Abstract

It is well known that the noise present in an image acquisition system plays important roles in solving inverse problems, such as the reconstruction of spectral reflectances of imaged objects from the sensor responses. Usually, a recovered spectral reflectance vector r^ by a matrix W is expressed by r^=Wp, where p is a sensor response vector. In this paper, the mean square errors (MSEs) between the recovered spectral reflectances with various reconstruction matrices W and actual spectral reflectances are divided into the noise independent MSE (MSEFREE) and the noise dependent MSE (MSENOISE). By dividing the MSE into two terms, the MSENOISE is defined as the estimated noise variance multiplied by the sum of the squared singular values of the matrix W. It is shown that the relation between the increase in the MSE and the MSENOISE agrees quite well with the experimental results by the multispectral camera, and that the estimated noise variances are of the same order of magnitude for various matrices W, but the increase in the MSE by the noise mainly results from the increase in the sum of the squared singular values for the unregularized reconstruction matrix W.

© 2010 Optical Society of America

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2009 (1)

2008 (3)

M. Hironaga and N. Shimano, “Influence of noise on estimating spectral reflectances,” in Proceedings of Color Forum Japan, (Colour Forum Japan, 2008), pp. 79–82.

M. Hironaga and N. Shimano, “Evaluating the quality of an image acquisition device aimed at the reconstruction of spectral reflectances using recovery models,” J. Imaging Sci. Technol. 52, 030503 (2008).
[CrossRef]

M. A. López-Álvarez, J. Hernández-Andrés, and J. Romero, “Developing an optimum computer-designed multispectral system comprising a monochrome CCD camera and a liquid-crystal tunable filter,” Appl. Opt. 47, 4381–4390(2008).
[CrossRef]

2007 (3)

2006 (2)

N. Shimano, “Recovery of spectral reflectances of objects being imaged without prior knowledge,” IEEE Trans. Image Process. 15, 1848–1856 (2006).
[CrossRef]

N. Shimano, “Optimization of spectral sensitivities with Gaussian distribution functions for a color image acquisition device in the presence of noise,” Opt. Eng. 45, 013201 (2006).
[CrossRef]

2005 (4)

Y. Zhao, L. A. Taplin, M. Nezamabadi, and R. S. Berns, “Using the matrix R method for spectral image archives,” in Proceedings of the Tenth Congress of the International Colour Association (AIC’5) (International Colour Association, 2005), pp. 469–472.

N. Shimano, “Application of a colorimetric evaluation model to multispectral color image acquisition systems,” J. Imaging Sci. Technol. 49, 588–593 (2005).

N. Shimano, “Evaluation of a multispectral image acquisition system aimed at reconstruction of spectral reflectances,” Opt. Eng. 44, 107005 (2005).
[CrossRef]

M. A. López-Álvarez, J. Hernández-Andrés, J. Romero, and R. L. Lee, Jr., “Designing a practical system for spectral imaging of skylight,” Appl. Opt. 44, 5688–5695 (2005).
[CrossRef]

2002 (3)

N. Shimano, “Influence of noise on color correction,” in Proceedings of the First European Conference on Colour in Graphics, Image and Vision (Society for Imaging Science and Technology, 2002), pp. 549–553.

N. Shimano, “Suppression of noise effect in color corrections by spectral sensitivities of image sensors,” Opt. Rev. 9, 81–88(2002).
[CrossRef]

S. Quan, N. Ohta, R. S. Berns, X. Jiang, and N. Katoh, “Unified measure of goodness and optimal design of spectral sensitivity functions,” J. Imaging Sci. Technol. 46, 485–497 (2002).

2001 (1)

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

1999 (1)

F. H. Imai and R. S. Berns, “Spectral estimation using trichromatic digital cameras,” in Proceedings of the International Symposium on Multispectral Imaging and Color Reproduction for Digital Archives (Society of Multispectral Imaging, 1999), pp. 42–49.

1998 (1)

G. Sharma, H. J. Trussell, and M. J. Vrhel, “Optimal nonnegative color scanning filters,” IEEE Trans. Image Process. 7, 129–133 (1998).
[CrossRef]

1997 (1)

G. Sharma and H. J. Trussell, “Figure of merit for color scanners,” IEEE Trans. Image Process. 6, 990–1001 (1997).
[CrossRef]

1996 (1)

G. H. Golub and C. F. V. Loan, Matrix Computations, 3rd ed. (Johns Hopkins University Press, 1996).

1993 (1)

1989 (1)

1986 (1)

1956 (1)

Arjona, M.

Berns, R. S.

Y. Zhao, L. A. Taplin, M. Nezamabadi, and R. S. Berns, “Using the matrix R method for spectral image archives,” in Proceedings of the Tenth Congress of the International Colour Association (AIC’5) (International Colour Association, 2005), pp. 469–472.

S. Quan, N. Ohta, R. S. Berns, X. Jiang, and N. Katoh, “Unified measure of goodness and optimal design of spectral sensitivity functions,” J. Imaging Sci. Technol. 46, 485–497 (2002).

F. H. Imai and R. S. Berns, “Spectral estimation using trichromatic digital cameras,” in Proceedings of the International Symposium on Multispectral Imaging and Color Reproduction for Digital Archives (Society of Multispectral Imaging, 1999), pp. 42–49.

Connah, D.

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

de Lasarte, M.

Golub, G. H.

G. H. Golub and C. F. V. Loan, Matrix Computations, 3rd ed. (Johns Hopkins University Press, 1996).

Hallikainen, J.

Hernández-Andrés, J.

Hironaga, M.

M. Hironaga and N. Shimano, “Noise robustness of a colorimetric evaluation model for image acquisition devices with different characterization models,” Appl. Opt. 48, 5354–5362(2009).
[CrossRef]

M. Hironaga and N. Shimano, “Evaluating the quality of an image acquisition device aimed at the reconstruction of spectral reflectances using recovery models,” J. Imaging Sci. Technol. 52, 030503 (2008).
[CrossRef]

M. Hironaga and N. Shimano, “Influence of noise on estimating spectral reflectances,” in Proceedings of Color Forum Japan, (Colour Forum Japan, 2008), pp. 79–82.

N. Shimano, K. Terai, and M. Hironaga, “Recovery of spectral reflectances of objects being imaged by multispectral cameras,” J. Opt. Soc. Am. A 24, 3211–3219 (2007).
[CrossRef]

Imai, F. H.

F. H. Imai and R. S. Berns, “Spectral estimation using trichromatic digital cameras,” in Proceedings of the International Symposium on Multispectral Imaging and Color Reproduction for Digital Archives (Society of Multispectral Imaging, 1999), pp. 42–49.

Jaaskelainen, T.

Jiang, X.

S. Quan, N. Ohta, R. S. Berns, X. Jiang, and N. Katoh, “Unified measure of goodness and optimal design of spectral sensitivity functions,” J. Imaging Sci. Technol. 46, 485–497 (2002).

Katoh, N.

S. Quan, N. Ohta, R. S. Berns, X. Jiang, and N. Katoh, “Unified measure of goodness and optimal design of spectral sensitivity functions,” J. Imaging Sci. Technol. 46, 485–497 (2002).

Lee, R. L.

Loan, C. F. V.

G. H. Golub and C. F. V. Loan, Matrix Computations, 3rd ed. (Johns Hopkins University Press, 1996).

López-Álvarez, M. A.

Maloney, L.

Neugebauer, H. E. J.

Nezamabadi, M.

Y. Zhao, L. A. Taplin, M. Nezamabadi, and R. S. Berns, “Using the matrix R method for spectral image archives,” in Proceedings of the Tenth Congress of the International Colour Association (AIC’5) (International Colour Association, 2005), pp. 469–472.

Ohta, N.

S. Quan, N. Ohta, R. S. Berns, X. Jiang, and N. Katoh, “Unified measure of goodness and optimal design of spectral sensitivity functions,” J. Imaging Sci. Technol. 46, 485–497 (2002).

Parkkinen, J.

Pujol, J.

Quan, S.

S. Quan, N. Ohta, R. S. Berns, X. Jiang, and N. Katoh, “Unified measure of goodness and optimal design of spectral sensitivity functions,” J. Imaging Sci. Technol. 46, 485–497 (2002).

Romero, J.

Sharma, G.

G. Sharma, H. J. Trussell, and M. J. Vrhel, “Optimal nonnegative color scanning filters,” IEEE Trans. Image Process. 7, 129–133 (1998).
[CrossRef]

G. Sharma and H. J. Trussell, “Figure of merit for color scanners,” IEEE Trans. Image Process. 6, 990–1001 (1997).
[CrossRef]

Shimano, N.

M. Hironaga and N. Shimano, “Noise robustness of a colorimetric evaluation model for image acquisition devices with different characterization models,” Appl. Opt. 48, 5354–5362(2009).
[CrossRef]

M. Hironaga and N. Shimano, “Evaluating the quality of an image acquisition device aimed at the reconstruction of spectral reflectances using recovery models,” J. Imaging Sci. Technol. 52, 030503 (2008).
[CrossRef]

M. Hironaga and N. Shimano, “Influence of noise on estimating spectral reflectances,” in Proceedings of Color Forum Japan, (Colour Forum Japan, 2008), pp. 79–82.

N. Shimano, K. Terai, and M. Hironaga, “Recovery of spectral reflectances of objects being imaged by multispectral cameras,” J. Opt. Soc. Am. A 24, 3211–3219 (2007).
[CrossRef]

N. Shimano, “Recovery of spectral reflectances of objects being imaged without prior knowledge,” IEEE Trans. Image Process. 15, 1848–1856 (2006).
[CrossRef]

N. Shimano, “Optimization of spectral sensitivities with Gaussian distribution functions for a color image acquisition device in the presence of noise,” Opt. Eng. 45, 013201 (2006).
[CrossRef]

N. Shimano, “Application of a colorimetric evaluation model to multispectral color image acquisition systems,” J. Imaging Sci. Technol. 49, 588–593 (2005).

N. Shimano, “Evaluation of a multispectral image acquisition system aimed at reconstruction of spectral reflectances,” Opt. Eng. 44, 107005 (2005).
[CrossRef]

N. Shimano, “Suppression of noise effect in color corrections by spectral sensitivities of image sensors,” Opt. Rev. 9, 81–88(2002).
[CrossRef]

N. Shimano, “Influence of noise on color correction,” in Proceedings of the First European Conference on Colour in Graphics, Image and Vision (Society for Imaging Science and Technology, 2002), pp. 549–553.

Taplin, L. A.

Y. Zhao, L. A. Taplin, M. Nezamabadi, and R. S. Berns, “Using the matrix R method for spectral image archives,” in Proceedings of the Tenth Congress of the International Colour Association (AIC’5) (International Colour Association, 2005), pp. 469–472.

Terai, K.

Thomson, M. G. A.

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

Trussell, H. J.

G. Sharma, H. J. Trussell, and M. J. Vrhel, “Optimal nonnegative color scanning filters,” IEEE Trans. Image Process. 7, 129–133 (1998).
[CrossRef]

G. Sharma and H. J. Trussell, “Figure of merit for color scanners,” IEEE Trans. Image Process. 6, 990–1001 (1997).
[CrossRef]

P. L. Vora and H. J. Trussell, “Measure of goodness of a set of color-scanning filters,” J. Opt. Soc. Am. A 10, 1499–1508 (1993).
[CrossRef]

Valero, E. M.

Vilaseca, M.

Vora, P. L.

Vrhel, M. J.

G. Sharma, H. J. Trussell, and M. J. Vrhel, “Optimal nonnegative color scanning filters,” IEEE Trans. Image Process. 7, 129–133 (1998).
[CrossRef]

Westland, S.

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

Zhao, Y.

Y. Zhao, L. A. Taplin, M. Nezamabadi, and R. S. Berns, “Using the matrix R method for spectral image archives,” in Proceedings of the Tenth Congress of the International Colour Association (AIC’5) (International Colour Association, 2005), pp. 469–472.

Appl. Opt. (4)

Color. Technol. (1)

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

IEEE Trans. Image Process. (3)

G. Sharma and H. J. Trussell, “Figure of merit for color scanners,” IEEE Trans. Image Process. 6, 990–1001 (1997).
[CrossRef]

G. Sharma, H. J. Trussell, and M. J. Vrhel, “Optimal nonnegative color scanning filters,” IEEE Trans. Image Process. 7, 129–133 (1998).
[CrossRef]

N. Shimano, “Recovery of spectral reflectances of objects being imaged without prior knowledge,” IEEE Trans. Image Process. 15, 1848–1856 (2006).
[CrossRef]

J. Imaging Sci. Technol. (3)

S. Quan, N. Ohta, R. S. Berns, X. Jiang, and N. Katoh, “Unified measure of goodness and optimal design of spectral sensitivity functions,” J. Imaging Sci. Technol. 46, 485–497 (2002).

N. Shimano, “Application of a colorimetric evaluation model to multispectral color image acquisition systems,” J. Imaging Sci. Technol. 49, 588–593 (2005).

M. Hironaga and N. Shimano, “Evaluating the quality of an image acquisition device aimed at the reconstruction of spectral reflectances using recovery models,” J. Imaging Sci. Technol. 52, 030503 (2008).
[CrossRef]

J. Opt. Soc. Am. (1)

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

Opt. Eng. (2)

N. Shimano, “Evaluation of a multispectral image acquisition system aimed at reconstruction of spectral reflectances,” Opt. Eng. 44, 107005 (2005).
[CrossRef]

N. Shimano, “Optimization of spectral sensitivities with Gaussian distribution functions for a color image acquisition device in the presence of noise,” Opt. Eng. 45, 013201 (2006).
[CrossRef]

Opt. Rev. (1)

N. Shimano, “Suppression of noise effect in color corrections by spectral sensitivities of image sensors,” Opt. Rev. 9, 81–88(2002).
[CrossRef]

Other (5)

N. Shimano, “Influence of noise on color correction,” in Proceedings of the First European Conference on Colour in Graphics, Image and Vision (Society for Imaging Science and Technology, 2002), pp. 549–553.

M. Hironaga and N. Shimano, “Influence of noise on estimating spectral reflectances,” in Proceedings of Color Forum Japan, (Colour Forum Japan, 2008), pp. 79–82.

Y. Zhao, L. A. Taplin, M. Nezamabadi, and R. S. Berns, “Using the matrix R method for spectral image archives,” in Proceedings of the Tenth Congress of the International Colour Association (AIC’5) (International Colour Association, 2005), pp. 469–472.

G. H. Golub and C. F. V. Loan, Matrix Computations, 3rd ed. (Johns Hopkins University Press, 1996).

F. H. Imai and R. S. Berns, “Spectral estimation using trichromatic digital cameras,” in Proceedings of the International Symposium on Multispectral Imaging and Color Reproduction for Digital Archives (Society of Multispectral Imaging, 1999), pp. 42–49.

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