基于二阶多项式回归和权重主成分分析法的多光谱降维算法研究

Research on multispectral dimensionality reduction algorithm based on second order polynomial regression and weighted principal component analysis

基于主成分或者权重主成分的多光谱降维方法实现高维多光谱数据和低维空间数据之间相互转换,但低维空间数据含有大量负值,不能和色度空间如CIELAB等连接起来,给光谱颜色复制的后续研究带来困扰;建立XYZ三刺激到多光谱数据的转换,在多光谱数据降维到XYZ三刺激值过程中保留更多的颜色信息;通过二阶多项式回归建立XYZ三刺激值与多光谱通过权重主成分降维的得到的三维空间数据对应关系,实现XYZ三刺激值到多光谱数据转换;在不同的训练样本,不同的测试样本时,相对于主成分和权重主成分,推荐的方法在多种照明条件下色度重建精度得到提高,可以较好地应用到多光谱图像的高保真降维和压缩。

The multispectral dimension reduction method based on principal component and weighted principal component realizes the mutual conversion between multispectral data and low dimensional spatial data.However,the low dimensional spatial data contains a large number of negative values and cannot be connected with chromaticity space such as CIELAB,which brings difficulties to the follow-up research of spectral color replication;Establish the conversion from XYZtristimulus to multispectral data,and retain more color information in the process of reducing the dimension of multispectral data to XYZtristimulus value;The corresponding relationship between tristimulus values and three-dimensional space obtained by dimensionality reduction through weighted principal components is established through second-order polynomial regression,and the mutual conversion relationship between multispectral data and tristimulus values is realized;In different training samples and different test samples,compared with the principal component and weighted principal component,the proposed method improves the accuracy of colorimetric reconstruction under various lighting conditions,and can be better applied to the high fidelity dimensionality reduction and compression of multispectral images.