Abstract

Several methods of spectral sensitivity estimation for color image scanners are developed and evaluated. The estimation procedure involves response measurements of the scanner through a set of spectrally selective filters. These measurements form the observations for generalized inverse, smoothing, and Wiener estimation processes. Wiener estimation is found to provide the best results.

© 1976 Optical Society of America

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References

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  1. B. W. Rust, W. R. Burrus, Mathematical Programming and the Numerical Solution of Linear Equations (American Elsevier, New York, 1972).
  2. F. A. Graybill, Introduction to Matrices with Applications in Statistics (Wadsworth, Belmont, Calif., 1969).
  3. C. R. Rao, S. K. Mitra, Generalized Inverse of Matrices and Its Applications (Wiley, New York, 1971).
  4. P. B. Liebelt, An Introduction to Optimal Estimation (Addison-Wesley, Reading, Mass., 1967).

Burrus, W. R.

B. W. Rust, W. R. Burrus, Mathematical Programming and the Numerical Solution of Linear Equations (American Elsevier, New York, 1972).

Graybill, F. A.

F. A. Graybill, Introduction to Matrices with Applications in Statistics (Wadsworth, Belmont, Calif., 1969).

Liebelt, P. B.

P. B. Liebelt, An Introduction to Optimal Estimation (Addison-Wesley, Reading, Mass., 1967).

Mitra, S. K.

C. R. Rao, S. K. Mitra, Generalized Inverse of Matrices and Its Applications (Wiley, New York, 1971).

Rao, C. R.

C. R. Rao, S. K. Mitra, Generalized Inverse of Matrices and Its Applications (Wiley, New York, 1971).

Rust, B. W.

B. W. Rust, W. R. Burrus, Mathematical Programming and the Numerical Solution of Linear Equations (American Elsevier, New York, 1972).

Other (4)

B. W. Rust, W. R. Burrus, Mathematical Programming and the Numerical Solution of Linear Equations (American Elsevier, New York, 1972).

F. A. Graybill, Introduction to Matrices with Applications in Statistics (Wadsworth, Belmont, Calif., 1969).

C. R. Rao, S. K. Mitra, Generalized Inverse of Matrices and Its Applications (Wiley, New York, 1971).

P. B. Liebelt, An Introduction to Optimal Estimation (Addison-Wesley, Reading, Mass., 1967).

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Figures (6)

Fig. 1
Fig. 1

Spectral shapes of absorption filters.

Fig. 2
Fig. 2

Spectral shapes of interference filters.

Fig. 3
Fig. 3

Comparison of actual and estimated spectral response for absorption filters obtained by computer simulation: (a) pseudoinverse estimate; (b) smoothing estimate; (c) Wiener estimate, SNR = 1000.

Fig. 4
Fig. 4

Comparison of actual and estimated spectral response for interference filters obtained by computer simulation: (a) pseudoinverse estimate; (b) smoothing estimate; (c) Wiener estimate, SNR = 1000.

Fig. 5
Fig. 5

Estimated spectral response for absorption filters for microdensitometer color scanner: (a) pseudoinverse estimate; (b) smoothing estimate; (c) Wiener estimate, SNR = 1000.

Fig. 6
Fig. 6

Estimated spectral response for interference filters for microdensitometer color scanner: (a) pseudoinverse estimate; (b) smoothing estimate; (c) Wiener estimate, SNR = 1000.

Equations (9)

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x i = c ( λ ) s i ( λ ) d λ + n i ,
x i = s i T c + n i ,
x = Sc + n ,
ĉ = S x + S T ( SS T ) 1 x .
ĉ = M 1 S T ( S M 1 S T ) 1 x ,
M = [ 1 2 1 0 0 0 0 . . . . 2 5 4 1 0 0 0 . 1 4 6 4 1 1 0 . 0 0 4 6 4 1 0 . 0 0 1 4 6 4 1 . . . . . . . . . . . 1 4 6 4 1 0 . 0 1 4 6 4 1 . 0 0 1 4 5 2 0 . . . . 0 0 0 1 2 1 ] .
ĉ = K c S T ( SK c S T + K n ) 1 x ,
K c = σ c 2 Q [ 1 ρ ρ 2 . . . ρ Q 1 ρ 1 ρ ρ Q 2 . . . . . . ρ Q 1 . . . . . 1 ] ,
K n = σ n 2 Q I ,

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