Abstract

We present a superresolving approach that allows one to exceed the diffraction limit and recover highly resolved contours of moving targets from a sequence of low-resolution images. The presented approach is suitable for remote sensing applications. The resolution decoding algorithm that is used to recover the high-resolution features of the target can be run partially via optical means and that way can be used to reduce the required computational complexity.

© 2006 Optical Society of America

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References

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  1. P.M.Narenda, ed., in Proc. SPIE 0302, (1981).
  2. Y. Gao, J. Li, and Z. Shen, in Proc. SPIE 5640, 341 (2005).
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  5. Z. Lu and T. Zhang, in Proc. SPIE 5102, 338 (2003).
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  8. Z. Zalevsky, D. Mendlovic, and A. W. Lohmann, in Progress in Optics (Elsevier, 1999), Vol. XL, Chap. 4.
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    [CrossRef]
  11. W. Lukosz, J. Opt. Soc. Am. 56, 1463 (1966).
    [CrossRef]
  12. A. I. Kartashev, Opt. Spektrosk. (USSR) 9, 204 (1960).
  13. W. Gartner and A. W. Lohmann, Z. Phys. 174, 18 (1963).
    [CrossRef]
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    [CrossRef] [PubMed]
  15. T. Szoplik, J. García, and C. Ferreira, Appl. Opt. 34, 267 (1995).
    [CrossRef] [PubMed]

2002 (1)

1997 (1)

1995 (1)

1966 (1)

1963 (1)

W. Gartner and A. W. Lohmann, Z. Phys. 174, 18 (1963).
[CrossRef]

1960 (1)

A. I. Kartashev, Opt. Spektrosk. (USSR) 9, 204 (1960).

Bui, T. H.

P. Russo, V. Markandev, T. H. Bui, and D. Shrode, Proc. SPIE 1383, 60 (1991).

Casasent, D. P.

A. A. Kostrzewski, G. D. Savant, P. I. Shnitser, M. A. Piliavin, S. Sandomirsky, A. A. Vasiliev, and D. P. Casasent, in Proc. SPIE 5129, 129 (2003).

Dale, J. L.

J. L. Dale, D. J. Dwyer, and J. Thornton, in Proc. SPIE 5612, 94 (2004).

Dwyer, D. J.

J. L. Dale, D. J. Dwyer, and J. Thornton, in Proc. SPIE 5612, 94 (2004).

Ferreira, C.

Gao, Y.

Y. Gao, J. Li, and Z. Shen, in Proc. SPIE 5640, 341 (2005).

García, J.

Gartner, W.

W. Gartner and A. W. Lohmann, Z. Phys. 174, 18 (1963).
[CrossRef]

Kartashev, A. I.

A. I. Kartashev, Opt. Spektrosk. (USSR) 9, 204 (1960).

Konforti, N.

Kostrzewski, A. A.

A. A. Kostrzewski, G. D. Savant, P. I. Shnitser, M. A. Piliavin, S. Sandomirsky, A. A. Vasiliev, and D. P. Casasent, in Proc. SPIE 5129, 129 (2003).

Lange, H.

H. Lange, in Proc. SPIE 3720, 202 (1999).

Li, J.

Y. Gao, J. Li, and Z. Shen, in Proc. SPIE 5640, 341 (2005).

Lohmann, A. W.

D. Mendlovic and A. W. Lohmann, J. Opt. Soc. Am. A 14, 558 (1997).
[CrossRef]

W. Gartner and A. W. Lohmann, Z. Phys. 174, 18 (1963).
[CrossRef]

Z. Zalevsky, D. Mendlovic, and A. W. Lohmann, in Progress in Optics (Elsevier, 1999), Vol. XL, Chap. 4.

Lu, Z.

Z. Lu and T. Zhang, in Proc. SPIE 5102, 338 (2003).

Lukosz, W.

Markandev, V.

P. Russo, V. Markandev, T. H. Bui, and D. Shrode, Proc. SPIE 1383, 60 (1991).

Marom, E.

Mendlovic, D.

A. Shemer, Z. Zalevsky, D. Mendlovic, N. Konforti, and E. Marom, Appl. Opt. 41, 7397 (2002).
[CrossRef] [PubMed]

D. Mendlovic and A. W. Lohmann, J. Opt. Soc. Am. A 14, 558 (1997).
[CrossRef]

Z. Zalevsky and D. Mendlovic, Optical Super Resolution (Springer, 2002).

Z. Zalevsky, D. Mendlovic, and A. W. Lohmann, in Progress in Optics (Elsevier, 1999), Vol. XL, Chap. 4.

Piliavin, M. A.

A. A. Kostrzewski, G. D. Savant, P. I. Shnitser, M. A. Piliavin, S. Sandomirsky, A. A. Vasiliev, and D. P. Casasent, in Proc. SPIE 5129, 129 (2003).

Russo, P.

P. Russo, V. Markandev, T. H. Bui, and D. Shrode, Proc. SPIE 1383, 60 (1991).

Sandomirsky, S.

A. A. Kostrzewski, G. D. Savant, P. I. Shnitser, M. A. Piliavin, S. Sandomirsky, A. A. Vasiliev, and D. P. Casasent, in Proc. SPIE 5129, 129 (2003).

Savant, G. D.

A. A. Kostrzewski, G. D. Savant, P. I. Shnitser, M. A. Piliavin, S. Sandomirsky, A. A. Vasiliev, and D. P. Casasent, in Proc. SPIE 5129, 129 (2003).

Shemer, A.

Shen, Z.

Y. Gao, J. Li, and Z. Shen, in Proc. SPIE 5640, 341 (2005).

Shnitser, P. I.

A. A. Kostrzewski, G. D. Savant, P. I. Shnitser, M. A. Piliavin, S. Sandomirsky, A. A. Vasiliev, and D. P. Casasent, in Proc. SPIE 5129, 129 (2003).

Shrode, D.

P. Russo, V. Markandev, T. H. Bui, and D. Shrode, Proc. SPIE 1383, 60 (1991).

Szoplik, T.

Thornton, J.

J. L. Dale, D. J. Dwyer, and J. Thornton, in Proc. SPIE 5612, 94 (2004).

Vasiliev, A. A.

A. A. Kostrzewski, G. D. Savant, P. I. Shnitser, M. A. Piliavin, S. Sandomirsky, A. A. Vasiliev, and D. P. Casasent, in Proc. SPIE 5129, 129 (2003).

Zalevsky, Z.

A. Shemer, Z. Zalevsky, D. Mendlovic, N. Konforti, and E. Marom, Appl. Opt. 41, 7397 (2002).
[CrossRef] [PubMed]

Z. Zalevsky and D. Mendlovic, Optical Super Resolution (Springer, 2002).

Z. Zalevsky, D. Mendlovic, and A. W. Lohmann, in Progress in Optics (Elsevier, 1999), Vol. XL, Chap. 4.

Zhang, T.

Z. Lu and T. Zhang, in Proc. SPIE 5102, 338 (2003).

Appl. Opt. (2)

J. Opt. Soc. Am. (1)

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

Opt. Spektrosk. (1)

A. I. Kartashev, Opt. Spektrosk. (USSR) 9, 204 (1960).

Z. Phys. (1)

W. Gartner and A. W. Lohmann, Z. Phys. 174, 18 (1963).
[CrossRef]

Other (9)

P.M.Narenda, ed., in Proc. SPIE 0302, (1981).

Y. Gao, J. Li, and Z. Shen, in Proc. SPIE 5640, 341 (2005).

J. L. Dale, D. J. Dwyer, and J. Thornton, in Proc. SPIE 5612, 94 (2004).

A. A. Kostrzewski, G. D. Savant, P. I. Shnitser, M. A. Piliavin, S. Sandomirsky, A. A. Vasiliev, and D. P. Casasent, in Proc. SPIE 5129, 129 (2003).

Z. Lu and T. Zhang, in Proc. SPIE 5102, 338 (2003).

H. Lange, in Proc. SPIE 3720, 202 (1999).

P. Russo, V. Markandev, T. H. Bui, and D. Shrode, Proc. SPIE 1383, 60 (1991).

Z. Zalevsky, D. Mendlovic, and A. W. Lohmann, in Progress in Optics (Elsevier, 1999), Vol. XL, Chap. 4.

Z. Zalevsky and D. Mendlovic, Optical Super Resolution (Springer, 2002).

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Figures (2)

Fig. 1
Fig. 1

Bottom, sample of the high-resolution image. Top, sample of the low-resolution image. The arrows signal the target position.

Fig. 2
Fig. 2

a, Summation of all the blurred images. b, Result of high-pass filtering of the raw reconstructed image. c, High-resolution reference target.

Equations (11)

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s 1 ( x ) = { 1 s ( x ) > 0 0 s ( x ) = 0 } .
t ( x , t ) = [ 1 s 1 ( x v t ) ] b ( x ) + s ( x v t ) ,
I ( x , t ) = t ( x , t ) p ( x x ) d x .
I ( x , t ) = b ( x ) p ( x x ) d x s 1 ( x v t ) b ( x ) p ( x x ) d x + s ( x v t ) p ( x x ) d x .
R ( x ) = I ( x + v t , t ) b ( x + v t ) d t ,
R ( x ) = b ( x + v t ) b ( x + v t ) p ( x x ) d x d t b ( x + v t ) [ s 1 ( x ) b ( x + v t ) p ( x x ) d x ] d t + b ( x + v t ) [ s ( x ) p ( x x ) d x ] d t .
b ( x + v t ) b ( x + v t ) d t = δ ( x x ) + k 1 ,
R ( x ) = k 3 s 1 ( x ) p ( 0 ) k 1 s 1 ( x ) p ( x x ) d x + k 2 s ( x ) p ( x x ) d x ,
k 2 = b ( x + v t ) d t , k 3 = p ( 0 ) + k 1 p ( x x ) d x .
k 2 s ( x ) k 1 s 1 ( x ) = k 4 s ( x ) ,
R ( x ) = k 3 + k 4 s ( x ) p ( x x ) d x s 1 ( x ) p ( 0 ) ,

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