publication . Preprint . Conference object . Other literature type . 2017

On the structures of Grassmannian frames

John I. Haas; Peter G. Casazza;
Open Access English
  • Published: 06 Mar 2017
Abstract
A common criterion in the design of finite Hilbert space frames is minimal coherence, as this leads to error reduction in various signal processing applications. Frames that achieve minimal coherence relative to all unit-norm frames are called Grassmannian frames, a class which includes the well-known equiangular tight frames. However, the notion of "coherence minimization" varies according to the constraints of the ambient optimization problem, so there are other types of "minimally coherent" frames one can speak of. In addition to Grassmannian frames, we consider the class of frames which minimize coherence over the space of frames which are both unit-norm and...
Subjects
free text keywords: Mathematics - Functional Analysis, 42C15, 52C35, Topology, Matrix decomposition, Computer science, Optimization problem, Grassmannian, Coherence (physics), Equiangular polygon, Signal processing, Robustness (computer science), Hilbert space, symbols.namesake, symbols
Funded by
NSF| ATD: Frame-Theoretic Algorithms for Smart Sensing
Project
  • Funder: National Science Foundation (NSF)
  • Project Code: 1321779
  • Funding stream: Directorate for Mathematical & Physical Sciences | Division of Mathematical Sciences
,
NSF| Applications of Frames to Problems in Mathematics and Engineering II
Project
  • Funder: National Science Foundation (NSF)
  • Project Code: 1307685
  • Funding stream: Directorate for Mathematical & Physical Sciences | Division of Mathematical Sciences
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