发表机构
Air Force Institute of Technology; The Ohio State University（空军理工学院; 俄亥俄州立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文刻画了由交叉格兰姆矩阵可交换的等距变换产生的特殊复等斜和等弦紧融合框架，证明滤波器组EITFF等价于等角紧框架直和，ECTFF等价于新提出的分层单位范数紧框架，并给出显式构造。
AI 中文摘要
等斜（EI）和等弦（EC）紧融合框架（TFFs）是最小相干（最大正交）子空间填充的类型，出现在压缩感知等若干应用中。它们似乎难以构造，且刻画其存在性的问题在很大程度上仍是开放的。在本文中，我们刻画了那些由交叉格兰姆矩阵可交换的等距变换产生的特殊复EITFFs和ECTFFs，正如滤波器组的情形。特别地，我们证明了每个滤波器组EITFF等价于等角紧框架（ETFs）的直和。更一般地，我们证明了每个滤波器组ECTFF类似地等价于一种新的ETFs推广，我们称之为分层单位范数紧框架（SUNTFs）。我们进一步建立了SUNTFs的一般理论，提供了它们的各种显式构造，以及它们存在性的一些必要条件。我们的所有技术都是显式的，产生了非相干滤波器组的直接构造。
英文摘要
Equi-isoclinic (EI) and equichordal (EC) tight fusion frames (TFFs) are types of minimally coherent (maximally orthogonal) subspace packings that arise in several applications, such as compressed sensing. They seem challenging to construct, and the problem of characterizing their existence remains mostly open. In this paper, we characterize those special complex EITFFs and ECTFFs that arise from isometries whose cross-Gram matrices commute, as is the case with filter banks. In particular, we show that every filter bank EITFF is equivalent to a direct sum of equiangular tight frames (ETFs). More generally, we show that every filter bank ECTFF is analogously equivalent to a novel generalization of ETFs that we dub stratified unit norm tight frames (SUNTFs). We further establish a general theory of SUNTFs, providing various explicit constructions of them, and some necessary conditions on their existence. All of our techniques are explicit, yielding direct constructions of incoherent filter banks.
