Abstract：Hyperspectral analysis of mixtures is a key technology for nondestructive testing of minerals. The spectral reflectance variation of mixtures in the 350 nm to 2 500 nm interval is regarded as a one-dimensional sequence signal with time-domain variation, and the mixture spectral separation is transformed into a blind source separation problem of time-domain signals in the paper. In order to analyze the influencing factors of the speed and accuracy of mixture spectral demixing, a blind source demixing test was conducted on the measured hyperspectral reflectance curve of the mixture using Fast ICA mathematical model, and the results of spectral demixing were analyzed from three aspects of the demixing process: the whitening mode, the initial power array, and the Gaussianity of the source spectrum, which provided a research basis for the later analysis of the mixture spectral detection. The chemically pure copper oxide and cuprous oxide mixtures, alkaline copper carbonate and copper hydroxide mixtures were selected as test objects. The source spectral Gaussianity was compared with the g-function, ZCA and PCA whitening methods, and three initial weights of unitary, random and specified weights on the unmixing spectral results using the unmixing performance index PI, the root mean square error of the spectrum and the angular distance of the spectrum as evaluation indexes. The experimental results show that the Fast ICA algorithm can effectively separate the mixture component source spectra based on unknown hyperspectral a priori information of mixed minerals. The sample separation accuracy PI values are all less than 0.18, and the effect of spectral blind source unmixing is remarkable. The spectral curves after unmixing are consistent with the source spectral curves in terms of characteristic trends, with the same absorption positions and characteristic peaks, but there are certain scale differences. In addition, the Gaussianity of the source spectrum and the selection of the unmixing g function directly affect the value of the unmixing results, and the separation accuracy of the sub-Gaussian interval curve is better than that of the super-Gaussian part. The absorption characteristics of the segmental demixing results based on Gaussianity are prominent, and the difference with the reflectance values of the source spectra increases; the whitening method of spectral preprocessing has a small impact on the accuracy of the demixing results, and the separation accuracy and spectral accuracy of the demixing results are slightly higher after ZCA whitening than PCA whitening; the comparison of the demixing results of the three initial weights of the Fast ICA model shows that the initial iterations with In the comparison of the three initial weights of the Fast ICA model, it was found that the separation accuracy, demixing accuracy and demixing time were the best and the demixing process was easier to converge when the specified weights calculated by the first iteration were used for the iterative demixing. The results show that the g-function is selected according to the full-band Gaussian performance to demix the best. The separation index PI is less than 0.14, the spectral angular distance is about 0.1, ZCA whitening has less effect on the demixing spectrum than PCA whitening, the separation index of the two groups of mixtures after ZCA whitening is about 0.1, and the separation index PI of PCA whitening is higher than 0.13 when the designation right is used as the initial weight, it helps to improve the convergence speed in the Newton iteration, so that the unmixing spectrum is closer to the known spectrum of the components, the unmixing time of the specified weight is less than 0.2 seconds, and the other two weighting methods are more than 0.3 seconds.
戴佳乐，汪金花，李孟倩，韩秀丽，缪若梵. 混合光谱曲线的Fast ICA盲源解混及影响因子研究[J]. 光谱学与光谱分析, 2024, 44(05): 1312-1320.
DAI Jia-le, WANG Jin-hua, LI Meng-qian, HAN Xiu-li, MIAO Ruo-fan. Research on Fast ICA Blind Separation Algorithm of Mixed Hyperspectral and Influencing Factors. SPECTROSCOPY AND SPECTRAL ANALYSIS, 2024, 44(05): 1312-1320.
