基于共形几何代数的高光谱遥感波段选择方法

Hyperspectral Band Selection Using Conformal Geometric Algebra

针对高光谱遥感数据具有的高维特征、海量数据、信息丰富、非结构化等特点导致的维数灾难问题,将共形几何代数引入到高光谱遥感影像波段选择研究。基于高光谱影像数据在高维空间分布的几何特征,利用内积、外积和几何积,结合MEAC和JM等信息测度,设计了高光谱遥感影像的新型特征提取算子,可以实现更简洁、快速、鲁棒的高光谱遥感波段选择。实验利用HYDICE和AVIRIS等高光谱遥感数据对算法的性能进行了评价,结果表明:所提出的新方法能更有效地选择最佳波段,与已有波段选择算法相比,在运行效率、分类精度等方面具有明显的优势。

Hyperspectral band selection is one of the widely used dimensionality reduction method for hyperspectral image analysis,but there are many open issues should be considered due to high dimensionality and algorithm complexity.Conformal Geometric Algebra（CGA）has several advantages such as consistent geometric representation,compact algebra formulae,efficient geometric computing,coordinate free,and dimension independent etc.As a new theoretical framework and geometric computing technology,CGA provides a new mathematical tool for dimensionality reduction of hyperspectral imagery.The efficient band selection approache based on CGA for hyperspectral remotely sensed imagery is proposed.In order to achieve a more concise,fast,robust hyperspectral dimensionality reduction,the non-linear information representation model in high-dimensional space in conformal space based on CGA is presented,the CGA-supported band selection operator in conformal space is designed for hyperspectral imagery.Two real hyperspectral data which acquired by HYDICE and AVIRIS sensors are used in the experiments.The experiment results show that the CGA-based band selection algorithm outperforms the popular Sequential Forward Selection（SFS）and PSO method with lower cost and higher classification accuracy for hyperspectral image analysis.The proposed CGA-based hyperspectral band selection method provide a new tool for hyperspectral dimensionality reduction.