Factor posets of frames and dual frames in finite dimensions

Kileen Berry, Martin S. Copenhaver, Eric Evert, Yeon Hyang Kim, Troy Klingler, Sivaram K. Narayan, Son T. Nghiem

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We consider frames in a finite-dimensional Hilbert space, where frames are exactly the spanning sets of the vector space. A factor poset of a frame is defined to be a collection of subsets of I , the index set of our vectors, ordered by inclusion so that nonempty J ⊆ I is in the factor poset if and only if {fi}i∈J is a tight frame. We first study when a poset P ⊆ 2I is a factor poset of a frame and then relate the two topics by discussing the connections between the factor posets of frames and their duals. Additionally we discuss duals with regard to ℓp-minimization.

Original languageEnglish
Pages (from-to)237-248
Number of pages12
JournalInvolve
Volume9
Issue number2
DOIs
StatePublished - 2016

Keywords

  • factor poset
  • frames
  • tight frames
  • ℓ-norm

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