Abstract

One can obtain either exact realizations or useful approximations of linear systems or matrix–vector products that arise in many different applications by implementing them in the form of multistage or multichannel fractional Fourier-domain filters, resulting in space–bandwidth-efficient systems with acceptable decreases in accuracy. Varying the number and the configuration of filters enables one to trade off between accuracy and efficiency in a flexible manner. The proposed scheme constitutes a systematic way of exploiting the regularity or structure of a given linear system or matrix, even when that structure is not readily apparent.

© 1998 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]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

1998 (3)

1997 (2)

B. Barshan, M. A. Kutay, and H. M. Ozaktas, Opt. Commun. 135, 32 (1997).
[CrossRef]

M. A. Kutay, H. M. Ozaktas, O. Ar?kan, and L. Onural, IEEE Trans. Signal Process. 45, 1129 (1997).
[CrossRef]

1996 (3)

M. F. Erden, H. M. Ozaktas, and D. Mendlovic, Opt. Commun. 125, 288 (1996).
[CrossRef]

Z. Zalevsky and D. Mendlovic, Appl. Opt. 35, 3930 (1996).
[CrossRef] [PubMed]

H. M. Ozaktas, O. Ar?kan, M. A. Kutay, and G. Bozdagi, IEEE Trans. Signal Process. 44, 2141 (1996).
[CrossRef]

1995 (1)

1994 (2)

1993 (2)

Almeida, L. B.

L. B. Almeida, IEEE Trans. Signal Process. 42, 3084 (1994).
[CrossRef]

Arikan, O.

M. A. Kutay, H. M. Ozaktas, O. Ar?kan, and L. Onural, IEEE Trans. Signal Process. 45, 1129 (1997).
[CrossRef]

H. M. Ozaktas, O. Ar?kan, M. A. Kutay, and G. Bozdagi, IEEE Trans. Signal Process. 44, 2141 (1996).
[CrossRef]

Barshan, B.

B. Barshan, M. A. Kutay, and H. M. Ozaktas, Opt. Commun. 135, 32 (1997).
[CrossRef]

H. M. Ozaktas, B. Barshan, D. Mendlovic, and L. Onural, J. Opt. Soc. Am. A 11, 547 (1994).
[CrossRef]

Bozdagi, G.

H. M. Ozaktas, O. Ar?kan, M. A. Kutay, and G. Bozdagi, IEEE Trans. Signal Process. 44, 2141 (1996).
[CrossRef]

Erden, M. F.

M. F. Erden and H. M. Ozaktas, J. Opt. Soc. Am. A 15, 1647 (1998).
[CrossRef]

M. F. Erden, H. M. Ozaktas, and D. Mendlovic, Opt. Commun. 125, 288 (1996).
[CrossRef]

M. F. Erden, “Repeated filtering in consecutive fractional Fourier domains,” Ph.D. dissertation (Bilkent University, Ankara, Turkey, 1997).

Kutay, M. A.

M. A. Kutay and H. M. Ozaktas, J. Opt. Soc. Am. A 15, 825 (1998).
[CrossRef]

M. A. Kutay, H. M. Ozaktas, O. Ar?kan, and L. Onural, IEEE Trans. Signal Process. 45, 1129 (1997).
[CrossRef]

B. Barshan, M. A. Kutay, and H. M. Ozaktas, Opt. Commun. 135, 32 (1997).
[CrossRef]

H. M. Ozaktas, O. Ar?kan, M. A. Kutay, and G. Bozdagi, IEEE Trans. Signal Process. 44, 2141 (1996).
[CrossRef]

Lohmann, A. W.

Mendlovic, D.

Onural, L.

M. A. Kutay, H. M. Ozaktas, O. Ar?kan, and L. Onural, IEEE Trans. Signal Process. 45, 1129 (1997).
[CrossRef]

H. M. Ozaktas, B. Barshan, D. Mendlovic, and L. Onural, J. Opt. Soc. Am. A 11, 547 (1994).
[CrossRef]

Ozaktas, H. M.

Sahin, A.

Zalevsky, Z.

Appl. Opt. (3)

IEEE Trans. Signal Process. (3)

H. M. Ozaktas, O. Ar?kan, M. A. Kutay, and G. Bozdagi, IEEE Trans. Signal Process. 44, 2141 (1996).
[CrossRef]

L. B. Almeida, IEEE Trans. Signal Process. 42, 3084 (1994).
[CrossRef]

M. A. Kutay, H. M. Ozaktas, O. Ar?kan, and L. Onural, IEEE Trans. Signal Process. 45, 1129 (1997).
[CrossRef]

J. Opt. Soc. Am. A (5)

Opt. Commun. (2)

B. Barshan, M. A. Kutay, and H. M. Ozaktas, Opt. Commun. 135, 32 (1997).
[CrossRef]

M. F. Erden, H. M. Ozaktas, and D. Mendlovic, Opt. Commun. 125, 288 (1996).
[CrossRef]

Other (1)

M. F. Erden, “Repeated filtering in consecutive fractional Fourier domains,” Ph.D. dissertation (Bilkent University, Ankara, Turkey, 1997).

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Figures (2)

Fig. 1
Fig. 1

(a) Fourier-domain filtering. (b) Space-domain filtering. (c) ath-order fractional Fourier-domain filtering. (d) ath-order fractional Fourier domain. (e) Multistage (serial) filtering. (f) Multichannel (parallel) filtering.

Fig. 2
Fig. 2

(a) Original image. (b) Blurred image. (c) Image restored by multistage filtering. (d) Image restored by multichannel filtering.

Equations (2)

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gs=F-aMΛMFa2-a1Λ1Fa1f,
gp=k=1M F-akΛkFakf,

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