Cluster Computing

, Volume 22, Supplement 1, pp 493–502 | Cite as

Study of spectral reflectance reconstruction based on regularization matrix R method

  • Ke WangEmail author
  • Huiqin Wang
  • Zhan Wang
  • Qinghua Gu
  • Ying Yin
  • Li Mao
  • Ying Lu


In order to solve the ill-posed problem in the process of reconstructing the spectral reflectance of the traditional matrix R method, a regularization matrix R method was proposed in this paper. Through analyzing the ill-posed equation of matrix R to reconstruct the spectral reflectance, the Tikhonov regularization method was researched to restrict the ill-posed problem to solve the Moore-Penrose pseudo inverse matrix. The L-curve method was used to obtain the optimal regularization parameter by training samples data in order to effectively restrict the ill-posed situation which was caused by the equation solving of spectral reconstruction. The experimental results verified that the proposed regularization matrix R method had higher spectral and chromatic accuracy of reconstructed spectrum than traditional matrix R method. At the same time, the proposed regularization matrix R method achieved good performance for color reproduction of real mural in practical application.


Spectral reflectance reconstruction Matrix R Tikhonov regularization 



The work has been supported by the Youth Fund of National Natural Science Foundation, China (Grant Nos. 51404182, 61701388), the International Science and Technology Cooperation Project of the Science and Technology Department of Shaanxi Province, China (Grant No. 2017KW-036), the Special fund of the Education Department of Shaanxi Province, China (Grant No. 17JK0431), the Soft Science Project of Science and Technology Bureau of Xi’an, China [Grant No. 2016043SF/RK06(3)], the Science and Technology Project of Science and Technology Bureau of Xi’an Beilin District, China (Grant Nos. GX1605, GX1606), and the Youth Science and Technology Fund Project of Xi’an University of Architecture And Technology, China (Grant No. QN1628).


  1. 1.
    Ren, P.Y., Liao, N.F., Chai, B.H., Yang, W.P., Li, S.X.: Spectral reflectance recovery based on multispectral imaging. Opt. Technol. 31(3), 427–429 (2005)Google Scholar
  2. 2.
    Yang, W.P., Xu, N., Duan, J.J.: Application and development of multispectral imaging technology in color reproduction. J. Yunnan Univ. Natly. 18(3), 191–197 (2009)Google Scholar
  3. 3.
    Liu, Z., Wan, X.X., Huang, X.G., Liu, Q., Li, C.: The study on spectral reflectance reconstruction based on wideband multi-spectral acquisition system. Spectrosc. Spectr. Anal. 33(4), 1076–1081 (2014)Google Scholar
  4. 4.
    Barakzehi, M., Amirshahi, S.H., Peyvandi, S.: Reconstruction of total radiance spectra of fluorescent samples by mean of nonlinear principle component analysis. J. Opt. Soc. Am. A 30(9), 1862–1870 (2013)CrossRefGoogle Scholar
  5. 5.
    Urban, P., Rosen, M.R., Berns, R.S.: Spectral image reconstruction using an edge preserving spatio-spectral wiener estimation. J. Opt. Soc. Am. A 26(8), 1865–1875 (2009)CrossRefGoogle Scholar
  6. 6.
    Wyszecki, G.: Valenzmetrische untersuchung des zusammenhanges wischen normaler und anomaler trichromasie. Die Farbe. 1953(2), 39–52 (1953)Google Scholar
  7. 7.
    Wyszecki, G.: Evaluation of metameric colors. Josa 48(7), 451–452 (1958)CrossRefGoogle Scholar
  8. 8.
    Cohen, J.B., Kappau, W.E.: Color mixture and fundamental metamers and Wyszecki’s metameric black. Am. J. Psychol. 95(4), 537–564 (1982)CrossRefGoogle Scholar
  9. 9.
    Cohen, J.B., Kappau, W.E.: Color mixture and fundamental metamers: theory, algebra, geometry, application. Am. J. Psychol. 98(2), 171–259 (1985)CrossRefGoogle Scholar
  10. 10.
    Fairman, H.S.: Recommender terminology for matrix R and metamerism. Color Res. Appl. 16(5), 337–341 (1991)Google Scholar
  11. 11.
    Neumaier, A.: Solving ill-conditioned and singular linear systems: a tutorial on regularization. Siam Rev. 40(3), 636–666 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Shimano, N., Terai, K., Hironaga, M.: Recovery of spectral reflectance of object being imaging by multispectral cameras. J. Opt. Soc. Am. A 24(10), 3211 (2007)CrossRefGoogle Scholar
  13. 13.
    Cohen, J.B.: Color and color mixture: scalar and vector fundamentals. Color Res. Appl. 13(1), 5–39 (1988)CrossRefGoogle Scholar
  14. 14.
    Cohen, J.B.: Visual Color and Color Mixture: The Fundamental Color Space. University of Illinois Press, Urbana (2001)Google Scholar
  15. 15.
    Zhao, Y.H., Berns, R.S.: Image-based spectral reflectance reconstruction using the matrix R method. Color Res. Appl. 32(5), 343–351 (2007)CrossRefGoogle Scholar
  16. 16.
    Imai, F.H., Rosen, M.R., Berns, R.S.: Comparative study of metrics for spectral match quality. In: Proceedings of the 1st European Conference on Color Graphics, Imaging and Vision (CGIV 2002). Spring filed, MA, pP. 492–496 (2002)Google Scholar
  17. 17.
    Markovsk, I., Huffel, S.V.: Overview of total least-squares methods. Signal Process. 87(10), 2283–2302 (2007)CrossRefzbMATHGoogle Scholar
  18. 18.
    Hansen, P.C., Oleary, D.P.: The use of L-curve in the regularization of discrete ill-posed problems. Siam J. Sci. Comput. 14(6), 1487–1503 (1993)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Tikhonov, A.N.: Solution of incorrectly formulated problems and the regularization method. Soviet Math. Dokl. 5(4), 1035–1038 (1963)zbMATHGoogle Scholar
  20. 20.
    Tikhonov, A.N., Arsenin, V.Y.: Solution of ill-posed problems. Math. Comput. 32(144), 491–491 (1977)Google Scholar
  21. 21.
    Bonesky, T.: Morozov’s discrepancy principle and Tikhonov-type functionals. Inverse Prob. 25(1), 015015 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Rezghi, M., Hosseini, S.M.: A new variant of L-curve for Tikonov regularization. J. Comput. Appl. Math. 231(2), 914–924 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Agahian, F., Funt, B.J.: Outlier modeling for spectral data reduction. J. Opt. Soc. Am. A 31(7), 1445 (2014)CrossRefGoogle Scholar
  24. 24.
    Li, N., Xu, Z., Zhao, H.J., Deng, K.W.: Improved support vector machines model based on multi-spectral parameters. Clust. Comput. 20(6), 1–10 (2017)Google Scholar
  25. 25.
    Banicescu, I., Velusamy, V., Devaprasad, J.: On the scalability of dynamic scheduling scientific applications with adaptive weighted factoring. Clust. Comput. 6(3), 215–226 (2003)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.School of ManagementXi’an University of Architecture and TechnologyXi’anChina
  2. 2.School of Information and Control EngineeringXi’an University of Architecture and TechnologyXi’anChina
  3. 3.Shaanxi Provincial Institute of Cultural Relics ProtectionXi’anChina

Personalised recommendations