SO（3）上的一维Radon变换及其在纹理测角中的应用

广义球面Radon变换及其在纹理分析中的应用

The Generalized Spherical Radon Transform and Its Application in Texture Analysis

广义球面Radon变换将球面环面上的平均值与定义在$\mathbb{S}^3 \subset \mathbb{H}$上的函数$f$相关联，其中$\mathbb{S}^3$的元素被认为是表示旋转的四元数。将其引入晶体学择优取向的分析中，并用与角分布函数$W$对应的概率密度函数进行了识别。最终，该通信提出了一种新的方法来从数据采样$W$恢复$f$的近似。与此同时，它提供了额外的澄清最近建议的方法，应用再生核和径向基函数的启发性的洞察力，在其涉及的几何形状。重点是几何和组特征的对应关系，但不是函数及其空间的映射。

Generalized splines for Radon transform on compact Lie groups with applications to crystallography

The Radon transform Rf of functions f on SO(3) has recently been applied extensively in texture analysis, i.e. the analysis of preferred crystallographic orientation. In practice one has to determine the orientation probability density function f \in L2(SO(3)) from Rf \in L2(S2\times S2) which is known only on a discrete set of points. Since one has only partial information about Rf the inversion of the Radon transform becomes an ill-posed inverse problem. Motivated by this problem we define a new notion of the Radon transform Rf of functions f on general compact Lie groups and introduce two a…