基于改进R矩阵方法的光谱反射率重建研究

为了解决传统R矩阵方法重建光谱反射率过程中的病态问题,提出了一种正则化R矩阵改进方法。研究了如何使用Tikhonov正则化来限制R矩阵方法求解Moore-Penrose伪逆矩阵中所产生的病态问题,同时使用L曲线方法从训练样本数据中得到有效限制病态情况的最优正则化参数。实验结果表明:与R矩阵方法相比,改进的正则化R矩阵方法重建的光谱精度的平均均方根误差值降低了0.004 25,平均适应度系数值提高了1.325%,色度精度的平均色差值降低了0.141 9,并且在实际的应用中具有较好的表现。该方法能够满足精度较高的文物艺术品颜色再现的需要。

Spectral reflectance reconstruction based on improved matrix R method

In order to solve the ill-posed problem in the process of reconstructing the spectral reflectance using the traditional matrix R method, an improved matrix R method was proposed in this paper. 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. The experimental results verified that compared with traditional matrix R method, the proposed regularization matrix R method had higher spectral and chromatic accuracy of reconstructed spectrum whose mean root mean square error value reduced 0.004 25, mean goodness of fit coefficient value improved 1.325%, and mean color difference value reduced 0.141 9. At the same time, the proposed regularization matrix R method achieved good performance in practical application. It can meet the high accuracy of cultural relics color reproduction needs.