Abstract

This study proposes a piecewise Wiener estimation method to reconstruct a spectral reflectance image from a three-band image by multipoint spectral information collected simultaneously with image acquisition. A three-band image is divided into several blocks and the spectral estimation is carried out using the Wiener estimation matrix assigned to each block. Each Wiener estimation matrix is constructed on the basis of spectral measurement data. The experimental results show that the proposed method reduces the average estimation error monotonically as the number of spectral measurements increases. In addition, the computational time of the piecewise Wiener estimation costs only severalfold of the computational time of the conventional single-matrix method.

© 2009 Optical Society of America

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2008 (2)

M. Yamaguchi, H. Hideaki, and N. Ohyama, “Beyond red-green-blue (RGB): spectrum-based color imaging technology,” J. Imag. Sci. Technol. 52, 010201 (2008).
[CrossRef]

X. Zhang and H. Xu, “Reconstructing spectral reflectance by dividing spectral space and extending the principal components in principal component analysis,” J. Opt. Soc. Am. A 25371-378 (2008).
[CrossRef]

2007 (3)

2006 (2)

2005 (2)

H. Fukuda, T. Uchiyama, H. Haneishi, M. Yamaguchi, and N. Ohyama, “Development of 16-band multispectral image archiving system,” Proc. SPIE 5667, 136-145 (2005).
[CrossRef]

M. T. Eismann and R. C. Hardie, “Hyperspectral resolution enhancement using high-resolution multispectral imagery with arbitrary response functions,” IEEE Trans. Geosci. Remote Sensing 43, 455-465 (2005).
[CrossRef]

2004 (3)

R. C. Hardie, M. T. Eismann, and G. L. Wilson, “MAP estimation for hyperspectral image resolution enhancement using an auxiliary sensor,” IEEE Trans. Image Process. 13, 1174-1184(2004).
[CrossRef] [PubMed]

M. T. Eismann and R. C. Hardie, “Application of the stochastic mixing model to hyperspectral resolution enhancement,” IEEE Trans. Geosci. Remote Sensing 42, 1924-1933(2004).
[CrossRef]

K. Ohsawa, T. Ajito, Y. Komiya, H. Haneishi, M. Yamaguchi, and N. Ohyama, “Six-band HDTV camera system for spectrum-based color reproduction,” J. Imag. Sci. Technol. 48, 85-92 (2004).

2003 (1)

2002 (3)

D. Dupont, “Study of the reconstruction of reflectance curves based on tristimulus values: comparison of methods of optimization,” Color Res. Appl. 27, 88-99 (2002).
[CrossRef]

J. Y. Hardeberg, F. Schmitt, and H. Brettel, “Multispectral color image capture using a liquid crystal tunable filter,” Opt. Eng. 41, 2532-2548 (2002).
[CrossRef]

Y. Murakami, T. Obi, M. Yamaguchi and N. Ohyama, “Nonlinear estimation of spectral reflectance based on Gaussian mixture distribution for color image reproduction,” Appl. Opt. 41, 4840-4847 (2002).

2001 (1)

M. Yamaguchi, T. Teraji, K. Ohsawa, T. Uchiyama, H. Motomura, Y. Murakami, and N. Ohyama, “Color image reproduction based on the multispectral and multiprimary imaging: experimental evaluation,” Proc. SPIE 4663, 15-26 (2001).

2000 (2)

1999 (1)

1997 (1)

M. Yamaguchi, R. Iwama, Y. Ohya, T. Obi, N. Ohyama, Y. Komiya, and T. Wada, “Natural color reproduction in the television system for telemedicine,” Proc. SPIE 3031, 482-489 (1997).
[CrossRef]

1994 (1)

D. P. Filiberti, S. E. Marsh, and R. A. Schowengerdt, “Synthesis of imagery with high spatial and spectral resolution from multiple image sources,” Opt. Eng. 33, 2520-2528 (1994).
[CrossRef]

1987 (1)

J. C. Price, “Combining panchromatic and multispectral imagery from dual resolution satellite instruments,” Remote Sens. Environ. 21, 119-128 (1987).
[CrossRef]

1980 (1)

J. S. Lim, “Image restoration by short space spectral subtraction,” IEEE Trans. Acoust. Speech Signal Process. 28191-197 (1980).
[CrossRef]

1976 (1)

Ajito, T.

K. Ohsawa, T. Ajito, Y. Komiya, H. Haneishi, M. Yamaguchi, and N. Ohyama, “Six-band HDTV camera system for spectrum-based color reproduction,” J. Imag. Sci. Technol. 48, 85-92 (2004).

Ayala, F.

Berns, P. D.

P. D. Berns and R. S. Berns, “Analysis of multispectral image capture,” in Proceedings of the 4th Color Imaging Conference (Society of Imaging Science and Technology, 1996), pp. 19-22.

Berns, R. S.

P. D. Berns and R. S. Berns, “Analysis of multispectral image capture,” in Proceedings of the 4th Color Imaging Conference (Society of Imaging Science and Technology, 1996), pp. 19-22.

Bochko, V.

V. Bochko, N. Tsumura, and Y. Miyake, “Spectral color imaging system for estimating spectral reflectance of paint,” J. Imag. Sci. Technol. 51, 70-78 (2007).
[CrossRef]

Brettel, H.

J. Y. Hardeberg, F. Schmitt, and H. Brettel, “Multispectral color image capture using a liquid crystal tunable filter,” Opt. Eng. 41, 2532-2548 (2002).
[CrossRef]

Cai, P.

DiCarlo, J. M.

Dupont, D.

D. Dupont, “Study of the reconstruction of reflectance curves based on tristimulus values: comparison of methods of optimization,” Color Res. Appl. 27, 88-99 (2002).
[CrossRef]

Echavarri, J. F.

Eismann, M. T.

M. T. Eismann and R. C. Hardie, “Hyperspectral resolution enhancement using high-resolution multispectral imagery with arbitrary response functions,” IEEE Trans. Geosci. Remote Sensing 43, 455-465 (2005).
[CrossRef]

M. T. Eismann and R. C. Hardie, “Application of the stochastic mixing model to hyperspectral resolution enhancement,” IEEE Trans. Geosci. Remote Sensing 42, 1924-1933(2004).
[CrossRef]

R. C. Hardie, M. T. Eismann, and G. L. Wilson, “MAP estimation for hyperspectral image resolution enhancement using an auxiliary sensor,” IEEE Trans. Image Process. 13, 1174-1184(2004).
[CrossRef] [PubMed]

Filiberti, D. P.

D. P. Filiberti, S. E. Marsh, and R. A. Schowengerdt, “Synthesis of imagery with high spatial and spectral resolution from multiple image sources,” Opt. Eng. 33, 2520-2528 (1994).
[CrossRef]

Finlayson, G. D.

Fukuda, H.

H. Fukuda, T. Uchiyama, H. Haneishi, M. Yamaguchi, and N. Ohyama, “Development of 16-band multispectral image archiving system,” Proc. SPIE 5667, 136-145 (2005).
[CrossRef]

Haneishi, H.

H. Fukuda, T. Uchiyama, H. Haneishi, M. Yamaguchi, and N. Ohyama, “Development of 16-band multispectral image archiving system,” Proc. SPIE 5667, 136-145 (2005).
[CrossRef]

K. Ohsawa, T. Ajito, Y. Komiya, H. Haneishi, M. Yamaguchi, and N. Ohyama, “Six-band HDTV camera system for spectrum-based color reproduction,” J. Imag. Sci. Technol. 48, 85-92 (2004).

H. Haneishi, T. Hasegawa, A. Hosoi, Y. Yokoyama, N. Tsumura, and Y. Miyake, “System design for accurately estimating spectral reflectance of art paintings,” Appl. Opt. 39, 6621-6632 (2000).
[CrossRef]

Hardeberg, J. Y.

J. Y. Hardeberg, F. Schmitt, and H. Brettel, “Multispectral color image capture using a liquid crystal tunable filter,” Opt. Eng. 41, 2532-2548 (2002).
[CrossRef]

Hardie, R. C.

M. T. Eismann and R. C. Hardie, “Hyperspectral resolution enhancement using high-resolution multispectral imagery with arbitrary response functions,” IEEE Trans. Geosci. Remote Sensing 43, 455-465 (2005).
[CrossRef]

M. T. Eismann and R. C. Hardie, “Application of the stochastic mixing model to hyperspectral resolution enhancement,” IEEE Trans. Geosci. Remote Sensing 42, 1924-1933(2004).
[CrossRef]

R. C. Hardie, M. T. Eismann, and G. L. Wilson, “MAP estimation for hyperspectral image resolution enhancement using an auxiliary sensor,” IEEE Trans. Image Process. 13, 1174-1184(2004).
[CrossRef] [PubMed]

Hasegawa, T.

Hauta-Kasari, M.

Hayashi, J.

H. Sugiura, T. Kuno, N. Watanabe, N. Matoba, J. Hayashi, and Y. Miyake, “Development of highly accurate multispectral cameras,” presented at International Symposium on Multispectral Imaging and Color Reproduction for Digital Archives, Chiba, Japan, 21-22 October 1999.

Hideaki, H.

M. Yamaguchi, H. Hideaki, and N. Ohyama, “Beyond red-green-blue (RGB): spectrum-based color imaging technology,” J. Imag. Sci. Technol. 52, 010201 (2008).
[CrossRef]

Hill, B.

B. Hill, “Color capture, color management and the problem of metamerism,” Proc. SPIE 3963, 2-14 (2000).
[CrossRef]

Hosoi, A.

Ietomi, K.

Y. Murakami, K. Ietomi, M. Yamaguchi, and N. Ohyama, “MAP estimation of spectral reflectance from color image and multipoint spectral measurements,” Appl. Opt. 46, 7068-7082 (2007).
[CrossRef] [PubMed]

K. Ietomi, Y. Murakami, M. Yamaguchi, and N. Ohyama, MAP estimation for spectral image reconstruction using 3-band image and multipoint spectral measurements, presented at 9th International Symposium on Multispectral Colour Science and Application, Taipei, Taiwan, May 2007.

Iwama, R.

M. Yamaguchi, R. Iwama, Y. Ohya, T. Obi, N. Ohyama, Y. Komiya, and T. Wada, “Natural color reproduction in the television system for telemedicine,” Proc. SPIE 3031, 482-489 (1997).
[CrossRef]

Komiya, Y.

K. Ohsawa, T. Ajito, Y. Komiya, H. Haneishi, M. Yamaguchi, and N. Ohyama, “Six-band HDTV camera system for spectrum-based color reproduction,” J. Imag. Sci. Technol. 48, 85-92 (2004).

M. Yamaguchi, R. Iwama, Y. Ohya, T. Obi, N. Ohyama, Y. Komiya, and T. Wada, “Natural color reproduction in the television system for telemedicine,” Proc. SPIE 3031, 482-489 (1997).
[CrossRef]

Kuno, T.

H. Sugiura, T. Kuno, N. Watanabe, N. Matoba, J. Hayashi, and Y. Miyake, “Development of highly accurate multispectral cameras,” presented at International Symposium on Multispectral Imaging and Color Reproduction for Digital Archives, Chiba, Japan, 21-22 October 1999.

Lim, J. S.

J. S. Lim, “Image restoration by short space spectral subtraction,” IEEE Trans. Acoust. Speech Signal Process. 28191-197 (1980).
[CrossRef]

Mancill, C. E.

Marsh, S. E.

D. P. Filiberti, S. E. Marsh, and R. A. Schowengerdt, “Synthesis of imagery with high spatial and spectral resolution from multiple image sources,” Opt. Eng. 33, 2520-2528 (1994).
[CrossRef]

Matoba, N.

H. Sugiura, T. Kuno, N. Watanabe, N. Matoba, J. Hayashi, and Y. Miyake, “Development of highly accurate multispectral cameras,” presented at International Symposium on Multispectral Imaging and Color Reproduction for Digital Archives, Chiba, Japan, 21-22 October 1999.

Miyake, Y.

V. Bochko, N. Tsumura, and Y. Miyake, “Spectral color imaging system for estimating spectral reflectance of paint,” J. Imag. Sci. Technol. 51, 70-78 (2007).
[CrossRef]

H. Haneishi, T. Hasegawa, A. Hosoi, Y. Yokoyama, N. Tsumura, and Y. Miyake, “System design for accurately estimating spectral reflectance of art paintings,” Appl. Opt. 39, 6621-6632 (2000).
[CrossRef]

H. Sugiura, T. Kuno, N. Watanabe, N. Matoba, J. Hayashi, and Y. Miyake, “Development of highly accurate multispectral cameras,” presented at International Symposium on Multispectral Imaging and Color Reproduction for Digital Archives, Chiba, Japan, 21-22 October 1999.

Miyazawa, K.

Morovic, P.

Motomura, H.

M. Yamaguchi, T. Teraji, K. Ohsawa, T. Uchiyama, H. Motomura, Y. Murakami, and N. Ohyama, “Color image reproduction based on the multispectral and multiprimary imaging: experimental evaluation,” Proc. SPIE 4663, 15-26 (2001).

Murakami, Y.

Y. Murakami, K. Ietomi, M. Yamaguchi, and N. Ohyama, “MAP estimation of spectral reflectance from color image and multipoint spectral measurements,” Appl. Opt. 46, 7068-7082 (2007).
[CrossRef] [PubMed]

Y. Murakami, T. Obi, M. Yamaguchi and N. Ohyama, “Nonlinear estimation of spectral reflectance based on Gaussian mixture distribution for color image reproduction,” Appl. Opt. 41, 4840-4847 (2002).

M. Yamaguchi, T. Teraji, K. Ohsawa, T. Uchiyama, H. Motomura, Y. Murakami, and N. Ohyama, “Color image reproduction based on the multispectral and multiprimary imaging: experimental evaluation,” Proc. SPIE 4663, 15-26 (2001).

K. Ietomi, Y. Murakami, M. Yamaguchi, and N. Ohyama, MAP estimation for spectral image reconstruction using 3-band image and multipoint spectral measurements, presented at 9th International Symposium on Multispectral Colour Science and Application, Taipei, Taiwan, May 2007.

Obi, T.

Y. Murakami, T. Obi, M. Yamaguchi and N. Ohyama, “Nonlinear estimation of spectral reflectance based on Gaussian mixture distribution for color image reproduction,” Appl. Opt. 41, 4840-4847 (2002).

M. Yamaguchi, R. Iwama, Y. Ohya, T. Obi, N. Ohyama, Y. Komiya, and T. Wada, “Natural color reproduction in the television system for telemedicine,” Proc. SPIE 3031, 482-489 (1997).
[CrossRef]

Ohsawa, K.

K. Ohsawa, T. Ajito, Y. Komiya, H. Haneishi, M. Yamaguchi, and N. Ohyama, “Six-band HDTV camera system for spectrum-based color reproduction,” J. Imag. Sci. Technol. 48, 85-92 (2004).

M. Yamaguchi, T. Teraji, K. Ohsawa, T. Uchiyama, H. Motomura, Y. Murakami, and N. Ohyama, “Color image reproduction based on the multispectral and multiprimary imaging: experimental evaluation,” Proc. SPIE 4663, 15-26 (2001).

Ohya, Y.

M. Yamaguchi, R. Iwama, Y. Ohya, T. Obi, N. Ohyama, Y. Komiya, and T. Wada, “Natural color reproduction in the television system for telemedicine,” Proc. SPIE 3031, 482-489 (1997).
[CrossRef]

Ohyama, N.

M. Yamaguchi, H. Hideaki, and N. Ohyama, “Beyond red-green-blue (RGB): spectrum-based color imaging technology,” J. Imag. Sci. Technol. 52, 010201 (2008).
[CrossRef]

Y. Murakami, K. Ietomi, M. Yamaguchi, and N. Ohyama, “MAP estimation of spectral reflectance from color image and multipoint spectral measurements,” Appl. Opt. 46, 7068-7082 (2007).
[CrossRef] [PubMed]

H. Fukuda, T. Uchiyama, H. Haneishi, M. Yamaguchi, and N. Ohyama, “Development of 16-band multispectral image archiving system,” Proc. SPIE 5667, 136-145 (2005).
[CrossRef]

K. Ohsawa, T. Ajito, Y. Komiya, H. Haneishi, M. Yamaguchi, and N. Ohyama, “Six-band HDTV camera system for spectrum-based color reproduction,” J. Imag. Sci. Technol. 48, 85-92 (2004).

Y. Murakami, T. Obi, M. Yamaguchi and N. Ohyama, “Nonlinear estimation of spectral reflectance based on Gaussian mixture distribution for color image reproduction,” Appl. Opt. 41, 4840-4847 (2002).

M. Yamaguchi, T. Teraji, K. Ohsawa, T. Uchiyama, H. Motomura, Y. Murakami, and N. Ohyama, “Color image reproduction based on the multispectral and multiprimary imaging: experimental evaluation,” Proc. SPIE 4663, 15-26 (2001).

M. Yamaguchi, R. Iwama, Y. Ohya, T. Obi, N. Ohyama, Y. Komiya, and T. Wada, “Natural color reproduction in the television system for telemedicine,” Proc. SPIE 3031, 482-489 (1997).
[CrossRef]

K. Ietomi, Y. Murakami, M. Yamaguchi, and N. Ohyama, MAP estimation for spectral image reconstruction using 3-band image and multipoint spectral measurements, presented at 9th International Symposium on Multispectral Colour Science and Application, Taipei, Taiwan, May 2007.

Parkkinen, J.

Pratt, W. K.

Price, J. C.

J. C. Price, “Combining panchromatic and multispectral imagery from dual resolution satellite instruments,” Remote Sens. Environ. 21, 119-128 (1987).
[CrossRef]

Renet, P.

Schmitt, F.

J. Y. Hardeberg, F. Schmitt, and H. Brettel, “Multispectral color image capture using a liquid crystal tunable filter,” Opt. Eng. 41, 2532-2548 (2002).
[CrossRef]

Schowengerdt, R. A.

D. P. Filiberti, S. E. Marsh, and R. A. Schowengerdt, “Synthesis of imagery with high spatial and spectral resolution from multiple image sources,” Opt. Eng. 33, 2520-2528 (1994).
[CrossRef]

Shao, S.

Shen, H.

Sugiura, H.

H. Sugiura, T. Kuno, N. Watanabe, N. Matoba, J. Hayashi, and Y. Miyake, “Development of highly accurate multispectral cameras,” presented at International Symposium on Multispectral Imaging and Color Reproduction for Digital Archives, Chiba, Japan, 21-22 October 1999.

Teraji, T.

M. Yamaguchi, T. Teraji, K. Ohsawa, T. Uchiyama, H. Motomura, Y. Murakami, and N. Ohyama, “Color image reproduction based on the multispectral and multiprimary imaging: experimental evaluation,” Proc. SPIE 4663, 15-26 (2001).

Toyooka, S.

Tsumura, N.

V. Bochko, N. Tsumura, and Y. Miyake, “Spectral color imaging system for estimating spectral reflectance of paint,” J. Imag. Sci. Technol. 51, 70-78 (2007).
[CrossRef]

H. Haneishi, T. Hasegawa, A. Hosoi, Y. Yokoyama, N. Tsumura, and Y. Miyake, “System design for accurately estimating spectral reflectance of art paintings,” Appl. Opt. 39, 6621-6632 (2000).
[CrossRef]

Uchiyama, T.

H. Fukuda, T. Uchiyama, H. Haneishi, M. Yamaguchi, and N. Ohyama, “Development of 16-band multispectral image archiving system,” Proc. SPIE 5667, 136-145 (2005).
[CrossRef]

M. Yamaguchi, T. Teraji, K. Ohsawa, T. Uchiyama, H. Motomura, Y. Murakami, and N. Ohyama, “Color image reproduction based on the multispectral and multiprimary imaging: experimental evaluation,” Proc. SPIE 4663, 15-26 (2001).

Wada, T.

M. Yamaguchi, R. Iwama, Y. Ohya, T. Obi, N. Ohyama, Y. Komiya, and T. Wada, “Natural color reproduction in the television system for telemedicine,” Proc. SPIE 3031, 482-489 (1997).
[CrossRef]

Wandell, B. A.

Watanabe, N.

H. Sugiura, T. Kuno, N. Watanabe, N. Matoba, J. Hayashi, and Y. Miyake, “Development of highly accurate multispectral cameras,” presented at International Symposium on Multispectral Imaging and Color Reproduction for Digital Archives, Chiba, Japan, 21-22 October 1999.

Wilson, G. L.

R. C. Hardie, M. T. Eismann, and G. L. Wilson, “MAP estimation for hyperspectral image resolution enhancement using an auxiliary sensor,” IEEE Trans. Image Process. 13, 1174-1184(2004).
[CrossRef] [PubMed]

Xin, J. H.

Xu, H.

Yamaguchi, M.

M. Yamaguchi, H. Hideaki, and N. Ohyama, “Beyond red-green-blue (RGB): spectrum-based color imaging technology,” J. Imag. Sci. Technol. 52, 010201 (2008).
[CrossRef]

Y. Murakami, K. Ietomi, M. Yamaguchi, and N. Ohyama, “MAP estimation of spectral reflectance from color image and multipoint spectral measurements,” Appl. Opt. 46, 7068-7082 (2007).
[CrossRef] [PubMed]

H. Fukuda, T. Uchiyama, H. Haneishi, M. Yamaguchi, and N. Ohyama, “Development of 16-band multispectral image archiving system,” Proc. SPIE 5667, 136-145 (2005).
[CrossRef]

K. Ohsawa, T. Ajito, Y. Komiya, H. Haneishi, M. Yamaguchi, and N. Ohyama, “Six-band HDTV camera system for spectrum-based color reproduction,” J. Imag. Sci. Technol. 48, 85-92 (2004).

Y. Murakami, T. Obi, M. Yamaguchi and N. Ohyama, “Nonlinear estimation of spectral reflectance based on Gaussian mixture distribution for color image reproduction,” Appl. Opt. 41, 4840-4847 (2002).

M. Yamaguchi, T. Teraji, K. Ohsawa, T. Uchiyama, H. Motomura, Y. Murakami, and N. Ohyama, “Color image reproduction based on the multispectral and multiprimary imaging: experimental evaluation,” Proc. SPIE 4663, 15-26 (2001).

M. Yamaguchi, R. Iwama, Y. Ohya, T. Obi, N. Ohyama, Y. Komiya, and T. Wada, “Natural color reproduction in the television system for telemedicine,” Proc. SPIE 3031, 482-489 (1997).
[CrossRef]

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Figures (16)

Fig. 1
Fig. 1

Schematic representation of the proposed method.

Fig. 2
Fig. 2

One-dimensional Hamming window when block size is 8.

Fig. 3
Fig. 3

Four windows used in estimation of area of D 1 / 2 × D 2 / 2 (indicated by black squares).

Fig. 4
Fig. 4

Spectral reflectance images used in simulations: (a) Toy, (b) Scarf, and (c) Flowers. Images are displayed in monochrome.

Fig. 5
Fig. 5

Example of (a) simulated measured spectra with and without error and (b) error spectra. Two types of errors, random white noise ( 50 dB ) and spectral blur ( 30 nm at half bandwidth), are considered.

Fig. 6
Fig. 6

NRMSE in estimated spectral reflectance image of Toy in the noise-free case obtained by varying the number of spectral measurements, number of blocks, and parameter ρ.

Fig. 7
Fig. 7

NRMSE with optimal ρ versus the horizontal and vertical number of blocks for (a) Toy, (b) Scarf, and (c) Flowers in the noise-free case.

Fig. 8
Fig. 8

Logarithm of optimal ρ versus inverse of block length.

Fig. 9
Fig. 9

NRMSE of estimated spectral reflectance image in the noise-free case obtained by varying the area of measurement region of spectrum for (a) Toy, (b) Scarf, and (c) Flowers.

Fig. 10
Fig. 10

Comparison of NRMSE from Wiener, SS-MAP, and PW estimations in the noise-free case obtained by varying the number of spectral measurements.

Fig. 11
Fig. 11

Comparison of (a) average and (b) maximum Δ E a b * of Toy under F2 illuminant obtained from Wiener, SS-MAP, and PW estimations in the noise-free case.

Fig. 12
Fig. 12

Influence of imaging noise and two types of errors of spectral measurements on (a) NRMSE, (b) average Δ E a b * , and (c) maximum Δ E a b * for Toy under F2 illuminant.

Fig. 13
Fig. 13

Comparison of (a) average and (b) maximum Δ E a b * of Toy under F2 illuminant obtained from Wiener, SS-MAP, and PW estimations in the noisy case.

Fig. 14
Fig. 14

Original and estimated spectral reflectance functions by Wiener, SS-MAP, and PW for two pixels in Toy image. The number of spectral measurements is 16 × 16 and a noise-free condition is assumed. Numeric values in parenthesis indicate NRMSE.

Fig. 15
Fig. 15

Visualized Δ E a b * images of a part of Scarf image under F2 illuminant in the noise-free case. The number of spectral measurements is 64 × 64 and the 8 bit pixel value corresponds to Δ E a b * × 20 .

Fig. 16
Fig. 16

Comparison of computation time of Wiener, SS-MAP, and PW estimations required to obtain (a) a spectral reflectance image and (b) an XYZ tristimulus value image.

Tables (1)

Tables Icon

Table 1 Comparison of Correlation Information Used in Estimation

Equations (18)

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f ( n 1 , n 2 ) = [ f ( n 1 , n 2 , 1 ) , f ( n 1 , n 2 , 2 ) , , f ( n 1 , n 2 , L ) ] T .
g ( n 1 , n 2 ) = Hf ( n 1 , n 2 ) + ε ( n 1 , n 2 ) ,
r ( m 1 , m 2 ) = r ( m ) = 1 | Ω m | Ω m f ( n ) ,
M k = C k H T ( HC k H T + N ) 1 ,
C = 1 M RR T
R = ( r ( 1 ) , r ( 2 ) , , r ( M ) ) .
C k = RA k R T ,
A k = 1 m = 1 M α k , m 2 ( α k , 1 2 α k ; M 2 ) ,
α k , m = ρ d ( k , m ) ,
f ^ k ( n ) = M k g ( n ) ,
f ^ ( n ) = Σ k W k ( n ) f ^ k ( n ) for     all   k   of   interest ,
Σ k W k ( n ) = 1 for     all   k   of   interest .
W k ( n ) = W k 1 k 2 ( n 1 , n 2 ) = w 1 [ n 1 + ( 1 2 k 1 ) D 1 ] w 2 [ n 2 + ( 1 2 k 2 ) D 2 ] ,
w 1 ( n 1 ) = { 0.5 0.5 cos ( 2 π n 1 2 D 1 ) 0 n 1 2 D 1 1 0 else ,
w 2 ( n 2 ) = { 0.5 0.5 cos ( 2 π n 2 2 D 2 ) 0 n 2 2 D 2 1 0 else ,
M k = RA k R T H T ( HRA k R T H T + N ) 1 .
α k , m = ρ d ( k , m ) = ( ρ D ) d ( k , m ) D = 0.1 d ( k , m ) D .
r ( i , j ) = g ( i ) T g ( j ) × ρ d ( i , j ) ,

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