Abstract

In this paper, we address the geometrical resolution limitation of an imaging sensor caused by the size of its pixels yielding insufficient spatial sampling of the image. The spatial blurring that is caused due to inadequate sampling can be resolved by placing a two-dimensional binary random mask in an intermediate image plane and shifting it along one direction while keeping the sensor as well as all other optical components fixed. Out of the set of images that are captured, a high resolution image can be decoded. In addition, this approach allows improved robustness to spatial noise.

© 2011 Optical Society of America

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  1. P. Cheeseman, B. Kanefsky, R. Kraft, J. Stutz, and R. Hanson, “Super-resolved surface reconstruction from multiple images,” in Maximum Entropy and Bayesian Methods, G.R.Heidbreder, ed. (Kluwer, 1996), pp. 293–308.
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    [CrossRef]
  3. B. C. Tom and A. K. Katsaggelos, “Reconstruction of a high-resolution image from multiple-degraded misregistered low-resolution images,” Proc. SPIE 2308, 971–981 (1994).
    [CrossRef]
  4. H. Stark and P. Oskoui, “High-resolution image recovery from image-plane arrays using convex projections,” J. Opt. Soc. Am. A 6, 1715–1726 (1989).
    [CrossRef]
  5. F. W. Wheeler, R. T. Hoctor, and E. B. Barrett, “Super-resolution image synthesis using projections onto convex sets in the frequency domain,” Proc. SPIE , 5674, 479–490 (2005).
    [CrossRef]
  6. M. Irani and S. Peleg, “Motion analysis for image enhancement: resolution, occlusion, and transparency,” J. Visual Commun. Image Represent 4, 324–335 (1993).
    [CrossRef]
  7. Z. Zalevsky, D. Mendlovic, and E. Marom, “Special sensor masking for exceeding system geometrical resolving power,” Opt. Eng. 39, 1936–1942 (2000).
    [CrossRef]
  8. Z. Zalevsky, N. Shamir, and D. Mendlovic, “Geometrical super-resolution in infra-red sensor: experimental verification,” Opt. Eng. 43, 1401–1406 (2004).
    [CrossRef]
  9. A. Borkowski, Z. Zalevsky, and B. Javidi, “Geometrical super resolved imaging using non periodic spatial masking,” J. Opt. Soc. Am. A 26, 589–601 (2009).
    [CrossRef]
  10. I. ul-Haq and A. A. Mudassar, “Geometrical superresolution of CCD-pixel,” Opt. Lett. 35, 2705–2707 (2010).
    [CrossRef]
  11. M. Sohail and A. A. Mudassar, “Geometric superresolution by using an optical mask,” Appl. Opt. 49, 3000–3005 (2010).
    [CrossRef]
  12. K. A. Nugent and B. Luther-Davies, “Penumbral imaging of high energy x-rays from laser-produced plasmas,” Opt. Commun. 49, 393–396 (1984).
    [CrossRef]
  13. K. A. Nugent, “Coded aperture imaging: a Fourier space analysis,” Appl. Opt. 26, 563–569 (1987).
    [CrossRef]
  14. Z. Zalevsky, J. Solomon, and D. Mendlovic, “Geometrical super resolution using code division multiplexing,” Appl. Opt. 42, 32–40 (2005).
  15. C. F. Van Loan, “The ubiquitous Kronecker product,” J. Comp. Appl. Math. 123, 85–100 (2000).
    [CrossRef]
  16. R. M. Gray, “Toeplitz and circulant matrices: a review,” Found. Trends Commun. Inf. Theory 2, 155–239 (2005).
    [CrossRef]
  17. H. Lev-Ari, “Efficient solution of linear matrix equations with application to multistatic antenna array processing,” Commun. Inf. Syst. 5, 123–130 (2005).
  18. G. H. Golub and C. F. Van Loan, Matrix Computations, 3rd ed. (Johns Hopkins, 1996), pp. 257–258.
  19. G. H. Golub, M. Heath, and G. Wahba, “Generalized cross-validation as a method for choosing a good ridge parameter,” Technometrics 21, 215–223 (1979).
    [CrossRef]
  20. G. H. Golub and U. von Matt, “Generalized cross-validation for large scale problems,” in Proceedings of the Second International Workshop on Recent Advances in Total Least Squares Techniques and Errors-in-Variables Modeling, S.Van Huffel, ed. (Society for Industrial and Applied Mathematics, 1997), pp. 139–148.
  21. A. Bouhamidi and K. Jbilou, “Sylvester Tikhonov-regularization methods in image restoration,” J. Comput. Appl. Math. 206, 86–98 (2007).
    [CrossRef]

2010

2009

2007

A. Bouhamidi and K. Jbilou, “Sylvester Tikhonov-regularization methods in image restoration,” J. Comput. Appl. Math. 206, 86–98 (2007).
[CrossRef]

2005

R. M. Gray, “Toeplitz and circulant matrices: a review,” Found. Trends Commun. Inf. Theory 2, 155–239 (2005).
[CrossRef]

H. Lev-Ari, “Efficient solution of linear matrix equations with application to multistatic antenna array processing,” Commun. Inf. Syst. 5, 123–130 (2005).

F. W. Wheeler, R. T. Hoctor, and E. B. Barrett, “Super-resolution image synthesis using projections onto convex sets in the frequency domain,” Proc. SPIE , 5674, 479–490 (2005).
[CrossRef]

Z. Zalevsky, J. Solomon, and D. Mendlovic, “Geometrical super resolution using code division multiplexing,” Appl. Opt. 42, 32–40 (2005).

2004

Z. Zalevsky, N. Shamir, and D. Mendlovic, “Geometrical super-resolution in infra-red sensor: experimental verification,” Opt. Eng. 43, 1401–1406 (2004).
[CrossRef]

2000

C. F. Van Loan, “The ubiquitous Kronecker product,” J. Comp. Appl. Math. 123, 85–100 (2000).
[CrossRef]

Z. Zalevsky, D. Mendlovic, and E. Marom, “Special sensor masking for exceeding system geometrical resolving power,” Opt. Eng. 39, 1936–1942 (2000).
[CrossRef]

1997

R. C. Hardie, K. J. Barnard, and E. 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]

1994

B. C. Tom and A. K. Katsaggelos, “Reconstruction of a high-resolution image from multiple-degraded misregistered low-resolution images,” Proc. SPIE 2308, 971–981 (1994).
[CrossRef]

1993

M. Irani and S. Peleg, “Motion analysis for image enhancement: resolution, occlusion, and transparency,” J. Visual Commun. Image Represent 4, 324–335 (1993).
[CrossRef]

1989

1987

1984

K. A. Nugent and B. Luther-Davies, “Penumbral imaging of high energy x-rays from laser-produced plasmas,” Opt. Commun. 49, 393–396 (1984).
[CrossRef]

1979

G. H. Golub, M. Heath, and G. Wahba, “Generalized cross-validation as a method for choosing a good ridge parameter,” Technometrics 21, 215–223 (1979).
[CrossRef]

Armstrong, E. E.

R. C. Hardie, K. J. Barnard, and E. 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]

Barnard, K. J.

R. C. Hardie, K. J. Barnard, and E. 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]

Barrett, E. B.

F. W. Wheeler, R. T. Hoctor, and E. B. Barrett, “Super-resolution image synthesis using projections onto convex sets in the frequency domain,” Proc. SPIE , 5674, 479–490 (2005).
[CrossRef]

Borkowski, A.

Bouhamidi, A.

A. Bouhamidi and K. Jbilou, “Sylvester Tikhonov-regularization methods in image restoration,” J. Comput. Appl. Math. 206, 86–98 (2007).
[CrossRef]

Cheeseman, P.

P. Cheeseman, B. Kanefsky, R. Kraft, J. Stutz, and R. Hanson, “Super-resolved surface reconstruction from multiple images,” in Maximum Entropy and Bayesian Methods, G.R.Heidbreder, ed. (Kluwer, 1996), pp. 293–308.

Golub, G. H.

G. H. Golub, M. Heath, and G. Wahba, “Generalized cross-validation as a method for choosing a good ridge parameter,” Technometrics 21, 215–223 (1979).
[CrossRef]

G. H. Golub and C. F. Van Loan, Matrix Computations, 3rd ed. (Johns Hopkins, 1996), pp. 257–258.

G. H. Golub and U. von Matt, “Generalized cross-validation for large scale problems,” in Proceedings of the Second International Workshop on Recent Advances in Total Least Squares Techniques and Errors-in-Variables Modeling, S.Van Huffel, ed. (Society for Industrial and Applied Mathematics, 1997), pp. 139–148.

Gray, R. M.

R. M. Gray, “Toeplitz and circulant matrices: a review,” Found. Trends Commun. Inf. Theory 2, 155–239 (2005).
[CrossRef]

Hanson, R.

P. Cheeseman, B. Kanefsky, R. Kraft, J. Stutz, and R. Hanson, “Super-resolved surface reconstruction from multiple images,” in Maximum Entropy and Bayesian Methods, G.R.Heidbreder, ed. (Kluwer, 1996), pp. 293–308.

Hardie, R. C.

R. C. Hardie, K. J. Barnard, and E. 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]

Heath, M.

G. H. Golub, M. Heath, and G. Wahba, “Generalized cross-validation as a method for choosing a good ridge parameter,” Technometrics 21, 215–223 (1979).
[CrossRef]

Hoctor, R. T.

F. W. Wheeler, R. T. Hoctor, and E. B. Barrett, “Super-resolution image synthesis using projections onto convex sets in the frequency domain,” Proc. SPIE , 5674, 479–490 (2005).
[CrossRef]

Irani, M.

M. Irani and S. Peleg, “Motion analysis for image enhancement: resolution, occlusion, and transparency,” J. Visual Commun. Image Represent 4, 324–335 (1993).
[CrossRef]

Javidi, B.

Jbilou, K.

A. Bouhamidi and K. Jbilou, “Sylvester Tikhonov-regularization methods in image restoration,” J. Comput. Appl. Math. 206, 86–98 (2007).
[CrossRef]

Kanefsky, B.

P. Cheeseman, B. Kanefsky, R. Kraft, J. Stutz, and R. Hanson, “Super-resolved surface reconstruction from multiple images,” in Maximum Entropy and Bayesian Methods, G.R.Heidbreder, ed. (Kluwer, 1996), pp. 293–308.

Katsaggelos, A. K.

B. C. Tom and A. K. Katsaggelos, “Reconstruction of a high-resolution image from multiple-degraded misregistered low-resolution images,” Proc. SPIE 2308, 971–981 (1994).
[CrossRef]

Kraft, R.

P. Cheeseman, B. Kanefsky, R. Kraft, J. Stutz, and R. Hanson, “Super-resolved surface reconstruction from multiple images,” in Maximum Entropy and Bayesian Methods, G.R.Heidbreder, ed. (Kluwer, 1996), pp. 293–308.

Lev-Ari, H.

H. Lev-Ari, “Efficient solution of linear matrix equations with application to multistatic antenna array processing,” Commun. Inf. Syst. 5, 123–130 (2005).

Luther-Davies, B.

K. A. Nugent and B. Luther-Davies, “Penumbral imaging of high energy x-rays from laser-produced plasmas,” Opt. Commun. 49, 393–396 (1984).
[CrossRef]

Marom, E.

Z. Zalevsky, D. Mendlovic, and E. Marom, “Special sensor masking for exceeding system geometrical resolving power,” Opt. Eng. 39, 1936–1942 (2000).
[CrossRef]

Mendlovic, D.

Z. Zalevsky, J. Solomon, and D. Mendlovic, “Geometrical super resolution using code division multiplexing,” Appl. Opt. 42, 32–40 (2005).

Z. Zalevsky, N. Shamir, and D. Mendlovic, “Geometrical super-resolution in infra-red sensor: experimental verification,” Opt. Eng. 43, 1401–1406 (2004).
[CrossRef]

Z. Zalevsky, D. Mendlovic, and E. Marom, “Special sensor masking for exceeding system geometrical resolving power,” Opt. Eng. 39, 1936–1942 (2000).
[CrossRef]

Mudassar, A. A.

Nugent, K. A.

K. A. Nugent, “Coded aperture imaging: a Fourier space analysis,” Appl. Opt. 26, 563–569 (1987).
[CrossRef]

K. A. Nugent and B. Luther-Davies, “Penumbral imaging of high energy x-rays from laser-produced plasmas,” Opt. Commun. 49, 393–396 (1984).
[CrossRef]

Oskoui, P.

Peleg, S.

M. Irani and S. Peleg, “Motion analysis for image enhancement: resolution, occlusion, and transparency,” J. Visual Commun. Image Represent 4, 324–335 (1993).
[CrossRef]

Shamir, N.

Z. Zalevsky, N. Shamir, and D. Mendlovic, “Geometrical super-resolution in infra-red sensor: experimental verification,” Opt. Eng. 43, 1401–1406 (2004).
[CrossRef]

Sohail, M.

Solomon, J.

Z. Zalevsky, J. Solomon, and D. Mendlovic, “Geometrical super resolution using code division multiplexing,” Appl. Opt. 42, 32–40 (2005).

Stark, H.

Stutz, J.

P. Cheeseman, B. Kanefsky, R. Kraft, J. Stutz, and R. Hanson, “Super-resolved surface reconstruction from multiple images,” in Maximum Entropy and Bayesian Methods, G.R.Heidbreder, ed. (Kluwer, 1996), pp. 293–308.

Tom, B. C.

B. C. Tom and A. K. Katsaggelos, “Reconstruction of a high-resolution image from multiple-degraded misregistered low-resolution images,” Proc. SPIE 2308, 971–981 (1994).
[CrossRef]

ul-Haq, I.

Van Loan, C. F.

C. F. Van Loan, “The ubiquitous Kronecker product,” J. Comp. Appl. Math. 123, 85–100 (2000).
[CrossRef]

G. H. Golub and C. F. Van Loan, Matrix Computations, 3rd ed. (Johns Hopkins, 1996), pp. 257–258.

von Matt, U.

G. H. Golub and U. von Matt, “Generalized cross-validation for large scale problems,” in Proceedings of the Second International Workshop on Recent Advances in Total Least Squares Techniques and Errors-in-Variables Modeling, S.Van Huffel, ed. (Society for Industrial and Applied Mathematics, 1997), pp. 139–148.

Wahba, G.

G. H. Golub, M. Heath, and G. Wahba, “Generalized cross-validation as a method for choosing a good ridge parameter,” Technometrics 21, 215–223 (1979).
[CrossRef]

Wheeler, F. W.

F. W. Wheeler, R. T. Hoctor, and E. B. Barrett, “Super-resolution image synthesis using projections onto convex sets in the frequency domain,” Proc. SPIE , 5674, 479–490 (2005).
[CrossRef]

Zalevsky, Z.

A. Borkowski, Z. Zalevsky, and B. Javidi, “Geometrical super resolved imaging using non periodic spatial masking,” J. Opt. Soc. Am. A 26, 589–601 (2009).
[CrossRef]

Z. Zalevsky, J. Solomon, and D. Mendlovic, “Geometrical super resolution using code division multiplexing,” Appl. Opt. 42, 32–40 (2005).

Z. Zalevsky, N. Shamir, and D. Mendlovic, “Geometrical super-resolution in infra-red sensor: experimental verification,” Opt. Eng. 43, 1401–1406 (2004).
[CrossRef]

Z. Zalevsky, D. Mendlovic, and E. Marom, “Special sensor masking for exceeding system geometrical resolving power,” Opt. Eng. 39, 1936–1942 (2000).
[CrossRef]

Appl. Opt.

Commun. Inf. Syst.

H. Lev-Ari, “Efficient solution of linear matrix equations with application to multistatic antenna array processing,” Commun. Inf. Syst. 5, 123–130 (2005).

Found. Trends Commun. Inf. Theory

R. M. Gray, “Toeplitz and circulant matrices: a review,” Found. Trends Commun. Inf. Theory 2, 155–239 (2005).
[CrossRef]

IEEE Trans. Image Process.

R. C. Hardie, K. J. Barnard, and E. 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]

J. Comp. Appl. Math.

C. F. Van Loan, “The ubiquitous Kronecker product,” J. Comp. Appl. Math. 123, 85–100 (2000).
[CrossRef]

J. Comput. Appl. Math.

A. Bouhamidi and K. Jbilou, “Sylvester Tikhonov-regularization methods in image restoration,” J. Comput. Appl. Math. 206, 86–98 (2007).
[CrossRef]

J. Opt. Soc. Am. A

J. Visual Commun. Image Represent

M. Irani and S. Peleg, “Motion analysis for image enhancement: resolution, occlusion, and transparency,” J. Visual Commun. Image Represent 4, 324–335 (1993).
[CrossRef]

Opt. Commun.

K. A. Nugent and B. Luther-Davies, “Penumbral imaging of high energy x-rays from laser-produced plasmas,” Opt. Commun. 49, 393–396 (1984).
[CrossRef]

Opt. Eng.

Z. Zalevsky, D. Mendlovic, and E. Marom, “Special sensor masking for exceeding system geometrical resolving power,” Opt. Eng. 39, 1936–1942 (2000).
[CrossRef]

Z. Zalevsky, N. Shamir, and D. Mendlovic, “Geometrical super-resolution in infra-red sensor: experimental verification,” Opt. Eng. 43, 1401–1406 (2004).
[CrossRef]

Opt. Lett.

Proc. SPIE

B. C. Tom and A. K. Katsaggelos, “Reconstruction of a high-resolution image from multiple-degraded misregistered low-resolution images,” Proc. SPIE 2308, 971–981 (1994).
[CrossRef]

F. W. Wheeler, R. T. Hoctor, and E. B. Barrett, “Super-resolution image synthesis using projections onto convex sets in the frequency domain,” Proc. SPIE , 5674, 479–490 (2005).
[CrossRef]

Technometrics

G. H. Golub, M. Heath, and G. Wahba, “Generalized cross-validation as a method for choosing a good ridge parameter,” Technometrics 21, 215–223 (1979).
[CrossRef]

Other

G. H. Golub and U. von Matt, “Generalized cross-validation for large scale problems,” in Proceedings of the Second International Workshop on Recent Advances in Total Least Squares Techniques and Errors-in-Variables Modeling, S.Van Huffel, ed. (Society for Industrial and Applied Mathematics, 1997), pp. 139–148.

G. H. Golub and C. F. Van Loan, Matrix Computations, 3rd ed. (Johns Hopkins, 1996), pp. 257–258.

P. Cheeseman, B. Kanefsky, R. Kraft, J. Stutz, and R. Hanson, “Super-resolved surface reconstruction from multiple images,” in Maximum Entropy and Bayesian Methods, G.R.Heidbreder, ed. (Kluwer, 1996), pp. 293–308.

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