Abstract

In earlier work [ J. Opt. Soc. Am. A 21, 13– 23 ( 2004)], we showed that a combination of linear models and optimum Gaussian sensors obtained by an exhaustive search can recover daylight spectra reliably from broadband sensor data. Thus our algorithm and sensors could be used to design an accurate, relatively inexpensive system for spectral imaging of daylight. Here we improve our simulation of the multispectral system by (1) considering the different kinds of noise inherent in electronic devices such as change-coupled devices (CCDs) or complementary metal-oxide semiconductors (CMOS) and (2) extending our research to a different kind of natural illumination, skylight. Because exhaustive searches are expensive computationally, here we switch to a simulated annealing algorithm to define the optimum sensors for recovering skylight spectra. The annealing algorithm requires us to minimize a single cost function, and so we develop one that calculates both the spectral and colorimetric similarity of any pair of skylight spectra. We show that the simulated annealing algorithm yields results similar to the exhaustive search but with much less computational effort. Our technique lets us study the properties of optimum sensors in the presence of noise, one side effect of which is that adding more sensors may not improve the spectral recovery.

© 2005 Optical Society of America

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References

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  1. J. Hernández-Andrés, J. L. Nieves, E. M. Valero, J. Romero, “Spectral-daylight recovery by use of only a few sensors,” J. Opt. Soc. Am. A 21, 13–23 (2004).
    [CrossRef]
  2. J. Hernández-Andrés, J. Romero, R. L. Lee, “Colorimetric and spectroradiometric characteristics of narrow-field-of-view clear skylight in Granada, Spain,” J. Opt. Soc. Am. A 18, 412–420 (2001).
    [CrossRef]
  3. J. Hernández-Andrés, J. Romero, R. L. Lee, “Calculating correlated color temperatures across the entire gamut of daylight and skylight chromaticities,” Appl. Opt. 38, 5703–5709 (1999).
    [CrossRef]
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    [CrossRef] [PubMed]
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  6. D. Connah, S. Westland, M. G. A. Thomson, “Optimization of a multispectral imaging system,” in Proceedings of the 1st European Conference on Colour Graphics, Image and Vision (Society for Imaging Science and Technology, Springfield, Va., 2002), pp. 619–622.
  7. N. Shimano, “Optimal spectral sensitivities of a color image acquisition device in the presence of noise,” in Proceedings of the 2nd European Conference on Colour Graphics, Imaging and Vision (Society for Imaging Science and Technology, Springfield, Va., 2004), pp. 379–383.
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    [CrossRef]
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    [CrossRef]
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  14. D. C. Day, “Filter selection for spectral estimation using a trichromatic camera,” Ph.D. dissertation (Rochester Institute of Technology, 2003).
  15. F. H. Imai, R. S. Berns, D. Y. Tzeng, “A comparative analysis of spectral reflectance estimated in various spaces using a trichromatic camera system,” J. Imag. Sci. and Technol. 44, 280–287 (2000).
  16. G. Buchsbaum, O. Bloch, “Color categories revealed by non-negative matrix factorization of Munsell color spectra,” Vis. Res. 42, 559–563 (2002).
    [CrossRef] [PubMed]
  17. Y. Yokoyama, N. Tsumura, H. Haneishi, J. Hayashi, M. Saito, “A new color management system based on human perception and its application to recording and reproduction of art paintings,” in Proceedings of the 5th Color Imaging Conference: Color Science, Systems and Applications (Society for Imaging Science and Technology, Springfield, Va., 1997), pp. 169–172.
  18. S. Franco, Design with Operational Amplifiers and Analog Integrated Circuits, 3rd ed. (McGraw-Hill, Boston, 2002), pp. 311–346.
  19. J. Y. Hardeberg, “Filter selection for multispectral color image acquisition,” in Proceedings of PICS 2003 (Society for Imaging Science and Technology, Springfield, Va., 2003), pp. 177–182.
  20. F. H. Imai, M. R. Rosen, R. S. Berns, “Comparative study of metrics for spectral match quality,” in Proceedings of the 1st European Conference on Colour in Graphics, Image and Vision, pp. 492–496 (2002).
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    [CrossRef]
  22. M. R. Luo, G. Cui, B. Rigg, “The development of the CIE 2000 colour-difference formula: CIEDE2000,” Color Res. Appl. 26, 340–350 (2001).
    [CrossRef]
  23. G. Wyszecki, W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae, 2nd ed. (Wiley, New York, 1982), pp. 117–248.
  24. J. A. S. Viggiano, “Metrics for evaluating spectral matches: a quantitative comparison,” in Proceedings of the 2nd European Conference on Colour Graphics, Imaging and Vision (Society for Imaging Science and Technology, Springfield, Va., 2004), pp. 286–291.
  25. J. A. S. Viggiano, “A perception-referenced method for comparison of radiance ratio spectra and its application as an index of metamerism,” Proc. SPIE 4421, 701–704 (2002).
    [CrossRef]
  26. J. J. Michalsky, “Estimation of continuous solar spectral distributions from discrete filter measurements: II. A demonstration of practicability,” Sol. Energy 34, 439–445 (1985).
    [CrossRef]
  27. W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing (Cambridge University, 1992).
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    [CrossRef]

2004 (1)

2003 (1)

2002 (2)

G. Buchsbaum, O. Bloch, “Color categories revealed by non-negative matrix factorization of Munsell color spectra,” Vis. Res. 42, 559–563 (2002).
[CrossRef] [PubMed]

J. A. S. Viggiano, “A perception-referenced method for comparison of radiance ratio spectra and its application as an index of metamerism,” Proc. SPIE 4421, 701–704 (2002).
[CrossRef]

2001 (3)

M. R. Luo, G. Cui, B. Rigg, “The development of the CIE 2000 colour-difference formula: CIEDE2000,” Color Res. Appl. 26, 340–350 (2001).
[CrossRef]

D. Connah, S. Westland, M. G. A. Thomson, “Recovering spectral information using digital camera systems,” Color Technol. 117, 309–312 (2001).
[CrossRef]

J. Hernández-Andrés, J. Romero, R. L. Lee, “Colorimetric and spectroradiometric characteristics of narrow-field-of-view clear skylight in Granada, Spain,” J. Opt. Soc. Am. A 18, 412–420 (2001).
[CrossRef]

2000 (1)

F. H. Imai, R. S. Berns, D. Y. Tzeng, “A comparative analysis of spectral reflectance estimated in various spaces using a trichromatic camera system,” J. Imag. Sci. and Technol. 44, 280–287 (2000).

1999 (1)

1997 (1)

1992 (1)

1986 (1)

1985 (1)

J. J. Michalsky, “Estimation of continuous solar spectral distributions from discrete filter measurements: II. A demonstration of practicability,” Sol. Energy 34, 439–445 (1985).
[CrossRef]

1953 (1)

N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, E. Teller, “Equations of state calculations by fast computing machines,” J. Chem. Phys. 21, 1087–1092 (1953).
[CrossRef]

Berns, R. S.

F. H. Imai, R. S. Berns, D. Y. Tzeng, “A comparative analysis of spectral reflectance estimated in various spaces using a trichromatic camera system,” J. Imag. Sci. and Technol. 44, 280–287 (2000).

P. D. Burns, R. S. Berns, “Quantization in multispectral color image acquisition,” in Proceedings of the 7th Color Imaging Conference: Color Science, Systems and Applications (IS&T, Scottsdale, Arizona, 1999), pp. 32–35.

F. H. Imai, M. R. Rosen, R. S. Berns, “Comparative study of metrics for spectral match quality,” in Proceedings of the 1st European Conference on Colour in Graphics, Image and Vision, pp. 492–496 (2002).

Bloch, O.

G. Buchsbaum, O. Bloch, “Color categories revealed by non-negative matrix factorization of Munsell color spectra,” Vis. Res. 42, 559–563 (2002).
[CrossRef] [PubMed]

Buchsbaum, G.

G. Buchsbaum, O. Bloch, “Color categories revealed by non-negative matrix factorization of Munsell color spectra,” Vis. Res. 42, 559–563 (2002).
[CrossRef] [PubMed]

Burns, P. D.

P. D. Burns, “Analysis of image noise in multispectral color acquisition,” Ph.D. dissertation (Rochester Institute of Technology, 1997).

P. D. Burns, R. S. Berns, “Quantization in multispectral color image acquisition,” in Proceedings of the 7th Color Imaging Conference: Color Science, Systems and Applications (IS&T, Scottsdale, Arizona, 1999), pp. 32–35.

Connah, D.

D. Connah, S. Westland, M. G. A. Thomson, “Recovering spectral information using digital camera systems,” Color Technol. 117, 309–312 (2001).
[CrossRef]

D. Connah, S. Westland, M. G. A. Thomson, “Optimization of a multispectral imaging system,” in Proceedings of the 1st European Conference on Colour Graphics, Image and Vision (Society for Imaging Science and Technology, Springfield, Va., 2002), pp. 619–622.

Cui, G.

M. R. Luo, G. Cui, B. Rigg, “The development of the CIE 2000 colour-difference formula: CIEDE2000,” Color Res. Appl. 26, 340–350 (2001).
[CrossRef]

Day, D. C.

D. C. Day, “Filter selection for spectral estimation using a trichromatic camera,” Ph.D. dissertation (Rochester Institute of Technology, 2003).

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing (Cambridge University, 1992).

Franco, S.

S. Franco, Design with Operational Amplifiers and Analog Integrated Circuits, 3rd ed. (McGraw-Hill, Boston, 2002), pp. 311–346.

García-Beltrán, A.

Haneishi, H.

Y. Yokoyama, N. Tsumura, H. Haneishi, J. Hayashi, M. Saito, “A new color management system based on human perception and its application to recording and reproduction of art paintings,” in Proceedings of the 5th Color Imaging Conference: Color Science, Systems and Applications (Society for Imaging Science and Technology, Springfield, Va., 1997), pp. 169–172.

Hardeberg, J. Y.

J. Y. Hardeberg, “Filter selection for multispectral color image acquisition,” in Proceedings of PICS 2003 (Society for Imaging Science and Technology, Springfield, Va., 2003), pp. 177–182.

J. Y. Hardeberg (2001), “Acquisition and reproduction of color images: colorimetric and multispectral approaches” ( Dissertation.com , Parkland, Fla., 2001) (revised second edition of Ph.D. dissertation, Ecole Nationale Supérieure des Télécommunications, Paris, 1999), pp. 157–174.

Hayashi, J.

Y. Yokoyama, N. Tsumura, H. Haneishi, J. Hayashi, M. Saito, “A new color management system based on human perception and its application to recording and reproduction of art paintings,” in Proceedings of the 5th Color Imaging Conference: Color Science, Systems and Applications (Society for Imaging Science and Technology, Springfield, Va., 1997), pp. 169–172.

Hernández-Andrés, J.

Imai, F. H.

F. H. Imai, R. S. Berns, D. Y. Tzeng, “A comparative analysis of spectral reflectance estimated in various spaces using a trichromatic camera system,” J. Imag. Sci. and Technol. 44, 280–287 (2000).

F. H. Imai, M. R. Rosen, R. S. Berns, “Comparative study of metrics for spectral match quality,” in Proceedings of the 1st European Conference on Colour in Graphics, Image and Vision, pp. 492–496 (2002).

Kuehni, R. G.

R. G. Kuehni, Color Space and its Divisions: Color Order from Antiquity to the Present, 1st ed. (Wiley, New York, 2003), pp. 204–270.
[CrossRef]

Lee, R. L.

Luo, M. R.

M. R. Luo, G. Cui, B. Rigg, “The development of the CIE 2000 colour-difference formula: CIEDE2000,” Color Res. Appl. 26, 340–350 (2001).
[CrossRef]

Maloney, L. T.

Marimont, D. H.

Metropolis, N.

N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, E. Teller, “Equations of state calculations by fast computing machines,” J. Chem. Phys. 21, 1087–1092 (1953).
[CrossRef]

Michalsky, J. J.

J. J. Michalsky, “Estimation of continuous solar spectral distributions from discrete filter measurements: II. A demonstration of practicability,” Sol. Energy 34, 439–445 (1985).
[CrossRef]

Nieves, J. L.

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing (Cambridge University, 1992).

Rigg, B.

M. R. Luo, G. Cui, B. Rigg, “The development of the CIE 2000 colour-difference formula: CIEDE2000,” Color Res. Appl. 26, 340–350 (2001).
[CrossRef]

Romero, J.

Rosen, M. R.

F. H. Imai, M. R. Rosen, R. S. Berns, “Comparative study of metrics for spectral match quality,” in Proceedings of the 1st European Conference on Colour in Graphics, Image and Vision, pp. 492–496 (2002).

Rosenbluth, A.

N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, E. Teller, “Equations of state calculations by fast computing machines,” J. Chem. Phys. 21, 1087–1092 (1953).
[CrossRef]

Rosenbluth, M.

N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, E. Teller, “Equations of state calculations by fast computing machines,” J. Chem. Phys. 21, 1087–1092 (1953).
[CrossRef]

Saito, M.

Y. Yokoyama, N. Tsumura, H. Haneishi, J. Hayashi, M. Saito, “A new color management system based on human perception and its application to recording and reproduction of art paintings,” in Proceedings of the 5th Color Imaging Conference: Color Science, Systems and Applications (Society for Imaging Science and Technology, Springfield, Va., 1997), pp. 169–172.

Shimano, N.

N. Shimano, “Optimal spectral sensitivities of a color image acquisition device in the presence of noise,” in Proceedings of the 2nd European Conference on Colour Graphics, Imaging and Vision (Society for Imaging Science and Technology, Springfield, Va., 2004), pp. 379–383.

Stiles, W. S.

G. Wyszecki, W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae, 2nd ed. (Wiley, New York, 1982), pp. 117–248.

Teller, A.

N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, E. Teller, “Equations of state calculations by fast computing machines,” J. Chem. Phys. 21, 1087–1092 (1953).
[CrossRef]

Teller, E.

N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, E. Teller, “Equations of state calculations by fast computing machines,” J. Chem. Phys. 21, 1087–1092 (1953).
[CrossRef]

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing (Cambridge University, 1992).

Thomson, M. G. A.

D. Connah, S. Westland, M. G. A. Thomson, “Recovering spectral information using digital camera systems,” Color Technol. 117, 309–312 (2001).
[CrossRef]

D. Connah, S. Westland, M. G. A. Thomson, “Optimization of a multispectral imaging system,” in Proceedings of the 1st European Conference on Colour Graphics, Image and Vision (Society for Imaging Science and Technology, Springfield, Va., 2002), pp. 619–622.

Tsumura, N.

Y. Yokoyama, N. Tsumura, H. Haneishi, J. Hayashi, M. Saito, “A new color management system based on human perception and its application to recording and reproduction of art paintings,” in Proceedings of the 5th Color Imaging Conference: Color Science, Systems and Applications (Society for Imaging Science and Technology, Springfield, Va., 1997), pp. 169–172.

Tzeng, D. Y.

F. H. Imai, R. S. Berns, D. Y. Tzeng, “A comparative analysis of spectral reflectance estimated in various spaces using a trichromatic camera system,” J. Imag. Sci. and Technol. 44, 280–287 (2000).

Valero, E. M.

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing (Cambridge University, 1992).

Viggiano, J. A. S.

J. A. S. Viggiano, “A perception-referenced method for comparison of radiance ratio spectra and its application as an index of metamerism,” Proc. SPIE 4421, 701–704 (2002).
[CrossRef]

J. A. S. Viggiano, “Metrics for evaluating spectral matches: a quantitative comparison,” in Proceedings of the 2nd European Conference on Colour Graphics, Imaging and Vision (Society for Imaging Science and Technology, Springfield, Va., 2004), pp. 286–291.

Wandell, B. A.

Westland, S.

D. Connah, S. Westland, M. G. A. Thomson, “Recovering spectral information using digital camera systems,” Color Technol. 117, 309–312 (2001).
[CrossRef]

D. Connah, S. Westland, M. G. A. Thomson, “Optimization of a multispectral imaging system,” in Proceedings of the 1st European Conference on Colour Graphics, Image and Vision (Society for Imaging Science and Technology, Springfield, Va., 2002), pp. 619–622.

Wyszecki, G.

G. Wyszecki, W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae, 2nd ed. (Wiley, New York, 1982), pp. 117–248.

Yokoyama, Y.

Y. Yokoyama, N. Tsumura, H. Haneishi, J. Hayashi, M. Saito, “A new color management system based on human perception and its application to recording and reproduction of art paintings,” in Proceedings of the 5th Color Imaging Conference: Color Science, Systems and Applications (Society for Imaging Science and Technology, Springfield, Va., 1997), pp. 169–172.

Appl. Opt. (2)

Color Res. Appl. (1)

M. R. Luo, G. Cui, B. Rigg, “The development of the CIE 2000 colour-difference formula: CIEDE2000,” Color Res. Appl. 26, 340–350 (2001).
[CrossRef]

Color Technol. (1)

D. Connah, S. Westland, M. G. A. Thomson, “Recovering spectral information using digital camera systems,” Color Technol. 117, 309–312 (2001).
[CrossRef]

J. Chem. Phys. (1)

N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, E. Teller, “Equations of state calculations by fast computing machines,” J. Chem. Phys. 21, 1087–1092 (1953).
[CrossRef]

J. Imag. Sci. and Technol. (1)

F. H. Imai, R. S. Berns, D. Y. Tzeng, “A comparative analysis of spectral reflectance estimated in various spaces using a trichromatic camera system,” J. Imag. Sci. and Technol. 44, 280–287 (2000).

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

Proc. SPIE (1)

J. A. S. Viggiano, “A perception-referenced method for comparison of radiance ratio spectra and its application as an index of metamerism,” Proc. SPIE 4421, 701–704 (2002).
[CrossRef]

Sol. Energy (1)

J. J. Michalsky, “Estimation of continuous solar spectral distributions from discrete filter measurements: II. A demonstration of practicability,” Sol. Energy 34, 439–445 (1985).
[CrossRef]

Vis. Res. (1)

G. Buchsbaum, O. Bloch, “Color categories revealed by non-negative matrix factorization of Munsell color spectra,” Vis. Res. 42, 559–563 (2002).
[CrossRef] [PubMed]

Other (14)

Y. Yokoyama, N. Tsumura, H. Haneishi, J. Hayashi, M. Saito, “A new color management system based on human perception and its application to recording and reproduction of art paintings,” in Proceedings of the 5th Color Imaging Conference: Color Science, Systems and Applications (Society for Imaging Science and Technology, Springfield, Va., 1997), pp. 169–172.

S. Franco, Design with Operational Amplifiers and Analog Integrated Circuits, 3rd ed. (McGraw-Hill, Boston, 2002), pp. 311–346.

J. Y. Hardeberg, “Filter selection for multispectral color image acquisition,” in Proceedings of PICS 2003 (Society for Imaging Science and Technology, Springfield, Va., 2003), pp. 177–182.

F. H. Imai, M. R. Rosen, R. S. Berns, “Comparative study of metrics for spectral match quality,” in Proceedings of the 1st European Conference on Colour in Graphics, Image and Vision, pp. 492–496 (2002).

R. G. Kuehni, Color Space and its Divisions: Color Order from Antiquity to the Present, 1st ed. (Wiley, New York, 2003), pp. 204–270.
[CrossRef]

G. Wyszecki, W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae, 2nd ed. (Wiley, New York, 1982), pp. 117–248.

J. A. S. Viggiano, “Metrics for evaluating spectral matches: a quantitative comparison,” in Proceedings of the 2nd European Conference on Colour Graphics, Imaging and Vision (Society for Imaging Science and Technology, Springfield, Va., 2004), pp. 286–291.

P. D. Burns, “Analysis of image noise in multispectral color acquisition,” Ph.D. dissertation (Rochester Institute of Technology, 1997).

P. D. Burns, R. S. Berns, “Quantization in multispectral color image acquisition,” in Proceedings of the 7th Color Imaging Conference: Color Science, Systems and Applications (IS&T, Scottsdale, Arizona, 1999), pp. 32–35.

D. C. Day, “Filter selection for spectral estimation using a trichromatic camera,” Ph.D. dissertation (Rochester Institute of Technology, 2003).

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing (Cambridge University, 1992).

J. Y. Hardeberg (2001), “Acquisition and reproduction of color images: colorimetric and multispectral approaches” ( Dissertation.com , Parkland, Fla., 2001) (revised second edition of Ph.D. dissertation, Ecole Nationale Supérieure des Télécommunications, Paris, 1999), pp. 157–174.

D. Connah, S. Westland, M. G. A. Thomson, “Optimization of a multispectral imaging system,” in Proceedings of the 1st European Conference on Colour Graphics, Image and Vision (Society for Imaging Science and Technology, Springfield, Va., 2002), pp. 619–622.

N. Shimano, “Optimal spectral sensitivities of a color image acquisition device in the presence of noise,” in Proceedings of the 2nd European Conference on Colour Graphics, Imaging and Vision (Society for Imaging Science and Technology, Springfield, Va., 2004), pp. 379–383.

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Figures (4)

Fig. 1
Fig. 1

Each row shows the spectral sensitivity curves of the best 3-, 4-, or 5-sensor systems, respectively (the numbers of eigenvectors and sensors are equal in each case). Solid curves represent sensors for SNR = 40 dB, while dashed curves represent sensors for SNR = 26 dB.

Fig. 2
Fig. 2

Means for the CSCM metric for 1567 skylight spectra measured in Granada, Spain, using 3–5 sensors and 3–5 eigenvectors at 12-bit quantization for various SNR.

Fig. 3
Fig. 3

Effects of quantization noise: mean values for metrics of the Granada skylight spectra using 5 sensors and 5 eigenvectors for SNR = 30 dB.

Fig. 4
Fig. 4

Original skylight spectrum (solid curve) measured in Owings, Maryland, and recovered (dotted curve) spectrum for SNR = 40 dB with 5 sensors, 5 eigenvectors, and 12-bit quantization for the 90th percentile of the CSCM.

Tables (4)

Tables Icon

Table 1 Means and Standard Deviations (SD) for 1567 Skylight Spectra Measured in Granada, Spain, Using 3 Sensors, 3 Eigenvectors, and 12-Bit Quantization in Recovering Spectra at Different Signal-to-Noise Ratios (SNR)

Tables Icon

Table 2 Comparison of Exhaustive and Simulated Annealing Searches for the Granada Skylight Spectra Recovered with 3 Sensors at 12-Bit Quantization for Different SNRa

Tables Icon

Table 3 Comparison of Best 3 Sensors Found Using Annealing Searches with Various Metrics, 3 Eigenvectors, and the Granada Skylight Spectraa

Tables Icon

Table 4 Means for the Granada Skylight Spectral Recoveries Using the Best Sets of 3 to 5 Sensors for Various SNR Levels and 12-Bit Quantizationa

Equations (7)

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

ρ k = λ min λ max E ( λ ) R k ( λ ) d λ ,
ρ k = m = 1 N E ( λ m ) R k ( λ m ) .
E ( λ m ) = n = 1 N ɛ n V n ( λ m ) .
ρ = R T V ɛ = Λ ɛ ,
E R ( λ m ) = V Λ + ρ .
ρ noise = ρ + σ ,
CSCM = Ln ( 1 + 1000 ( 1 - GFC ) ) + Δ E * a b + IIE ( % ) .

Metrics