基于共形几何代数的高光谱遥感影像降维与分类

Conformal Geometric Algebra (CGA) has several advantages such as consistent geometric representation, compact algebra formulae, efficient geometric computing, coordinate free, and dimension independent etc., the new theoretical framework and geometric computing technology based on CGA provides a new mathematical tool for dimensionality reduction and classification of hyperspectral imagery. In this project, the efficient dimensionality reduction and high-reliable classification approaches for hyperspectral remotely sensed imagery based on CGA and pattern recognition technology are proposed. In order to achieve a more concise, fast, robust hyperspectral imagery dimensionality reduction, the non-linear information representation model in high-dimensional space and the information description model for hyperspectral imagery in conformal space based on CGA are put forward. Learned from the advantages of the geometric analysis in high-dimensional space, the CGA-supported nonlinear feature extraction methods in conformal space for hyperspectral imagery are designed. For high-reliable classification of hyperspectral images in the case of small number of samples, the distribution characteristics of the ground truth samples in high dimensional space will be studied, and then the hypersphere classifier with SVM based on the CGA can be built. The experiment results of this project are expected to provide a new foundation theory for hyperspectral image analysis, will expand the development of hyperspectral remote sensing theory and technology, and promote the applications of hyperspectral remote sensing.

共形几何代数具有统一几何表示、简洁代数形式和高效几何计算等特点，以共形几何代数为核心的新型理论框架和几何计算技术，为高光谱遥感影像的降维与分类研究提供了新的数学工具。本课题拟在共形几何代数与模式识别理论的基础上，研究基于共形几何代数的高光谱遥感影像的高效降维与高可信分类新方法。以实现更简洁、快速、鲁棒的高光谱遥感影像降维为切入点，研究基于共形几何代数的高维空间非线性信息表达模型、共形空间中高光谱影像信息描述模型；借鉴高维空间几何分析方法的优势，研究共形空间中基于共形几何代数的高光谱影像非线性特征提取方法；研究样本点在高维空间中的分布特征，构建基于共形几何代数的超球体分类器，实现小样本情况下高光谱遥感影像的高可信分类。本课题成果有望为高光谱遥感影像分析方法新增基础理论，推动高光谱遥感理论与技术的发展，促进高光谱遥感应用的深入。

高光谱遥感数据具有数据量大、冗余度高、小样本等特点，为了实现高光谱遥感影像高效降维和鲁棒分类，课题研究了基于共形几何代数的高光谱遥感影像的降维和分类方法。针对高光谱遥感影像的特点，基于信息理论分析了高维信息的空间分布状态，得到了高光谱遥感影像信息分布特征。引入共形几何代数理论，建立了共形空间下高光谱影像数据对象的映射机制，实现了基于共形空间的高光谱遥感影像信息表达方法，并构建了色域映射支持、波段选择约束的真彩色合成、CIR合成、假彩色合成和扩展CMF合成等信息表示模型。基于内积、外积和几何积，构建了高光谱影像特征距离计算算子，设计了共形空间下的距离测度方法(MEAC，JM)，提出了基于共形几何代数的高光谱遥感影像波段选择方法。设计和优化了共形空间中的超球体SVM分类器，构建了耦合光谱和空间信息的多分类器动态集成系统（DCS-SSI），并应用于高光谱遥感影像分类研究。实验结果表明，本课题提出的方法具有较好性能，大大提升了高光谱遥感影像降维的效率，提高了高光谱遥感影像分类的鲁棒性，为高光谱遥感应用的深入提供了坚实的理论基础。