基于非线性光谱字典学习的单幅RGB图像光谱重建方法研究

针对单幅RGB图像重建光谱图像中的病态问题，提出一种基于非线性光谱字典学习的非线性重建方法。为了适应线性和非线性数据，该方法首先改进了基于自联想神经网络模型的非线性主成分分析算法，并利用其从训练光谱集中学习低维光谱字典，用于光谱重建的求逆方程中，以缓解病态状况。再在此光谱字典基础上，利用阻尼高斯牛顿法结合截断奇异值分解的正则化方法，进一步缓解该非线性反演的病态问题，实现单幅RGB图像重建光谱图像。在实验中，采用Munsell以及Munsell+Pantone两个光谱训练集学习光谱字典，同时利用CAVE和UEA光谱图像库进行光谱重建测试。该方法测试结果与现有方法比较发现，该方法在不同光谱训练集下重建CAVE和UEA两库光谱图像的均方根差的平均值最低，分别为0.212 4, 0.255 4, 0.229 4和0.294 9,均方根差的标准偏差接近最好方法的效果，分别为0.068 5, 0.084 7, 0.066 8和0.087 0。此结果表明该方法针对单幅RGB图像重建光谱图像在重建精度和稳定性上均存在优势。

Research on Spectral Image Reconstruction Based on Nonlinear Spectral Dictionary Learning From Single RGB Image

A nonlinear reconstruction method based on nonlinear spectral dictionary learning was proposed to solve the ill-posed problem of spectral image reconstruction from a single RGB image. In order to adapt to the linear and nonlinear data, the method firstly improves the nonlinear principal component analysis algorithm based on a modified self-association neural network model. It uses to learn the low-dimensional spectral dictionary from the training spectrum set, which is used in the inverse equation of spectral reconstruction to alleviate the ill condition. In addition, based on the spectral dictionary, the damped Gaussian Newton method combined with the truncated singular value decomposition regularization method is used further to alleviate the ill-posed problem of the nonlinear inversion, and the spectral image can be reconstructed from a single RGB image. In the experiment, two different spectral training sets, Munsell and Munsell+Pantone, were used to learn the spectral dictionary. Meanwhile, CAVE and UEA spectral image libraries were used for the spectral reconstruction tests. Compared with the existing methods, it is found that the average root means square error of CAVE and UEA spectral images reconstructed by this method under different spectral training sets were the lowest, which were 0.212 4, 0.255 4, 0.229 4 and 0.294 9 respectively. The standard deviations of root mean square error was close to the effect of the best method, which was 0.068 5, 0.084 7, 0.066 8 and 0.087 0 respectively. The results show that the method for reconstructing the spectral image from a single RGB image has advantages in accuracy and stability.