Abstract

Hybrid imaging systems employing cubic phase modulation in the pupil-plane enable significantly increased depth of field, but artifacts in the recovered images are a major problem. We present a parametric blind-deconvolution algorithm, based on minimization of the high-frequency content of the restored image that enables recovery of artifact-free images for a wide range of defocus. We show that the algorithm enables robust matching of the image recovery kernel with the optical point-spread function to enable, for the first time, optimally low noise levels in recovered images.

© 2010 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  13. J. Kautsky, J. Flusser, B. Zitová, and S. Simberová, “A new wavelet-based measure of image focus,” Pattern Recognit. Lett. 23(14), 1785–1794 (2002).
    [CrossRef]
  14. G. Deng, and L. W. Cahill, “An adaptive Gaussian filter for noise reduction and edge detection, ” Nuclear Science Symposium and Medical Imaging Conference, IEEE Conference Record, 3, 1615–1619 (1993).

2010

2009

2008

Q. Liu, T. Zhao, W. Zhang, and F. Yu, “Image restoration based on generalized minimal residual methods with antireflective boundary conditions in a wavefront coding system,” Opt. Eng. 47(12), 127005–1 (2008).
[CrossRef]

2005

M. Donatelli and S. Serra-Capizzano, “Anti-reflective boundary conditions and re-blurring,” Inverse Probl. 21(1), 169–182 (2005).
[CrossRef]

G. Muyo and A. R. Harvey, “Decomposition of the optical transfer function: wavefront coding imaging systems,” Opt. Lett. 30(20), 2715–2717 (2005).
[CrossRef] [PubMed]

2003

J. G. Nagy, M. K. Ng, and L. Perrone, “Kronecker Product Approximations for Image Restoration with Reflexive Boundary Conditions,” SIAM J. Matrix Anal. Appl. 25(3), 829–841 (2003).
[CrossRef]

2002

J. Kautsky, J. Flusser, B. Zitová, and S. Simberová, “A new wavelet-based measure of image focus,” Pattern Recognit. Lett. 23(14), 1785–1794 (2002).
[CrossRef]

2001

N. Nguyen, P. Milanfar, and G. Golub, “Efficient generalized cross-validation with applications to parametric image restoration and resolution enhancement,” IEEE Trans. Image Process. 10(9), 1299–1308 (2001).
[CrossRef]

1997

I. M. Johnstone and B. W. Silverman, “Wavelet Threshold Estimators for Data with Correlated Noise,” J. R. Stat. Soc., B 59(2), 319–351 (1997).
[CrossRef]

1995

1992

S. J. Reeves and R. M. Mersereau, “Blur identification by the method of generalized cross-validation,” IEEE Trans. Image Process. 1(3), 301–311 (1992).
[CrossRef] [PubMed]

Bustin, N.

Cathey, W. T.

Demenikov, M.

Donatelli, M.

M. Donatelli and S. Serra-Capizzano, “Anti-reflective boundary conditions and re-blurring,” Inverse Probl. 21(1), 169–182 (2005).
[CrossRef]

Dowski, J. E. R.

Findlay, E.

Flusser, J.

J. Kautsky, J. Flusser, B. Zitová, and S. Simberová, “A new wavelet-based measure of image focus,” Pattern Recognit. Lett. 23(14), 1785–1794 (2002).
[CrossRef]

Golub, G.

N. Nguyen, P. Milanfar, and G. Golub, “Efficient generalized cross-validation with applications to parametric image restoration and resolution enhancement,” IEEE Trans. Image Process. 10(9), 1299–1308 (2001).
[CrossRef]

Harvey, A. R.

Johnstone, I. M.

I. M. Johnstone and B. W. Silverman, “Wavelet Threshold Estimators for Data with Correlated Noise,” J. R. Stat. Soc., B 59(2), 319–351 (1997).
[CrossRef]

Kautsky, J.

J. Kautsky, J. Flusser, B. Zitová, and S. Simberová, “A new wavelet-based measure of image focus,” Pattern Recognit. Lett. 23(14), 1785–1794 (2002).
[CrossRef]

Liu, Q.

Q. Liu, T. Zhao, W. Zhang, and F. Yu, “Image restoration based on generalized minimal residual methods with antireflective boundary conditions in a wavefront coding system,” Opt. Eng. 47(12), 127005–1 (2008).
[CrossRef]

Mersereau, R. M.

S. J. Reeves and R. M. Mersereau, “Blur identification by the method of generalized cross-validation,” IEEE Trans. Image Process. 1(3), 301–311 (1992).
[CrossRef] [PubMed]

Milanfar, P.

N. Nguyen, P. Milanfar, and G. Golub, “Efficient generalized cross-validation with applications to parametric image restoration and resolution enhancement,” IEEE Trans. Image Process. 10(9), 1299–1308 (2001).
[CrossRef]

Muyo, G.

Nagy, J. G.

J. G. Nagy, M. K. Ng, and L. Perrone, “Kronecker Product Approximations for Image Restoration with Reflexive Boundary Conditions,” SIAM J. Matrix Anal. Appl. 25(3), 829–841 (2003).
[CrossRef]

Ng, M. K.

J. G. Nagy, M. K. Ng, and L. Perrone, “Kronecker Product Approximations for Image Restoration with Reflexive Boundary Conditions,” SIAM J. Matrix Anal. Appl. 25(3), 829–841 (2003).
[CrossRef]

Nguyen, N.

N. Nguyen, P. Milanfar, and G. Golub, “Efficient generalized cross-validation with applications to parametric image restoration and resolution enhancement,” IEEE Trans. Image Process. 10(9), 1299–1308 (2001).
[CrossRef]

Perrone, L.

J. G. Nagy, M. K. Ng, and L. Perrone, “Kronecker Product Approximations for Image Restoration with Reflexive Boundary Conditions,” SIAM J. Matrix Anal. Appl. 25(3), 829–841 (2003).
[CrossRef]

Reeves, S. J.

S. J. Reeves and R. M. Mersereau, “Blur identification by the method of generalized cross-validation,” IEEE Trans. Image Process. 1(3), 301–311 (1992).
[CrossRef] [PubMed]

Serra-Capizzano, S.

M. Donatelli and S. Serra-Capizzano, “Anti-reflective boundary conditions and re-blurring,” Inverse Probl. 21(1), 169–182 (2005).
[CrossRef]

Silverman, B. W.

I. M. Johnstone and B. W. Silverman, “Wavelet Threshold Estimators for Data with Correlated Noise,” J. R. Stat. Soc., B 59(2), 319–351 (1997).
[CrossRef]

Simberová, S.

J. Kautsky, J. Flusser, B. Zitová, and S. Simberová, “A new wavelet-based measure of image focus,” Pattern Recognit. Lett. 23(14), 1785–1794 (2002).
[CrossRef]

Vettenburg, T.

Yu, F.

Q. Liu, T. Zhao, W. Zhang, and F. Yu, “Image restoration based on generalized minimal residual methods with antireflective boundary conditions in a wavefront coding system,” Opt. Eng. 47(12), 127005–1 (2008).
[CrossRef]

Zhang, W.

Q. Liu, T. Zhao, W. Zhang, and F. Yu, “Image restoration based on generalized minimal residual methods with antireflective boundary conditions in a wavefront coding system,” Opt. Eng. 47(12), 127005–1 (2008).
[CrossRef]

Zhao, T.

Q. Liu, T. Zhao, W. Zhang, and F. Yu, “Image restoration based on generalized minimal residual methods with antireflective boundary conditions in a wavefront coding system,” Opt. Eng. 47(12), 127005–1 (2008).
[CrossRef]

Zitová, B.

J. Kautsky, J. Flusser, B. Zitová, and S. Simberová, “A new wavelet-based measure of image focus,” Pattern Recognit. Lett. 23(14), 1785–1794 (2002).
[CrossRef]

Appl. Opt.

IEEE Trans. Image Process.

S. J. Reeves and R. M. Mersereau, “Blur identification by the method of generalized cross-validation,” IEEE Trans. Image Process. 1(3), 301–311 (1992).
[CrossRef] [PubMed]

N. Nguyen, P. Milanfar, and G. Golub, “Efficient generalized cross-validation with applications to parametric image restoration and resolution enhancement,” IEEE Trans. Image Process. 10(9), 1299–1308 (2001).
[CrossRef]

Inverse Probl.

M. Donatelli and S. Serra-Capizzano, “Anti-reflective boundary conditions and re-blurring,” Inverse Probl. 21(1), 169–182 (2005).
[CrossRef]

J. R. Stat. Soc., B

I. M. Johnstone and B. W. Silverman, “Wavelet Threshold Estimators for Data with Correlated Noise,” J. R. Stat. Soc., B 59(2), 319–351 (1997).
[CrossRef]

Opt. Eng.

Q. Liu, T. Zhao, W. Zhang, and F. Yu, “Image restoration based on generalized minimal residual methods with antireflective boundary conditions in a wavefront coding system,” Opt. Eng. 47(12), 127005–1 (2008).
[CrossRef]

Opt. Express

Opt. Lett.

Pattern Recognit. Lett.

J. Kautsky, J. Flusser, B. Zitová, and S. Simberová, “A new wavelet-based measure of image focus,” Pattern Recognit. Lett. 23(14), 1785–1794 (2002).
[CrossRef]

SIAM J. Matrix Anal. Appl.

J. G. Nagy, M. K. Ng, and L. Perrone, “Kronecker Product Approximations for Image Restoration with Reflexive Boundary Conditions,” SIAM J. Matrix Anal. Appl. 25(3), 829–841 (2003).
[CrossRef]

Other

J. van der Gracht, J. Nagy, V. Pauca, and R. Plemmons, “Iterative restoration of wavefront coded imagery for focus invariance,” in Integrated Computational Imaging Systems, OSA Technical Digest Series (2001).

G. Deng, and L. W. Cahill, “An adaptive Gaussian filter for noise reduction and edge detection, ” Nuclear Science Symposium and Medical Imaging Conference, IEEE Conference Record, 3, 1615–1619 (1993).

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Figures (5)

Fig. 1
Fig. 1

(a) Cameraman image. (b) DWT of the cameraman image using a Daubechies filter with l = 2 and (c) schematic illustration of a 2-level DWT.

Fig. 2
Fig. 2

Normalized variation of MADS applied to the cameraman image with 0≤ W 20 r ≤5λ for (a) SNR = 80dB and (b) SNR = 40dB, for W 20 = 0.31575λ, 1.39658λ, 1.80218λ, 2.76166λ and 4.30275λ.

Fig. 3
Fig. 3

Average of |W 20- W ˜ 20 r | for the five arbitrary W 20 and nine images as a function of SNR. The solid black curve shows the average of the nine image-specific curves.

Fig. 4
Fig. 4

Images of (a) boat, (b) Lena, (c) man (d) mandrill, (e) plastic, (f) spoke target, (g) straws and (h) US air force test chart.

Fig. 5
Fig. 5

Average of |W 20- W ˜ 20 r | for the five arbitrary W 20 and the cameraman image as a function of the amplitude, α, of the pupil-plane phase function.

Equations (4)

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

W ˜ 20 r   = Argmin W 20 { [ i ( W 20 r ) ] } ,
W ˜ 20 r   = Argmin W 20 { [ 1 [ H * ( W 20 r ) H ( W 20 ) | H ( W 20 r ) | 2 + K I diff ] ] } ,
(i( W 20 r ))  = MAD { H L 2 , 1 ( G ( i ( W 20 r ) ) ) } + MAD { L H 2 , 1 ( G ( i ( W 20 r ) ) ) }
W ˜ 20 r   = Argmin W 20 { MAD [ H L 2 , 1 { G ( 1 [ H * ( W 20 r ) H ( W 20 ) | H ( W 20 r ) | 2 + K I diff ] ) } ]                            + MAD [ H L 2 , 1 { G ( 1 [ H * ( W 20 r ) H ( W 20 ) | H ( W 20 r ) | 2 + K I diff ] ) } ] }

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