Polytopes of Eigensteps of Finite Equal Norm Tight Frames
Polytopes of Eigensteps of Finite Equal Norm Tight Frames
复制标题
有限等范紧框架本征步的多胞形
DOI：
10.1007/s00454-016-9799-x
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发表时间：
2015
影响因子：
0.8
通讯作者：
Christoph Pegel
中科院分区：
文献类型：
--
作者：
Tim Haga;Christoph Pegel
Hilbert空间框架推广了标准正交基，在保持良好重构性质的同时，允许矢量表示中的冗余。帧带有一个关联的帧操作符，该操作符编码帧的基本属性。我们研究了在构造具有给定框架向量长度和框架算子谱的所有有限框架的算法中出现的一个多面体，它是一个Gelfand-Tsetlin多面体。对于等范数紧框架，我们用方程和不等式的形式给出了多面体的非冗余描述。由此我们得到了多面体的尺寸和面数。在研究多面体时，我们发现了两个仿射同构，并说明了它们与底层框架上的运算之间的关系。
Hilbert space frames generalize orthonormal bases to allow redundancy in representations of vectors while keeping good reconstruction properties. A frame comes with an associated frame operator encoding essential properties of the frame. We study a polytope that arises in an algorithm for constructing all finite frames with given lengths of frame vectors and spectrum of the frame operator, which is a Gelfand–Tsetlin polytope. For equal norm tight frames, we give a non-redundant description of the polytope in terms of equations and inequalities. From this we obtain the dimension and number of facets of the polytope. While studying the polytope, we find two affine isomorphisms and show how they relate to operations on the underlying frames.