*Regular Paper*

[OPTICAL REVIEW Vol. 21, No. 6 (2014) 816-825]

© 2014 The Japan Society of Applied Physics

## A Hybrid of Weighted Regression and Linear Models for Extraction of Reflectance Spectra from CIEXYZ Tristimulus Values

**Morteza Maali AMIRI and Seyed Hossein AMIRSHAHI**

*Department of Textile Engineering, Amirkabir University of Technology (Tehran Ploytechnic), Tehran 15914, Iran*

(Received May 21, 2014; Accepted September 5, 2014)

**The principal component analysis (PCA) and the non-negative matrix factorization (NNMF) methods are boosted for the recovery of the reflectance spectra from the corresponding CIEXYZ tristimulus values under a given set of viewing conditions by the estimation of CIEXYZ tristimulus values under the second set of illumination through the implementation of weighted regression technique. The weighting function is determined on the basis of the colorimetric differences of desired sample with the samples of testing set. The calculated weights are then used in a weighted regression procedure in an attempt for better estimation of CIEXYZ tristimulus values of samples under the second illuminant. In this manner, the tristimulus values of the training samples under two sets of viewing conditions become available. Two sets of bases, i.e., the six positive-negative eigenvectors and the six non-negative features of reflectance spectra data, are used for spectral recovery purpose. The suggested method increases the spectral and colorimetric performances of recovery.**

Key words: reflectance, spectrum recovery, principal component analysis, non-negative matrix factorization, regression technique