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.
Source Publication
Linear Algebra and its Applications (ISSN 0024-3795 | e-ISSN 1873-1856)
Recommended Citation
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
Comments
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Reviewed at MR2890902
Previous version: arXiv:1009.5730 [math.FA]. Date of arXiv submission: 29 Sep 2010.