Abstract

The performance of uniform and nonuniform detector arrays for application to the PANOPTES (processing arrays of Nyquist-limited observations to produce a thin electro-optic sensor) flat camera design is analyzed for measurement noise environments including quantization noise and Gaussian and Poisson processes. Image data acquired from a commercial camera with 8  bit and 14  bit output options are analyzed, and estimated noise levels are computed. Noise variances estimated from the measurement values are used in the optimal linear estimators for superresolution image reconstruction.

© 2008 2008 Optical Society of America

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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]
  13. H.-B. Lan, S. L. Wood, M. P. Christensen, and D. Rajan, “Benefits of optical system diversity for multiplexed image reconstruction,” Appl. Opt. 45, 2859-2870 (2006).
    [CrossRef] [PubMed]
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  18. S. Mitra, Digital Signal Processing, 3rd ed. (Prentice-Hall, 2006).
  19. A. Jain, Fundamentals of Digital Image Processing (Prentice-Hall, 1989).

2006 (4)

2004 (2)

2001 (2)

J. Tanida, T. Kumagai, K. Yamada, S. Miyatake, K. Ishida, T. Morimoto, N. Kondou, D. Miyazaki, and Y. Ichioka, “Thin observation module by bound optics (TOMBO): concept and experimental verification,” Appl. Opt. 40, 1806-1813 (2001).
[CrossRef]

M. Elad and Y. Hel-Or, “A fast super-resolution reconstruction algorithm for pure translational motion and common space invariant blur,” IEEE Trans. Image Process. 10, 1187-1193(2001).
[CrossRef]

1997 (1)

M. Elad and A. Feuer, “Restoration of a single superresolution image from several blurred, noisy, and undersampled measured images,” IEEE Trans. Image Process. 6, 1646-1658(1997).
[CrossRef]

Bhakta, V.

Bracewell, R. N.

R. N. Bracewell, Two-Dimensional Imaging (Prentice-Hall, 1995).

Cho, Z.-H.

Z.-H. Cho, J. P. Jones, and M. Singh, Foundations of Medical Imaging (Wiley, 1993).

Christensen, M.

S. L. Wood, Hsueh-Ban Lan, D. Rajan, and M. Christensen, “Improved multiplexed image reconstruction performance through optical system diversity design,” IEEE International Conference on Image Processing (IEEE, 2006), p. 2717.
[CrossRef]

Christensen, M. P.

M. P. Christensen, V. Bhakta, D. Rajan, S. C. Douglas, S. L. Wood, and M. W. Haney, “Adaptive flat multiresolution multiplexed computational imaging architecture utilizing micromirror arrays to steer subimager field of views,” Appl. Opt. 45, 2884-2892 (2006).
[CrossRef] [PubMed]

H.-B. Lan, S. L. Wood, M. P. Christensen, and D. Rajan, “Benefits of optical system diversity for multiplexed image reconstruction,” Appl. Opt. 45, 2859-2870 (2006).
[CrossRef] [PubMed]

S. L. Wood, G. Yang, M. P. Christensen, and D. Rajan, “Effect of measurement precision on super-resolution image reconstruction”, presented at the OSA Topical Meeting on Computational Optical Sensing and Imaging (COSI), Vancouver, British Columbia, 18-20 June 2007..

S. L. Wood, B. J. Smithson, D. Rajan, and M. P. Christensen, “Performance of a MVE algorithm for compound eye image reconstruction using lens diversity,” IEEE International Conference on Acoustics, Speech and Signal Processing (IEEE, 2005), Vol. II, pp. 593-596.

Douglas, S. C.

Elad, M.

S. Farsiu, D. Robinson, M. Elad, and P. Milanfar, “Fast and robust multiframe super-resolution, ” IEEE Trans. Image Process. 13, 1327-1344 (2004).
[CrossRef]

M. Elad and Y. Hel-Or, “A fast super-resolution reconstruction algorithm for pure translational motion and common space invariant blur,” IEEE Trans. Image Process. 10, 1187-1193(2001).
[CrossRef]

M. Elad and A. Feuer, “Restoration of a single superresolution image from several blurred, noisy, and undersampled measured images,” IEEE Trans. Image Process. 6, 1646-1658(1997).
[CrossRef]

Farsiu, S.

D. Robinson, S. Farsiu, and P. Milanfar, “Optimal registration of aliased images using variable projection with applications to superresolution ,” Comput. J. (April/May 2007).
[CrossRef]

S. Farsiu, D. Robinson, M. Elad, and P. Milanfar, “Fast and robust multiframe super-resolution, ” IEEE Trans. Image Process. 13, 1327-1344 (2004).
[CrossRef]

Feuer, A.

M. Elad and A. Feuer, “Restoration of a single superresolution image from several blurred, noisy, and undersampled measured images,” IEEE Trans. Image Process. 6, 1646-1658(1997).
[CrossRef]

Haney, M. W.

Hel-Or, Y.

M. Elad and Y. Hel-Or, “A fast super-resolution reconstruction algorithm for pure translational motion and common space invariant blur,” IEEE Trans. Image Process. 10, 1187-1193(2001).
[CrossRef]

Ichioka, Y.

Ishida, K.

Jain, A.

A. Jain, Fundamentals of Digital Image Processing (Prentice-Hall, 1989).

Jones, J. P.

Z.-H. Cho, J. P. Jones, and M. Singh, Foundations of Medical Imaging (Wiley, 1993).

Kitamura, Y.

Kondou, N.

Kumagai, T.

Lan, H.-B.

Lan, Hsueh-Ban

S. L. Wood, Hsueh-Ban Lan, D. Rajan, and M. Christensen, “Improved multiplexed image reconstruction performance through optical system diversity design,” IEEE International Conference on Image Processing (IEEE, 2006), p. 2717.
[CrossRef]

Macovski, A.

A. Macovski, Medical Imaging Systems (Prentice-Hall, 1983).

Masaki, Y.

Milanfar, P.

D. Robinson, S. Farsiu, and P. Milanfar, “Optimal registration of aliased images using variable projection with applications to superresolution ,” Comput. J. (April/May 2007).
[CrossRef]

S. Farsiu, D. Robinson, M. Elad, and P. Milanfar, “Fast and robust multiframe super-resolution, ” IEEE Trans. Image Process. 13, 1327-1344 (2004).
[CrossRef]

Mitra, S.

S. Mitra, Digital Signal Processing, 3rd ed. (Prentice-Hall, 2006).

Miyamoto, M.

Miyatake, S.

Miyazaki, D.

Morimoto, T.

Nitta, K.

Rajan, D.

M. P. Christensen, V. Bhakta, D. Rajan, S. C. Douglas, S. L. Wood, and M. W. Haney, “Adaptive flat multiresolution multiplexed computational imaging architecture utilizing micromirror arrays to steer subimager field of views,” Appl. Opt. 45, 2884-2892 (2006).
[CrossRef] [PubMed]

H.-B. Lan, S. L. Wood, M. P. Christensen, and D. Rajan, “Benefits of optical system diversity for multiplexed image reconstruction,” Appl. Opt. 45, 2859-2870 (2006).
[CrossRef] [PubMed]

S. L. Wood, B. J. Smithson, D. Rajan, and M. P. Christensen, “Performance of a MVE algorithm for compound eye image reconstruction using lens diversity,” IEEE International Conference on Acoustics, Speech and Signal Processing (IEEE, 2005), Vol. II, pp. 593-596.

S. L. Wood, G. Yang, M. P. Christensen, and D. Rajan, “Effect of measurement precision on super-resolution image reconstruction”, presented at the OSA Topical Meeting on Computational Optical Sensing and Imaging (COSI), Vancouver, British Columbia, 18-20 June 2007..

S. L. Wood, Hsueh-Ban Lan, D. Rajan, and M. Christensen, “Improved multiplexed image reconstruction performance through optical system diversity design,” IEEE International Conference on Image Processing (IEEE, 2006), p. 2717.
[CrossRef]

Robinson, D.

D. Robinson, S. Farsiu, and P. Milanfar, “Optimal registration of aliased images using variable projection with applications to superresolution ,” Comput. J. (April/May 2007).
[CrossRef]

S. Farsiu, D. Robinson, M. Elad, and P. Milanfar, “Fast and robust multiframe super-resolution, ” IEEE Trans. Image Process. 13, 1327-1344 (2004).
[CrossRef]

Shogenji, R.

Singh, M.

Z.-H. Cho, J. P. Jones, and M. Singh, Foundations of Medical Imaging (Wiley, 1993).

Smithson, B. J.

S. L. Wood, B. J. Smithson, D. Rajan, and M. P. Christensen, “Performance of a MVE algorithm for compound eye image reconstruction using lens diversity,” IEEE International Conference on Acoustics, Speech and Signal Processing (IEEE, 2005), Vol. II, pp. 593-596.

Süsstrunk, S.

P. Vandewalle, S. Süsstrunk, and M. Vetterli, “A frequency domain approach to registration of aliased images with application to super-resolution, EURASIP J. Appl. Signal Process. 2006, 71459 (2006).

Tanida, J.

Vandewalle, P.

P. Vandewalle, S. Süsstrunk, and M. Vetterli, “A frequency domain approach to registration of aliased images with application to super-resolution, EURASIP J. Appl. Signal Process. 2006, 71459 (2006).

Vetterli, M.

P. Vandewalle, S. Süsstrunk, and M. Vetterli, “A frequency domain approach to registration of aliased images with application to super-resolution, EURASIP J. Appl. Signal Process. 2006, 71459 (2006).

Wood, S. L.

M. P. Christensen, V. Bhakta, D. Rajan, S. C. Douglas, S. L. Wood, and M. W. Haney, “Adaptive flat multiresolution multiplexed computational imaging architecture utilizing micromirror arrays to steer subimager field of views,” Appl. Opt. 45, 2884-2892 (2006).
[CrossRef] [PubMed]

H.-B. Lan, S. L. Wood, M. P. Christensen, and D. Rajan, “Benefits of optical system diversity for multiplexed image reconstruction,” Appl. Opt. 45, 2859-2870 (2006).
[CrossRef] [PubMed]

S. L. Wood, Hsueh-Ban Lan, D. Rajan, and M. Christensen, “Improved multiplexed image reconstruction performance through optical system diversity design,” IEEE International Conference on Image Processing (IEEE, 2006), p. 2717.
[CrossRef]

S. L. Wood, B. J. Smithson, D. Rajan, and M. P. Christensen, “Performance of a MVE algorithm for compound eye image reconstruction using lens diversity,” IEEE International Conference on Acoustics, Speech and Signal Processing (IEEE, 2005), Vol. II, pp. 593-596.

S. L. Wood, G. Yang, M. P. Christensen, and D. Rajan, “Effect of measurement precision on super-resolution image reconstruction”, presented at the OSA Topical Meeting on Computational Optical Sensing and Imaging (COSI), Vancouver, British Columbia, 18-20 June 2007..

Yamada, K.

Yang, G.

S. L. Wood, G. Yang, M. P. Christensen, and D. Rajan, “Effect of measurement precision on super-resolution image reconstruction”, presented at the OSA Topical Meeting on Computational Optical Sensing and Imaging (COSI), Vancouver, British Columbia, 18-20 June 2007..

Appl. Opt. (5)

EURASIP J. Appl. Signal Process. (1)

P. Vandewalle, S. Süsstrunk, and M. Vetterli, “A frequency domain approach to registration of aliased images with application to super-resolution, EURASIP J. Appl. Signal Process. 2006, 71459 (2006).

IEEE Trans. Image Process. (3)

M. Elad and A. Feuer, “Restoration of a single superresolution image from several blurred, noisy, and undersampled measured images,” IEEE Trans. Image Process. 6, 1646-1658(1997).
[CrossRef]

M. Elad and Y. Hel-Or, “A fast super-resolution reconstruction algorithm for pure translational motion and common space invariant blur,” IEEE Trans. Image Process. 10, 1187-1193(2001).
[CrossRef]

S. Farsiu, D. Robinson, M. Elad, and P. Milanfar, “Fast and robust multiframe super-resolution, ” IEEE Trans. Image Process. 13, 1327-1344 (2004).
[CrossRef]

Optimal registration of aliased images using variable projection with applications to superresolution (1)

D. Robinson, S. Farsiu, and P. Milanfar, “Optimal registration of aliased images using variable projection with applications to superresolution ,” Comput. J. (April/May 2007).
[CrossRef]

Other (9)

S. L. Wood, B. J. Smithson, D. Rajan, and M. P. Christensen, “Performance of a MVE algorithm for compound eye image reconstruction using lens diversity,” IEEE International Conference on Acoustics, Speech and Signal Processing (IEEE, 2005), Vol. II, pp. 593-596.

S. L. Wood, Hsueh-Ban Lan, D. Rajan, and M. Christensen, “Improved multiplexed image reconstruction performance through optical system diversity design,” IEEE International Conference on Image Processing (IEEE, 2006), p. 2717.
[CrossRef]

R. N. Bracewell, Two-Dimensional Imaging (Prentice-Hall, 1995).

A. Macovski, Medical Imaging Systems (Prentice-Hall, 1983).

Z.-H. Cho, J. P. Jones, and M. Singh, Foundations of Medical Imaging (Wiley, 1993).

S. L. Wood, G. Yang, M. P. Christensen, and D. Rajan, “Effect of measurement precision on super-resolution image reconstruction”, presented at the OSA Topical Meeting on Computational Optical Sensing and Imaging (COSI), Vancouver, British Columbia, 18-20 June 2007..

S. Mitra, Digital Signal Processing, 3rd ed. (Prentice-Hall, 2006).

A. Jain, Fundamentals of Digital Image Processing (Prentice-Hall, 1989).

S. Chaudhuri, ed. Super-Resolution Imaging (Kluwer Academic, 2001).

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Figures (6)

Fig. 1
Fig. 1

Block diagram of image acquisition and reconstruction.

Fig. 2
Fig. 2

(a) Mean value of 300 480 × 640 pixel images of 1951 U.S. Air Force resolution test chart; (b) magnified 200 × 200 pixel section of a single frame showing groups 0 and 1; (c) magnified 50 × 50 pixel section of a single frame showing groups 2 and 3.

Fig. 3
Fig. 3

(a, b) Two 50 × 50 LR images of groups 0 and 1 after resolution is reduced by a factor of 4. (c) Aligned and up-sampled 200 × 200 pixel combination of 16 LR images. (d) Comparison of vertical intensity profiles through group 0 in images in Figs.  2b and 3c and group 2 in Fig.  2c.

Fig. 4
Fig. 4

Expected error as a function of measurement variance for reconstruction matrices for four subimager geometries.

Fig. 5
Fig. 5

(a) Variance value of 300 480 × 640 images of 1951 US Air Force resolution test chart; (b) scatter plot of variance versus mean value for a typical set of 300 images from Sony camera; (c) histograms of pixel values at three pixel positions for 8 - bit and 14 - bit data.

Fig. 6
Fig. 6

(a) Single image (b) computed high resolution image from set of 20 image frames; (c) detected relative shift in pixels for 20 frames; (d) plot of vertical intensity profile through group 2 of computed image compared to two columns from a single frame.

Equations (10)

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

g = H f + η .
f ^ = f 0 + K ( g H f 0 ) ,
K = R f g ( R g g ) 1 .
K = R ^ f f H T ( H R ^ f f H T + R ^ η η ) 1 .
K z = A R ^ z z H z T ( H z R ^ z z H z T + R ^ η η ) 1 .
g = [ g I g II g III ] = [ H I H II H III ] f + η ,
K = ( H T ( R ^ η η ) 1 H + ( R ^ f f ) 1 ) 1 H T ( R ^ η η ) 1 = ( H I T ( R ^ η η I ) 1 H I + H II T ( R ^ η η II ) 1 H II + H III T ( R ^ η η III ) 1 H III + ( R ^ f f ) 1 ) 1 H T ( R ^ η η ) 1 .
E f ˜ f ˜ T = E ( f K g ) ( f K g ) T = R f f K R g f R f g K T + K R g g K T ,
E [ f ˜ f ˜ T ] = ( I K H ) E [ f f T ] ( I K H ) T + K E [ η η T ] K T = ( I K H ) R f f ( I K H ) T + K R η η K T .
K R ^ f f H T ( R ^ η η ) 1 .

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