Abstract

We describe a new algorithm for superresolving a binary object from multiple undersampled low-resolution (LR) images that are degraded by diffraction-limited optical blur, detector blur, and additive white Gaussian noise. Two-dimensional distributed data detection (2D4) is an iterative algorithm that employs a message-passing technique for estimating the object pixel likelihoods. We present a novel non-training-based complexity-reduction technique that makes the algorithm suitable even for channels with support size as large as 5×5 object pixels. We compare the performance and computational complexity of 2D4 with that of iterative backprojection (IBP). In an imaging system with an optical blur spot matched to the object pixel size, 2×2 undersampled measurement pixels, and four LR images, the reconstruction error measured in terms of the number of pixel mismatches for 2D4 is 300 times smaller than that for IBP at a signal-to-noise ratio of 38 dB.

© 2007 Optical Society of America

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  1. K. Aizawa, T. Komatsu, and T. Saito, "A scheme for acquiring very high resolution images using multiple cameras," in IEEE International Conference on Acoustics, Speech, and Signal Processing (IEEE, 1992), pp. 23-26.
  2. R. Tsai and T. Huang, "Multiframe image restoration and registration," in Advances in Computer Vision and Image Processing (JAI, 1984), pp. 317-339.
  3. H. Ur and D. Gross, "Improved resolution from subpixel shifted pictures," CVGIP: Graph. Models Image Process. 54, 181-186 (1992).
    [CrossRef]
  4. M. Irani and S. Peleg, "Improving resolution by image registration," CVGIP: Graph. Models Image Process. 53, 231-239 (1991).
    [CrossRef]
  5. S. Chaudhuri, ed., Super-Resolution Imaging (Kluwer, 2001).
  6. R. Hardie, K. Bernard, and E. Armstrong, "Joint MAP registration and high-resolution image estimation using a sequence of undersampled images," IEEE Trans. Image Process. 6, 1621-1633 (1997).
    [CrossRef]
  7. P. Shankar, W. Hassenplaugh, R. Morrison, R. Stack, and M. Neifeld, "Multiaperture imaging," Appl. Opt. 45, 2871-2883 (2006).
    [CrossRef]
  8. P. Vandewalle, L. Sbaiz, J. Vandewalle, and M. Vetterli, "How to take advantage of aliasing in bandlimited signals," in IEEE Conference on Accoustics, Speech, and Signal Processing (IEEE, 2004), pp. 948-951.
  9. H. Andrews and B. Hunt, Digital Image Restoration (Prentice-Hall, 1977).
  10. R. Molina, J. Mateos, A. Katsaggelos, and M. Vega, "Bayesian multichannel image restoration using compound Gauss-Markov random fields," IEEE Trans. Image Process. 12, 1642-1654 (2003).
    [CrossRef]
  11. R. Hardie, K. Barnard, J. Bognar, E. Armstrong, and E. Watson, "High-resolution image reconstruction from a sequence of rotated and translated frames and its application to an infrared imaging system," Opt. Eng. 37, 247-260 (1998).
    [CrossRef]
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    [CrossRef]
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  16. M. A. Turk and A. P. Pentland, "Face recognition using eigenfaces," in IEEE Proceedings on Computer Vision and Pattern Recognition (IEEE, 1991), pp. 586-591.
  17. X. Chen, K. Chugg, and M. Neifeld, "Near-optimal parallel distributed data detection for page-oriented optical memories," IEEE J. Sel. Top. Quantum Electron. 4, 866-879 (1998).
    [CrossRef]
  18. K. Chugg, A. Anastasopoulos, and X. Chen, Iterative Detection: Adaptivity, Complexity Reduction, and Applications (Kluwer Academic, 2001).
  19. H. Barrett and K. Myers, Foundations of Image Science (Wiley, 2004).
  20. C. Berrou, A. Glavieux, and P. Thitimajshima, "Near Shannon limit error-correcting coding and decoding: Turbo-codes(1)," in Proceedings of the IEEE International Conference on Communications (IEEE, 1993), pp. 1064-1070.
  21. R. McEliece, D. MacKay, and J. Cheng, "Turbo decoding as an instance of Pearl's 'belief propagation' algorithm," IEEE J. Sel. Areas Commun. 16, 140-152 (1998).
    [CrossRef]
  22. F. Kschischang, B. Frey, and H. Loeliger, "Factor graphs and the sum-product algorithm," IEEE Trans. Inf. Theory 47, 498-519 (2001).
    [CrossRef]

2006 (1)

2003 (1)

R. Molina, J. Mateos, A. Katsaggelos, and M. Vega, "Bayesian multichannel image restoration using compound Gauss-Markov random fields," IEEE Trans. Image Process. 12, 1642-1654 (2003).
[CrossRef]

2002 (2)

S. Baker and T. Kanade, "Limits on super-resolution and how to break them," IEEE Trans. Pattern Anal. Mach. Intell. 24, 1167-1183 (2002).
[CrossRef]

M. Neifeld and Y. Wu, "Parallell image restoration with a two-dimensional likelihood-based algorithm," Appl. Opt. 41, 4812-4824 (2002).

2001 (1)

F. Kschischang, B. Frey, and H. Loeliger, "Factor graphs and the sum-product algorithm," IEEE Trans. Inf. Theory 47, 498-519 (2001).
[CrossRef]

2000 (2)

1998 (3)

X. Chen, K. Chugg, and M. Neifeld, "Near-optimal parallel distributed data detection for page-oriented optical memories," IEEE J. Sel. Top. Quantum Electron. 4, 866-879 (1998).
[CrossRef]

R. McEliece, D. MacKay, and J. Cheng, "Turbo decoding as an instance of Pearl's 'belief propagation' algorithm," IEEE J. Sel. Areas Commun. 16, 140-152 (1998).
[CrossRef]

R. Hardie, K. Barnard, J. Bognar, E. Armstrong, and E. Watson, "High-resolution image reconstruction from a sequence of rotated and translated frames and its application to an infrared imaging system," Opt. Eng. 37, 247-260 (1998).
[CrossRef]

1997 (1)

R. Hardie, K. Bernard, and E. Armstrong, "Joint MAP registration and high-resolution image estimation using a sequence of undersampled images," IEEE Trans. Image Process. 6, 1621-1633 (1997).
[CrossRef]

1992 (1)

H. Ur and D. Gross, "Improved resolution from subpixel shifted pictures," CVGIP: Graph. Models Image Process. 54, 181-186 (1992).
[CrossRef]

1991 (1)

M. Irani and S. Peleg, "Improving resolution by image registration," CVGIP: Graph. Models Image Process. 53, 231-239 (1991).
[CrossRef]

Aizawa, K.

K. Aizawa, T. Komatsu, and T. Saito, "A scheme for acquiring very high resolution images using multiple cameras," in IEEE International Conference on Acoustics, Speech, and Signal Processing (IEEE, 1992), pp. 23-26.

Anastasopoulos, A.

K. Chugg, A. Anastasopoulos, and X. Chen, Iterative Detection: Adaptivity, Complexity Reduction, and Applications (Kluwer Academic, 2001).

Andrews, H.

H. Andrews and B. Hunt, Digital Image Restoration (Prentice-Hall, 1977).

Armstrong, E.

R. Hardie, K. Barnard, J. Bognar, E. Armstrong, and E. Watson, "High-resolution image reconstruction from a sequence of rotated and translated frames and its application to an infrared imaging system," Opt. Eng. 37, 247-260 (1998).
[CrossRef]

R. Hardie, K. Bernard, and E. Armstrong, "Joint MAP registration and high-resolution image estimation using a sequence of undersampled images," IEEE Trans. Image Process. 6, 1621-1633 (1997).
[CrossRef]

Baker, S.

S. Baker and T. Kanade, "Limits on super-resolution and how to break them," IEEE Trans. Pattern Anal. Mach. Intell. 24, 1167-1183 (2002).
[CrossRef]

Barnard, K.

R. Hardie, K. Barnard, J. Bognar, E. Armstrong, and E. Watson, "High-resolution image reconstruction from a sequence of rotated and translated frames and its application to an infrared imaging system," Opt. Eng. 37, 247-260 (1998).
[CrossRef]

Barrett, H.

H. Barrett and K. Myers, Foundations of Image Science (Wiley, 2004).

Bernard, K.

R. Hardie, K. Bernard, and E. Armstrong, "Joint MAP registration and high-resolution image estimation using a sequence of undersampled images," IEEE Trans. Image Process. 6, 1621-1633 (1997).
[CrossRef]

Berrou, C.

C. Berrou, A. Glavieux, and P. Thitimajshima, "Near Shannon limit error-correcting coding and decoding: Turbo-codes(1)," in Proceedings of the IEEE International Conference on Communications (IEEE, 1993), pp. 1064-1070.

Bognar, J.

R. Hardie, K. Barnard, J. Bognar, E. Armstrong, and E. Watson, "High-resolution image reconstruction from a sequence of rotated and translated frames and its application to an infrared imaging system," Opt. Eng. 37, 247-260 (1998).
[CrossRef]

Chaudhuri, S.

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

Chen, X.

X. Chen, K. Chugg, and M. Neifeld, "Near-optimal parallel distributed data detection for page-oriented optical memories," IEEE J. Sel. Top. Quantum Electron. 4, 866-879 (1998).
[CrossRef]

K. Chugg, A. Anastasopoulos, and X. Chen, Iterative Detection: Adaptivity, Complexity Reduction, and Applications (Kluwer Academic, 2001).

Cheng, J.

R. McEliece, D. MacKay, and J. Cheng, "Turbo decoding as an instance of Pearl's 'belief propagation' algorithm," IEEE J. Sel. Areas Commun. 16, 140-152 (1998).
[CrossRef]

Chugg, K.

X. Chen, K. Chugg, and M. Neifeld, "Near-optimal parallel distributed data detection for page-oriented optical memories," IEEE J. Sel. Top. Quantum Electron. 4, 866-879 (1998).
[CrossRef]

K. Chugg, A. Anastasopoulos, and X. Chen, Iterative Detection: Adaptivity, Complexity Reduction, and Applications (Kluwer Academic, 2001).

Frey, B.

F. Kschischang, B. Frey, and H. Loeliger, "Factor graphs and the sum-product algorithm," IEEE Trans. Inf. Theory 47, 498-519 (2001).
[CrossRef]

Glavieux, A.

C. Berrou, A. Glavieux, and P. Thitimajshima, "Near Shannon limit error-correcting coding and decoding: Turbo-codes(1)," in Proceedings of the IEEE International Conference on Communications (IEEE, 1993), pp. 1064-1070.

Gross, D.

H. Ur and D. Gross, "Improved resolution from subpixel shifted pictures," CVGIP: Graph. Models Image Process. 54, 181-186 (1992).
[CrossRef]

Hardie, R.

R. Hardie, K. Barnard, J. Bognar, E. Armstrong, and E. Watson, "High-resolution image reconstruction from a sequence of rotated and translated frames and its application to an infrared imaging system," Opt. Eng. 37, 247-260 (1998).
[CrossRef]

R. Hardie, K. Bernard, and E. Armstrong, "Joint MAP registration and high-resolution image estimation using a sequence of undersampled images," IEEE Trans. Image Process. 6, 1621-1633 (1997).
[CrossRef]

Hassenplaugh, W.

Huang, T.

R. Tsai and T. Huang, "Multiframe image restoration and registration," in Advances in Computer Vision and Image Processing (JAI, 1984), pp. 317-339.

Hunt, B.

Irani, M.

M. Irani and S. Peleg, "Improving resolution by image registration," CVGIP: Graph. Models Image Process. 53, 231-239 (1991).
[CrossRef]

Kanade, T.

S. Baker and T. Kanade, "Limits on super-resolution and how to break them," IEEE Trans. Pattern Anal. Mach. Intell. 24, 1167-1183 (2002).
[CrossRef]

Katsaggelos, A.

R. Molina, J. Mateos, A. Katsaggelos, and M. Vega, "Bayesian multichannel image restoration using compound Gauss-Markov random fields," IEEE Trans. Image Process. 12, 1642-1654 (2003).
[CrossRef]

Komatsu, T.

K. Aizawa, T. Komatsu, and T. Saito, "A scheme for acquiring very high resolution images using multiple cameras," in IEEE International Conference on Acoustics, Speech, and Signal Processing (IEEE, 1992), pp. 23-26.

Kschischang, F.

F. Kschischang, B. Frey, and H. Loeliger, "Factor graphs and the sum-product algorithm," IEEE Trans. Inf. Theory 47, 498-519 (2001).
[CrossRef]

Loeliger, H.

F. Kschischang, B. Frey, and H. Loeliger, "Factor graphs and the sum-product algorithm," IEEE Trans. Inf. Theory 47, 498-519 (2001).
[CrossRef]

MacKay, D.

R. McEliece, D. MacKay, and J. Cheng, "Turbo decoding as an instance of Pearl's 'belief propagation' algorithm," IEEE J. Sel. Areas Commun. 16, 140-152 (1998).
[CrossRef]

Marcellin, M.

Mateos, J.

R. Molina, J. Mateos, A. Katsaggelos, and M. Vega, "Bayesian multichannel image restoration using compound Gauss-Markov random fields," IEEE Trans. Image Process. 12, 1642-1654 (2003).
[CrossRef]

McEliece, R.

R. McEliece, D. MacKay, and J. Cheng, "Turbo decoding as an instance of Pearl's 'belief propagation' algorithm," IEEE J. Sel. Areas Commun. 16, 140-152 (1998).
[CrossRef]

Miller, C.

Molina, R.

R. Molina, J. Mateos, A. Katsaggelos, and M. Vega, "Bayesian multichannel image restoration using compound Gauss-Markov random fields," IEEE Trans. Image Process. 12, 1642-1654 (2003).
[CrossRef]

Morrison, R.

Myers, K.

H. Barrett and K. Myers, Foundations of Image Science (Wiley, 2004).

Neifeld, M.

Peleg, S.

M. Irani and S. Peleg, "Improving resolution by image registration," CVGIP: Graph. Models Image Process. 53, 231-239 (1991).
[CrossRef]

Pentland, A. P.

M. A. Turk and A. P. Pentland, "Face recognition using eigenfaces," in IEEE Proceedings on Computer Vision and Pattern Recognition (IEEE, 1991), pp. 586-591.

Saito, T.

K. Aizawa, T. Komatsu, and T. Saito, "A scheme for acquiring very high resolution images using multiple cameras," in IEEE International Conference on Acoustics, Speech, and Signal Processing (IEEE, 1992), pp. 23-26.

Sbaiz, L.

P. Vandewalle, L. Sbaiz, J. Vandewalle, and M. Vetterli, "How to take advantage of aliasing in bandlimited signals," in IEEE Conference on Accoustics, Speech, and Signal Processing (IEEE, 2004), pp. 948-951.

Shankar, P.

Stack, R.

Thitimajshima, P.

C. Berrou, A. Glavieux, and P. Thitimajshima, "Near Shannon limit error-correcting coding and decoding: Turbo-codes(1)," in Proceedings of the IEEE International Conference on Communications (IEEE, 1993), pp. 1064-1070.

Tsai, R.

R. Tsai and T. Huang, "Multiframe image restoration and registration," in Advances in Computer Vision and Image Processing (JAI, 1984), pp. 317-339.

Turk, M. A.

M. A. Turk and A. P. Pentland, "Face recognition using eigenfaces," in IEEE Proceedings on Computer Vision and Pattern Recognition (IEEE, 1991), pp. 586-591.

Ur, H.

H. Ur and D. Gross, "Improved resolution from subpixel shifted pictures," CVGIP: Graph. Models Image Process. 54, 181-186 (1992).
[CrossRef]

Vandewalle, J.

P. Vandewalle, L. Sbaiz, J. Vandewalle, and M. Vetterli, "How to take advantage of aliasing in bandlimited signals," in IEEE Conference on Accoustics, Speech, and Signal Processing (IEEE, 2004), pp. 948-951.

Vandewalle, P.

P. Vandewalle, L. Sbaiz, J. Vandewalle, and M. Vetterli, "How to take advantage of aliasing in bandlimited signals," in IEEE Conference on Accoustics, Speech, and Signal Processing (IEEE, 2004), pp. 948-951.

Vega, M.

R. Molina, J. Mateos, A. Katsaggelos, and M. Vega, "Bayesian multichannel image restoration using compound Gauss-Markov random fields," IEEE Trans. Image Process. 12, 1642-1654 (2003).
[CrossRef]

Vetterli, M.

P. Vandewalle, L. Sbaiz, J. Vandewalle, and M. Vetterli, "How to take advantage of aliasing in bandlimited signals," in IEEE Conference on Accoustics, Speech, and Signal Processing (IEEE, 2004), pp. 948-951.

Watson, E.

R. Hardie, K. Barnard, J. Bognar, E. Armstrong, and E. Watson, "High-resolution image reconstruction from a sequence of rotated and translated frames and its application to an infrared imaging system," Opt. Eng. 37, 247-260 (1998).
[CrossRef]

Wu, Y.

Xuan, R.

Appl. Opt. (3)

CVGIP: Graph. Models Image Process. (2)

H. Ur and D. Gross, "Improved resolution from subpixel shifted pictures," CVGIP: Graph. Models Image Process. 54, 181-186 (1992).
[CrossRef]

M. Irani and S. Peleg, "Improving resolution by image registration," CVGIP: Graph. Models Image Process. 53, 231-239 (1991).
[CrossRef]

IEEE J. Sel. Areas Commun. (1)

R. McEliece, D. MacKay, and J. Cheng, "Turbo decoding as an instance of Pearl's 'belief propagation' algorithm," IEEE J. Sel. Areas Commun. 16, 140-152 (1998).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

X. Chen, K. Chugg, and M. Neifeld, "Near-optimal parallel distributed data detection for page-oriented optical memories," IEEE J. Sel. Top. Quantum Electron. 4, 866-879 (1998).
[CrossRef]

IEEE Trans. Image Process. (2)

R. Hardie, K. Bernard, and E. Armstrong, "Joint MAP registration and high-resolution image estimation using a sequence of undersampled images," IEEE Trans. Image Process. 6, 1621-1633 (1997).
[CrossRef]

R. Molina, J. Mateos, A. Katsaggelos, and M. Vega, "Bayesian multichannel image restoration using compound Gauss-Markov random fields," IEEE Trans. Image Process. 12, 1642-1654 (2003).
[CrossRef]

IEEE Trans. Inf. Theory (1)

F. Kschischang, B. Frey, and H. Loeliger, "Factor graphs and the sum-product algorithm," IEEE Trans. Inf. Theory 47, 498-519 (2001).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell. (1)

S. Baker and T. Kanade, "Limits on super-resolution and how to break them," IEEE Trans. Pattern Anal. Mach. Intell. 24, 1167-1183 (2002).
[CrossRef]

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

Opt. Eng. (1)

R. Hardie, K. Barnard, J. Bognar, E. Armstrong, and E. Watson, "High-resolution image reconstruction from a sequence of rotated and translated frames and its application to an infrared imaging system," Opt. Eng. 37, 247-260 (1998).
[CrossRef]

Other (9)

P. Vandewalle, L. Sbaiz, J. Vandewalle, and M. Vetterli, "How to take advantage of aliasing in bandlimited signals," in IEEE Conference on Accoustics, Speech, and Signal Processing (IEEE, 2004), pp. 948-951.

H. Andrews and B. Hunt, Digital Image Restoration (Prentice-Hall, 1977).

K. Aizawa, T. Komatsu, and T. Saito, "A scheme for acquiring very high resolution images using multiple cameras," in IEEE International Conference on Acoustics, Speech, and Signal Processing (IEEE, 1992), pp. 23-26.

R. Tsai and T. Huang, "Multiframe image restoration and registration," in Advances in Computer Vision and Image Processing (JAI, 1984), pp. 317-339.

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

M. A. Turk and A. P. Pentland, "Face recognition using eigenfaces," in IEEE Proceedings on Computer Vision and Pattern Recognition (IEEE, 1991), pp. 586-591.

K. Chugg, A. Anastasopoulos, and X. Chen, Iterative Detection: Adaptivity, Complexity Reduction, and Applications (Kluwer Academic, 2001).

H. Barrett and K. Myers, Foundations of Image Science (Wiley, 2004).

C. Berrou, A. Glavieux, and P. Thitimajshima, "Near Shannon limit error-correcting coding and decoding: Turbo-codes(1)," in Proceedings of the IEEE International Conference on Communications (IEEE, 1993), pp. 1064-1070.

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