Abstract

It is shown how to incorporate prior knowledge into the restoration of an image from a finite number of its expansion coefficients in some basis. The significant image enhancement obtained for simple prior knowledge suggests an application to image-transform coding. A computer simulation is presented that demonstrates that compression ratios greater than 13:1 are possible.

© 1982 Optical Society of America

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References

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  1. B. Cochrane, K. P. Dawson, M. A. Fiddy, T. J. Hall, “Sampling and interpolation in two dimensions,” in Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (Institute of Electrical and Electronics Engineers, New York, 1982), pp. 471–474.
  2. R. M. Young, An Introduction to Nonharmonic Fourier Series (Academic, New York, 1980).
  3. G. A. Merchant, T. W. Parkes, “Efficient solution of a Toeplitz-plus-Hankel coefficient matrix system of equations,” IEEE Trans. Acoustics Speech Signal Process. ASSP-30, 40–44 (1982).
    [CrossRef]
  4. A. K. Jain, “Image data compression: a review,” Proc. IEEE 69, 349–389 (1981).
    [CrossRef]

1982

G. A. Merchant, T. W. Parkes, “Efficient solution of a Toeplitz-plus-Hankel coefficient matrix system of equations,” IEEE Trans. Acoustics Speech Signal Process. ASSP-30, 40–44 (1982).
[CrossRef]

1981

A. K. Jain, “Image data compression: a review,” Proc. IEEE 69, 349–389 (1981).
[CrossRef]

Cochrane, B.

B. Cochrane, K. P. Dawson, M. A. Fiddy, T. J. Hall, “Sampling and interpolation in two dimensions,” in Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (Institute of Electrical and Electronics Engineers, New York, 1982), pp. 471–474.

Dawson, K. P.

B. Cochrane, K. P. Dawson, M. A. Fiddy, T. J. Hall, “Sampling and interpolation in two dimensions,” in Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (Institute of Electrical and Electronics Engineers, New York, 1982), pp. 471–474.

Fiddy, M. A.

B. Cochrane, K. P. Dawson, M. A. Fiddy, T. J. Hall, “Sampling and interpolation in two dimensions,” in Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (Institute of Electrical and Electronics Engineers, New York, 1982), pp. 471–474.

Hall, T. J.

B. Cochrane, K. P. Dawson, M. A. Fiddy, T. J. Hall, “Sampling and interpolation in two dimensions,” in Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (Institute of Electrical and Electronics Engineers, New York, 1982), pp. 471–474.

Jain, A. K.

A. K. Jain, “Image data compression: a review,” Proc. IEEE 69, 349–389 (1981).
[CrossRef]

Merchant, G. A.

G. A. Merchant, T. W. Parkes, “Efficient solution of a Toeplitz-plus-Hankel coefficient matrix system of equations,” IEEE Trans. Acoustics Speech Signal Process. ASSP-30, 40–44 (1982).
[CrossRef]

Parkes, T. W.

G. A. Merchant, T. W. Parkes, “Efficient solution of a Toeplitz-plus-Hankel coefficient matrix system of equations,” IEEE Trans. Acoustics Speech Signal Process. ASSP-30, 40–44 (1982).
[CrossRef]

Young, R. M.

R. M. Young, An Introduction to Nonharmonic Fourier Series (Academic, New York, 1980).

IEEE Trans. Acoustics Speech Signal Process.

G. A. Merchant, T. W. Parkes, “Efficient solution of a Toeplitz-plus-Hankel coefficient matrix system of equations,” IEEE Trans. Acoustics Speech Signal Process. ASSP-30, 40–44 (1982).
[CrossRef]

Proc. IEEE

A. K. Jain, “Image data compression: a review,” Proc. IEEE 69, 349–389 (1981).
[CrossRef]

Other

B. Cochrane, K. P. Dawson, M. A. Fiddy, T. J. Hall, “Sampling and interpolation in two dimensions,” in Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (Institute of Electrical and Electronics Engineers, New York, 1982), pp. 471–474.

R. M. Young, An Introduction to Nonharmonic Fourier Series (Academic, New York, 1980).

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Figures (1)

Fig. 1
Fig. 1

(a) Original image, (b) compressed image without prior knowledge, (c) prior-knowledge image, (d) compressed image with prior knowledge.

Equations (9)

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

C n = ( f , θ n ) H 1 .
f 1 = m a m θ m ,
C n = m a m ( θ m , θ n ) H 1 .
( f , g ) = Ω 1 f g * d t ,
C n = F ( x n ) = Ω 1 f ( t ) exp ( i x n t ) d t = ( f , g n ) .
C n = ( f , ψ n ) H 2 ,
( f , g ) = Ω 2 w 1 f g * d t ,
C n = ( f , w g n ) H 2 ,
f 2 = w m a m g m .

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