Document Type

Article

Publication Date

3-1-2012

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

Sourced from the preprint at arXiv:1009.5730v1 [math.FA]. https://arxiv.org/abs/1009.5730v1
Date of arXiv submission [v1]: 29 Sep 2010.

The published version of record is available at ScienceDirect:
Fickus, M., Mixon, D. G., & Tremain, J. C. (2012). Steiner equiangular tight frames. Linear Algebra and Its Applications, 436(5), 1014–1027. https://doi.org/10.1016/j.laa.2011.06.027

DOI

10.1016/j.laa.2011.06.027

Source Publication

Linear Algebra and its Applications

Included in

Algebra Commons

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