F. Luisier, T. Blu, and M. Unser, “Image denoising in mixed Poisson-Gaussian noise,” IEEE Trans. Image Process.20(3), 696–708 (2011).
[CrossRef] [PubMed]

IEEE Trans. Inf. Theory (1)

D. Donoho, “De-noising by soft-thresholding,” IEEE Trans. Inf. Theory41(3), 613–627 (1995).
[CrossRef]

IEEE Trans. Med. Imaging (1)

H. M. Salinas and D. C. Fernández, “Comparison of PDE-based nonlinear diffusion approaches for image enhancement and denoising in optical coherence tomography,” IEEE Trans. Med. Imaging26(6), 761–771 (2007).
[CrossRef] [PubMed]

J. Comput. Graph. Statist. (1)

P. Fryzlewicz and G. P. Nason, “A Haar-Fisz algorithm for Poisson intensity estimation,” J. Comput. Graph. Statist.13(3), 621–638 (2004).
[CrossRef]

Signal Process. (1)

F. Luisier, C. Vonesch, T. Blu, and M. Unser, “Fast interscale wavelet denoising of Poisson-corrupted images,” Signal Process.90(2), 415–427 (2010).
[CrossRef]

Other (7)

D. L. Donoho, “Nonlinear wavelet methods for recovery of signals, densities, and spectra from indirect and noisy data,” in Proceedings of Symposia in Applied Mathematics. Vol 47. Different Perspectives on Wavelets, I. Daubechies, ed. (American Mathematical Society, 1993).

S. Delpretti, F. Luisier, S. Ramani, T. Blu, and M. Unser, “Multiframe sure-let denoising of timelapse fluorescence microscopy images,” in 5th IEEE International Symposium on Biomedical Imaging: from Nano to Macro, 2008. ISBI 2008 (IEEE, 2008), pp. 149–152.

Q. Wu, F. A. Merchant, and K. R. Castleman, Microscope Image Processing (Academic, Amsterdam, 2008).

N. Kingsbury, “The dual-tree complex wavelet transform: a new efficient tool for image restoration and enhancement,” in Proceedings of the 9th European Signal Processing Conference (EUSIPCO 98), (Typorama, 1998), pp. 319–322.

F. Daniels, “Quantification of collagen orientation in 3D engineered tissue,” in Biomedical Engineering (Eindhoven University of Technology, Eindhoven, 2006).

N. Kingsbury, “The dual-tree complex wavelet transform: a new technique for shift invariance and directional filters,” in Proceedings of the 8th IEEE DSP Workshop, Utah (IEEE, 1998), Vol. 8, p. 86

V. Musoko, “Biomedical signal and image processing,” in Computing and Control Engineering (Institute of Chemical Technology, Prague, 2005).

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 (4)

Fig. 1
Fig. 1

Decomposition with 2D DT-CWT.

Fig. 2
Fig. 2

Test images.

Fig. 3
Fig. 3

Aliasing effect.

Fig. 4
Fig. 4

(a) Collagen fiber image. (Left) Recorded image. (Right) Enhanced image using proposed method. (b) Image feature selection on magnified images.

Tables (4)

Tables Icon

Table 1 First level coefficients of the analysis filters

Tables Icon

Table 2 Remaining levels coefficients of the analysis filters

Tables Icon

Table 3 Comparison of proposed method with other methods in terms of RMSE

Tables Icon

Table 4 Contrast enhancement effect of proposed method on collagen fiber image

Equations (10)

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

ψ r (t)= 2 n H a (n) φ r (2tn)
ψ i (t)= 2 n H b (n) φ i (2tn)
φ r (t)= 2 n L a (n)ψ(2tn)
φ i (t)= 2 n L b (n) ψ i (2tn)
1. ( LH a +  LH b )/ 2          3. ( HL a +  HL b )/  2         5. ( HH a +  HH b )/  2 2. ( LH a - LH b )/  2            4. ( HL a - HL b )/   2            6. ( HH a - HH b )/   2
T real =0.001× a r1 2 + a r2 2 +.... a rn 2
T imag =0.001× a i1 2 + a i2 2 +.... a in 2
{ | x |>Tf(x)=sgn(x)(| x |T) | x |Tf(x)=0
RMSE= 1 mn i=0 m1 j=0 n1 [ G( i,j )F(i,j) ] 2
CNR=10log( μ t μ r σ t 2 + σ r 2   )

Metrics