基于迭代Tikhonov正规化的三刺激值重建光谱方法研究

光谱图像中的反射率光谱数据维数高，且与光源、设备均无关，能够比较全面、真实、客观地描述图像中物体的颜色信息。针对三色相机的光谱图像获取系统中三维色度数据重建多维光谱数据产生的光谱信息丢失、以及伴随而生的颜色信息丢失问题，提出了迭代Tikhonov正规化的光谱重建方法。首先依据色度学理论中色度值与反射率光谱之间的关系，构建反射率光谱重建方程建立起相机所获三维色度数据与高维反射率光谱数据的映射关系;然后，通过反射率光谱重建方程的病态分析，在Moore-Penrose伪逆矩阵求解思想的基础上构建迭代Tikhonov正规化方法求解反射率光谱，并利用训练样本数据通过L-曲线方法训练获取迭代Tikhonov正规化的最优正规化参数，以有效控制并改善反射率光谱重建方程求解的病态、减少重建光谱的光谱信息丢失。实验通过选取样本数据对光谱重建方法进行验证。验证实验的结果表明所提出的光谱重建方法改善了三色相机的光谱图像获取系统中重建光谱的光谱信息丢失程度，使得重建光谱的光谱误差和色度误差较其他光谱重建方法均有明显降低。

Iterated Tikhonov Regularization for Spectral Recovery from Tristimulus

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 recon‐struct 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 regu‐larized 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 colori‐metric errors compared with the previous method .