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Journal of Spectroscopy
Volume 2014 (2014), Article ID 345193, 8 pages
Research Article

Spectral Separation for Multispectral Image Reproduction Based on Constrained Optimization Method

1School of Printing and Packing Engineering, Xi'an University of Technology, Xi'an 710048, China
2School of Automation and Information Engineering, Xi'an University of Technology, Xi'an 710048, China

Received 11 May 2014; Accepted 2 June 2014; Published 22 June 2014

Academic Editor: Qingrui Zhang

Copyright © 2014 Bangyong Sun et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The constrained optimization method is employed to calculate the colorant values of the multispectral images. Because the spectral separation from the 31-dimensional spectral reflectance to low dimensional colorant values is very complex, an inverse process based on spectral Neugebauer model and constrained optimization method is performed. Firstly, the spectral Neugebauer model is applied to predict the colorants’ spectral reflectance values, and it is modified by using the Yule-Nielsen -value and the effective area coverages. Then, the spectral reflectance root mean square (RRMS) error is established as the objective function for the optimization method, while the colorant values are constrained to 0~1. At last, when the nonlinear constraints and related parameters are set appropriately, the colorant values are accurately calculated for the multispectral images corresponding to the minimum RRMS errors. In the experiment, the colorant errors of the cyan, magenta and yellow inks are all below 2.5% and the average spectral error is below 5%, which indicate that the precision of the spectral separation method in this paper is acceptable.