Title

Steiner Equiangular Tight Frames

Document Type

Article

Publication Date

2012

Abstract

We provide a new method for constructing equiangular tight frames (ETFs). The construction is valid in both the real and complex settings, and shows that many of the few previously-known examples of ETFs are but the first representatives of infinite families of such frames. It provides great freedom in terms of the frame's size and redundancy. This method also explicitly constructs the frame vectors in their native domain, as opposed to implicitly defining them via their Gram matrix. Moreover, in this domain, the frame vectors are very sparse. The construction is extremely simple: a tensor-like combination of a Steiner system and a regular simplex. This simplicity permits us to resolve an open question regarding ETFs and the restricted isometry property (RIP): we show that the RIP behavior of some ETFs is unfortunately no better than their coherence indicates.

Comments

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Published under an Elsevier Open Access publishing agreement. The publisher retains permissions to re-use and distribute this article.

Reviewed at MR2890902

Previous version: arXiv:1009.5730 [math.FA]. Date of arXiv submission: 29 Sep 2010.

DOI

10.1016/j.laa.2011.06.027

Source Publication

Linear Algebra and its Applications

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