Abstract

Two-dimensional phase retrieval by use of a window function is considered. First the uniqueness and the reconstruction of a two-dimensional signal from the Fourier intensities of the three signals, an original signal, the signal windowed by a window wm,n, and the signal windowed by its complementary window wcm,n=1-wm,n, are addressed. Then phase retrieval without a complementary window is considered. Conditions under which a signal can be uniquely specified from the Fourier intensities of the original signal and the windowed signal by wm,n are developed, and a reconstruction algorithm is presented.

© 2001 Optical Society of America

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References

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    [CrossRef]
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1993

W. Kim and M. H. Hayes, IEEE Trans. Signal Process. ASSP-41, 1409 (1993).
[CrossRef]

1988

1987

1986

J. R. Fienup and C. C. Wakerman, J. Opt. Soc. Am. A 3, 1879 (1986).

1983

S. H. Nawab, T. F. Quatieri, and J. S. Lim, IEEE Trans. Acoust. Speech Signal Process. ASSP-31, 986 (1983).
[CrossRef]

1982

M. H. Hayes and J. H. McClellan, Proc. IEEE 70, 197 (1982).
[CrossRef]

M. H. Hayes, IEEE Trans. Acoust. Speech Signal Process. ASSP-30, 140 (1982).
[CrossRef]

1981

Burge, R. E.

Fiddy, M. A.

Fienup, J. R.

J. R. Fienup and C. C. Wakerman, J. Opt. Soc. Am. A 3, 1879 (1986).

Gonsalves, R. A.

Hayes, M. H.

W. Kim and M. H. Hayes, IEEE Trans. Signal Process. ASSP-41, 1409 (1993).
[CrossRef]

M. H. Hayes and J. H. McClellan, Proc. IEEE 70, 197 (1982).
[CrossRef]

M. H. Hayes, IEEE Trans. Acoust. Speech Signal Process. ASSP-30, 140 (1982).
[CrossRef]

Kim, W.

W. Kim and M. H. Hayes, IEEE Trans. Signal Process. ASSP-41, 1409 (1993).
[CrossRef]

Lim, J. S.

S. H. Nawab, T. F. Quatieri, and J. S. Lim, IEEE Trans. Acoust. Speech Signal Process. ASSP-31, 986 (1983).
[CrossRef]

McClellan, J. H.

M. H. Hayes and J. H. McClellan, Proc. IEEE 70, 197 (1982).
[CrossRef]

Nakajima, N.

Nawab, S. H.

S. H. Nawab, T. F. Quatieri, and J. S. Lim, IEEE Trans. Acoust. Speech Signal Process. ASSP-31, 986 (1983).
[CrossRef]

Quatieri, T. F.

S. H. Nawab, T. F. Quatieri, and J. S. Lim, IEEE Trans. Acoust. Speech Signal Process. ASSP-31, 986 (1983).
[CrossRef]

Wakerman, C. C.

J. R. Fienup and C. C. Wakerman, J. Opt. Soc. Am. A 3, 1879 (1986).

Wood, J. W.

IEEE Trans. Acoust. Speech Signal Process.

M. H. Hayes, IEEE Trans. Acoust. Speech Signal Process. ASSP-30, 140 (1982).
[CrossRef]

S. H. Nawab, T. F. Quatieri, and J. S. Lim, IEEE Trans. Acoust. Speech Signal Process. ASSP-31, 986 (1983).
[CrossRef]

IEEE Trans. Signal Process.

W. Kim and M. H. Hayes, IEEE Trans. Signal Process. ASSP-41, 1409 (1993).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Lett.

Proc. IEEE

M. H. Hayes and J. H. McClellan, Proc. IEEE 70, 197 (1982).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Reconstruction algorithm 1 for theorem 1.

Fig. 2
Fig. 2

Reconstruction example using the algorithm in Fig.  1: (a) original image, (b) window function, (c) reconstructed image after 100 iterations.

Fig. 3
Fig. 3

Reconstruction algorithm 2 for theorem 2.

Fig. 4
Fig. 4

Image reconstructed by use of algorithm 2 after 100 iterations.

Fig. 5
Fig. 5

Performance comparison of the two algorithms in terms of mean squared error.

Equations (5)

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

ym,n=xm,nwm,n,zm,n=xm,nwcm,n.
wm,nwM-1-m,N-1-n.
wm,nwM-1-m,N-1-n.
wm,n=0if m,n10,110×10,1101otherwise,
MSE=1MNm,nRM,Nxrm,n-x0m,n2,

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