Iterated Tikhonov Regularization for Spectral Recovery from Tristimulus
XIE De-hong1, LI Rui1, WAN Xiao-xia2, LIU Qiang2, ZHU Wen-feng1
1. Jiangsu Province Key Lab of Pulp and Paper Science and Technology, Nanjing Forestry University, Nanjing 210037, China 2. Department of Printing and Packaging, Wuhan University, Wuhan 430079, China
Abstract：Reflective spectra in a multispectral image can objectively and originally represent color information due to their high dimensionality, illuminant independent and device independent. Aiming to the problem of loss of spectral information when the spectral data reconstructed from three-dimensional colorimetric data in the trichromatic camera-based spectral image acquisition system and its subsequent problem of loss of color information, this work proposes an iterated Tikhonov regularization to reconstruct the reflectance spectra. First of all, according to relationship between the colorimetric value and the reflective spectra in the colorimetric theory, this work constructs a spectral reconstruction equation which can reconstruct high dimensional spectral data from three dimensional colorimetric data acquired by the trichromatic camera. Then, the iterated Tikhonov regularization, inspired by the idea of the pseudo inverse Moore-Penrose, is used to cope with the linear ill-posed inverse problem during solving the equation of reconstructing reflectance spectra. Meanwhile, the work also uses the L-curve method to obtain an optimal regularized parameter of the iterated Tikhonov regularization by training a set of samples. Through these methods, the ill condition of the spectral reconstruction equation can be effectively controlled and improved, and subsequently loss of spectral information of the reconstructed spectral data can be reduced. The verification experiment is performed under another set of training samples. The experimental results show that the proposed method reconstructs the reflective spectra with less spectral information loss in the trichromatic camera-based spectral image acquisition system, which reflects in obvious decreases of spectral errors and colorimetric errors compared with the previous method.
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