Algebraic and geometric spread in finite frames
Algebraic and geometric spread in finite frames
复制标题
有限框架中的代数和几何扩展
DOI：
10.1117/12.2188541
复制
发表时间：
2015
期刊：
影响因子：
--
通讯作者：
E. King
中科院分区：
文献类型：
--
作者：
E. King
当搜索有限单位标准框架（FUNTF）在哪些中产生强大的表示形式时，人们与查找由框架向量组成的框架，这些框架在某种意义上是在某种意义上分开的。两种最常用的镜头，具有最佳代数范围，称为全火花，并且n帧向量的任何子集合都是？n Grassmannian框架是满足Grassmannian包装问题的FUNTF；也就不同的矢量产品是相等的。但是，现在已经知道这是无限的相等框架的无限级别的，这将在本演讲中进一步探索。框架错过了最佳的代数或几何传播。
When searching for finite unit norm tight frames (FUNTFs) of M vectors in ?N which yield robust representations, one is concerned with finding frames consisting of frame vectors which are in some sense as spread apart as possible. Algebraic spread and geometric spread are the two most commonly used measures of spread. A frame with optimal algebraic spread is called full spark and is such that any subcollection of N frame vectors is a basis for ?N. A Grassmannian frame is a FUNTF which satisfies the Grassmannian packing problem; that is, the frame vectors are optimally geometrically spread given fixed M and N. A particular example of a Grassmannian frame is an equiangular frame, which is such that the absolute value of all inner products of distinct vectors is equal. The relationship between these two types of optimal spread is complicated. The folk knowledge for many years was that equiangular frames were full spark; however, this is now known not to hold for an infinite class of equiangular frames. The exact relationship between these types of spread will be further explored in this talk, as well as Plücker coordinates and coherence, which are measures of how much a frame misses being optimally algebraically or geometrically spread.